5th Grade Math student-ebook-course-11

Example 1
The speed of light is about 186,000 miles per second. Write 186,000
in expanded notation using exponents.

Solution

We write each nonzero digit (1, 8, and 6) multiplied by its place value.
186,000 = (1 ∙ 105) + (8 ∙ 104) + (6 ∙ 103)

order of In the order of operations, we simplify expressions with exponents or roots
operations before we multiply or divide.

with Order of Operations
exponents
1. Simplify within parentheses.
2. Simplify powers and roots.
3. Multiply and divide from left to right.
4. Add and subtract from left to right.

Some students remember the order of operations by using this memory aid:
Please
Excuse
My Dear
Aunt Sally

The first letter of each word is meant to remind us of the order of operations.
Parentheses
Exponents
Multiplication Division
Addition Subtraction

Example 2

Simplify: 55∙((88 + 88)) ∙ 16 + 322 ∙ 22 5  (8  8)  216  32  2 5

Visit www. Solution

SaxonPublishers.

com/ActivitiesC1 We follow the order of operations. original p5roble1m6  216  32  2
for a graphing 55−(8(8+88)) ÷ 216 + 322 × 2 simplified5inp1a6renth2es1e6s 32  2
simplified powers and roots
8  8) calcu1la6tor ac3ti2vity. 2

8  8)  16  32  2 5  (58 − 186) ÷ 216 + 322 × 2

5 − 16 ÷ 4 + 9 × 2

5 − 4 + 18 multiplied and divided

19 added and subtracted

480 Saxon Math Course 1

powers of We may use exponents with fractions and with decimals. With fractions,
fractions
parentheses help clarify that an exponent applies to the whole fraction, not

just its numerator.

a12ab123b3 means 1 21 1 21 21 1 a23ab322b2 2 2
2 2 2 3 3

(0.1)2 means 0.1 × 0.1

a12b3 E12xa m21 Sp i21lme p3lify: a 2 2 223 29 9 a3213ab31332b3 4 a1a211b212b2
3 9
b

a12 3 Solution
21a312Pb2193ra c21t12aic13eb213Se21aata13213b21b2b32Webaaa..w213WWb21ri2btrre2iittee23at2a1ha,s25i2112sa0bb9n023fua,0mc320tbo0arei12nrtwbien3i23xcspet2a1aa32a(13nn5nbaddd21×312ea94tdbrh1d23321en0nno921o)32tmat+at21uito(il2o94tninp21aa×u:l213ay2s.1b12212in20b9bg832)21exap2123obn2ent23s21a. 13a32b213b2
b

29 a12b3 1 2 a2332b2 4
29 2 3 9

2 2
3 3
a1 12b2
2 
3
Simplify:
1 3 1 2
c. 10 + 23 × 3 − (7 + 2) ÷ 29 a 3 a1 2
b b

d. a12 3 122921 e .21(0.1)2 aa1323bb32 f. a2 1 1 2 2  2  4
2 3 3 9
b b

g. (2 + 3)2 − (22 + 32) 3

Written Practic1e. a212Ebx93plaSintreTnhgethwe12enaai13nt21bhg3eCr21ofonrceceapststasa32t1ab212tebd2 2 2  2  4
3 3 3 9

that the chance of rain for
(58) Wednesday is 40%. Does this forecast mean that it is more likely to rain
2or9not to rain? aW13hby3? a1 12b2

2. A set of 36 shape cards contains an equal number of cards with
(58, 74) hexagons, squares, circles, and triangles. What is the probability of

drawing a square from this set of cards? Express the probability ratio as

a fraction and as a decimal.

3. Connect If the sum of three numbers is 144, what is the average of the
(18) three numbers?

4. Verify “All quadrilaterals are polygons.” True or false?
(60)
29 265*4(9462)1. 2 ∙ 32( 2−44)28( 369) + (3 − 1)3 5 2100 (244)8(361)2 5
* 5. 2441 6 225 6

(89)

* 7. Write the formula for the perimeter of a rectangle. Then substitute 12 in.
(91) for the length and 6 in. for the width. Solve the equation to find the

perimeter of the rectangle.

4 5 w 4 5 w Lesson 92 481
7 8 48 7 8 48
 100  334 100  3 3
4

8. Arrange these numbers in order from2le4a4s1t to greates2t:9 5 (24) (36)
6 48

2441 1(((47709047)))..2IR2f4e5649d1oufctehebe3f0o(r2me24e4m65)9m8(3ub6lte)iprslywineg(r2eo14rp4,65)d8r0(e3i,vs60ie2d)2.n1in1t,2g,0−5h:0o1(w244m)8(a3n62y)7421m1220e255610m04b04e11r5s 12 5  15 1
29 6 3
31w2e2re85120a50b2s4we89nt? 5
2441 6

1236543 15 1
3

5 22944(1244)8(36) 5629* 11. 2(241)0(0356) 1(225644)8(232611)5205310 12. 12226512050 15 1 12 5  15 1
6 24285 6 3 6 3
(92) (59)

13. 100 − 9.9 14. 4  100 5  w 3 3
7 8 48 4
(38) (29)
4 5 w
7  100 15. 8  48 3 3 16. 0.25 × $4.60
4 sRaou2ucne9dpathneisa6n74sinwceh56r1et0so0. tWhehanteia(s258re4t4hs)8(et34w68)
(42) (39) 3
4 5 w 3 4
7  100 8  48 * 17. saEqre3su1ta43ia0mro0aefteitnhceThch. ie(rU85cdusileaamr43wb8.e1at4esref2ooorf4fπa4t.hc1)3eir43cpualna?r 210

(86) 22

4
7

00 3 3 54  4w1800 38534 4w1(8784). Write 3 3 as a decimal number and subtract that number from 7.4.
4 87 4

19. What percent of the first ten letters of the alphabet are vowels?

(75)

* 20. Connect Bobby rode his bike north. At Grand Avenue he turned left 90°.
(90) When he reached Arden Road, he turned left 90°. In what direction was
21. BEostbimbyateridiFnigndonthAerdperondR74uocat do1?f060.95 and8512.14wt8o the nea3re43st
(51) whole number.

* 22. Analyze Write and solve a proportion for this statement:
(85) 16 is to 10 as what number is to 25?

23. What is the area of the triangle below?

(79)

11 cm

6 cm

8 cm

24. This figure is a rectangular prism.

(Inv. 6)

a. How many faces does it have?
b. How m1a161n16y edg1e16s do1e16s111i61t6,h,18a18,v,1e3161?316,6,14, 14,18,, 111366,, 1814,, 136, 14,

25. WPrheadticat reEtahcehnteexrtmfoinurthteisrmsesqinuetnhceeseisq1u16enmcoer?e than th1e16p,r18e,vi1o36u,s14t,erm.

(17)

1 116, 18, 136, 14, , , , , . . .
16

3366ftf2t2 36 ft2 36 ft2
44ftft 4 ft 4 ft

482 Saxon Math Course 1 36 ft2
36 ft2 4 ft

Use a ruler to find the length and width of this 116, 18, 136, 14,

rectangle to the nearest quarter of an inch. Then
refer to the rectangle to answer problems 26116
and 27.

* 26. What is the perimeter of the rectangle?
(91)

* 27. What is the area of the rectangle?
(91)

28. Connect The coordinates of the vertices of a parallelogram are (4, 3),
(Inv. 7)
(−2, 3), (0,1 −2), and (−6,1−162, )18.,W136h,at14,is the area of the parallelogram?

16

*1126(891). Sai.m(1p2lifyc:m)1(186,c18m,)136, 14, b. 36 ft2
4 ft

30. Fernando poured water from one-pint bottles into a three-gallon bucket.
(78) How many pints of water could the bucket hold?

Early Finishers There are close to 4 million people living on the island of Puerto Rico, making

Math and it one of the mo3s6tfdt2ensely populated islands in the world. If the population
Geography density is appro4xifmt ately 1,000 people per square mile, how many people

l3iv6eftin2 a 3.5 square mile area? Write and solv1e a proportion t6o00answer this 236
q4ueftstion. 2 30

116, 18, 136, 14,

1 600 236
2 30

1 600 236
2 30

600 236
30

Lesson 92 483

LESSON Classifying Triangles

93

Power Up Building Power

facts Power Up I
mental
a. Number Sense: 40 ∙ 60
math b. Number Sense: 234 − 50
c. Percent: 25% of 24
d. Calculation: $5.99 + $2.47
e. Decimals: 1.2 ÷ 100
f. Number Sense: 30 × 25

1

g. Algebra: If x = 5, what does 54x equal?
h. Calculation: 8 × 9, + 3, ÷ 3, 2 , × 6, + 3, ÷ 3, − 10

problem Benjamin put 2 purple marbles, 7 irne170da;nm13d0;ac1r3hb0;ole32oss,easnad 1 brown marble in a bag
solving and shook the bag. If he reaches marble without looking,

what is the probability that he chooses a red marble? A purple or brown

marble? What is the probability of not choosing a red marble? If Benjamin

does choose a red marble, but gives it away, what is the probability he will

choose another red marble?

New Concept Increasing Knowledge

Thinking Skill All three-sided polygons are triangles, but not all triangles are alike. We
distinguish between different types of triangles by using the lengths of their
Generalize sides and the measures of their angles. We will first classify triangles based
on the lengths of their sides.
Explain in your
own words how Triangles Classified by Their Sides
the number of
equal sides of a Name Example Description
triangle compares
to the number of Equilateral triangle All three sides are
equal angles it equal in length.
has.

Isosceles triangle At least two of the three
sides are equal in length.

Scalene triangle All three sides have
different lengths.

An equilateral triangle has three equal sides and three equal angles.
An isosceles triangle has at least two equal sides and two equal angles.
A scalene triangle has three unequal sides and three unequal angles.

484 Saxon Math Course 1

Thinking Skill Next, we consider triangles classified by their angles. In Lesson 28 we
learned the names of three different kinds of angles: acute, right, and
Justify obtuse. We can also use these words to describe triangles.

Is an equilateral Triangles Classified by Their Angles
triangle also
an isosceles Name Example Description
triangle? Why or
why not?

Acute triangle All three angles are acute.

Right triangle One angle is a right angle.

Obtuse triangle One angle is an obtuse
angle.

Practice Set Each angle of an equilateral triangle measures 60°, so an equilateral triangle
is also an acute triangle. An isosceles triangle may be an acute triangle, a
right triangle, or an obtuse triangle. A scalene triangle may also be an acute
triangle, a right triangle, or an obtuse triangle.

a. One side of an equilateral triangle measures 15 cm. What is the
perimeter of the triangle?

b. Verify “An equilateral triangle is also an acute triangle.” True or
false?

c. Verify “All acute triangles are equilateral triangles.” True or
false?

d. Two sides of a triangle measure 3 inches and 4 inches. If the perimeter
is 10 inches, what type of triangle is it?

e. Verify “Every right triangle is a scalene triangle.” True or false?

Written Practice Strengthening Concepts

* 1. Model Draw a ratio box for this problem. Then solve the problem using
(88) a proportion.

The ratio of the length to the width of the rectangular lot was 5 to 2.
If the lot was 60 ft wide, how long was the lot?

* 2. Mitch does not know the correct answer to two multiple-choice
(Inv. 9) questions. The choices are A, B, C, and D. If Mitch just guesses, what is

the probability that Mitch will guess both answers correctly?

3. If the sum of four numbers is 144, what is the average of the four
(18) numbers?

Lesson 93 485

9 3 1 a212 2 29  2100
5
4. The rectangular prism shown below25is b
(82) constructed of 1-cubic-centimeter blocks.

What is the volume of the prism?

9 (*74F41,111(((((((i69277774n2836554317w2333345719))))))))d5........ew2WwWTW(m905ACwa9a.e4rrhonc331eiismnatta34h)neelc3tyt4blthuuzw23w2ny9934ee5den5w2u519roe9kw25sm9ar5afnaw231Is9fvst5bot4I49hiontaowea443he34313tr4dween43od15tw2i434d9eswfh5ern334cw2e“ac9you499551isntimem5m931t13odts9%4ay13o”bo?a(913347pl4fez93lv6a53331noee)tnr34.o231551h:ufw2n3uto12915e5mQe8m3b15923fms03m2mb51t131251b9?0reteRiea65eo134am2rm2rn343“ab12*ag5a6yb51n3w2ben29el21(e35de2m851rd4s12r5s099s)”aba.w83av32rm13svideo45a6n05a6oadt224365a2atpe2356a21e212pli4drlt2b1515a6sb12oe9t34323m12t20?22mbyhbro09b3*0c0212emrl32eme09eb13s31(2039me256anm..029502tW).sa651.3231.22121i20dWh152b12102932ea91mb2hv02st9032moa90f0t9rtt292heaa56i2esdc21221tst0122in10ho2a1b90o00en3m20m1,0900s0otehu20fa65lemte22hn1n?212e0g1256wb30t032192mhh3200a?t3m20 21090  2100
25

w

16. What mixed number is 3 of 100? 29 2 1
8 2
(42)
3810 + 6832 ÷ 32−929 × 323 9 1
* 17. Analyz38e 2 1 2 1 2 2
(92) 2 2
29 2 1
3 18. has2 h12 ow 8 2
8 A trian2gu9lar prism faces?
(Inv. 6) many

1(79883). 83HthRoeewpprerm38sime38an38ent yfaqUc2ustoa38e9rr2tiazsaf9oatifcotmn2o2irol29ktfr9ie89se020t12o2u2gsfi9a12innldlgonteh2sxe221po212pof12rnmimeinlekt2?sf12a. ctors of 800. Then write
20.

(65, 73)

21. Round the decimal number one hundred twenty-five thousandths to the
(51) nearest tenth.

* 22. 0.08n = $1.20
(87)

23. The diagonal segment through this rectangle divides the rectangle
(79) into two congruent right triangles. What is the area of one of the

triangles?

18 mm

26 mm

24. Write 17 as a percent.
20
(75)

486 Saxon Math Course 1

20 20 20 17 20
20

* 25. Estimate On2107this number line the arrow could be pointing to which of
(89) the following?

17 17 17
20 20 0 20 1 2

21 A 212121 117721B22217 22217 2223C2323 2423424 D 24
221200 20 220 2 23 24
* 26. Write this number in standard notation:
(92)

21 (7 × 109) +2(22× 108) + (5 2× 3107) 24

17 27. a. What is the probability of rolling a 6 with a single roll of a number
20 (58)
cube?

21 22 22 23 b. rW2o2lhl4ao3tf is nthuem2pbreo4rbcaubbiliety? of rolling a number less than 6 with a single 24
a 21 22 23

c. AbNeaAtmwbAe2ehetbh2nAhebt2h2eh2evA1bet12wnh1t1o6ab1,p2n21h618rdo,111bi1816t3as,6b11,1821c36i614,lo2i,,1t12m3i18141e6251,ps,621.l1,143e56638,1m,,15214e38613n,,62t138,5.6,14T,,h2381e5,26n22,3d383e, scr2ibe322th44e2r3ela2tio4nsh2ip4

28. Represent (0T, Ah2e),c(3ob,2oh2r)d, iannadte(s51,o16−f,t2h18)e,. 1Wf3o6hu, ar14t,vie1s5r6tt,ihc38ee,snaomf ae quadrilateral are
(64, for this type of
Inv. 7) (−3, −2),

quadrilateral?
21 22 23 24
* 29. Explain The formula for the area of a triangle is
(91)
A  bh A  bh 116, 18, 136, 14, 156, 38,
2 A 11b62h, 18, 136, 14,111656, ,1838, ,136, 14, 156, 38, 2

If the base omfeAtAhaseutrrbe2ibah2shnA2g0lec?mb2EAhxa1p11n61l6da,b,i182nth18h, ,ye13o1631hu61,6er,14,i14gt,18h,h1,i51nt6151163km,66i,38,n,e38,18g14a,,.,s1u1356r6e,,s1438,1, 1556c,m38,, then what
is the area

30. Generalize Write the rule for this sequence. Then write the next
(10, 17) four numbers.

A  bh 116, 18, 136, 14, 156, 38, , , , , ...
2

Early Finishers A teacher emptied a 1.5 oz snack-sized box of raisins into a dish. The
teacher then asked for volunteers to estimate the number of raisins in the
Real-World dish. Twelve volunteers gave the following estimates.
Application
84 100 50 75 66 75 70 90 85 77 91 80

a. Which type of display—a circle graph or a stem-and-leaf plot—is the
most appropriate way to display this data? Draw your display and justify
your choice.

b. The dish contained exactly 85 raisins. How many volunteers made a
reasonable estimate? Give a reason to support your answer. (Hint: You
might think of how far off an estimate is in terms of a percent of 85.)

Lesson 93 487

7 x 33 3  100 7 �5, 2x, 33 3 � 100 5, 2,

LESSON Writing Fractions and Decimals
as Percents, Part 2
94

Power Up Building Power 23 23232x513 3100734323213x251,252,41002733 �3322x5213, 522,5 �33431252,�52, 12004

facts Power Up K 3  21 3  1�003 52, 52,
mental 7 x 7 
11
math a. Number Sense: 50 ∙ 70 63

problem b. Number Sense: 572 + 150
solving
c. Percent: 50% of 80

d. Calculation: $10.00 − $6.36

e. Decimals: 100 × 0.02

f. Number 2S3ens2e: 2625400233 24225 21122343422 25262244033016  24225 234 11 42  24

124

g. Algebra: If r = 6, what does 9r equal?

h. Calculation: 4 × 5, + 1, ÷ 3, × 8, − 1, ÷ 5, × 4, − 2, ÷ 2

What are the next four numbers in this sequence: 112, 16, 14, 13, . . . 2 1
3 6

New Concept Increasing Knowledge

640 640 1 6401 1 640 1 1 1 1 11 1 1 11
Since Lesson2705 we have 2p0ra12cticed cha2n01g2in6g a frac2t0io1n2o6 r d4ecimal12to6a 4 3 6 43

percent by writing an equivalent fraction with a denominator of 100.

3  60  60% 0.4  0.40  40  40% 3
5 100 100 5

3  60  60% 0.4  0.40  40  40% 3 3  100%  300% 3
5 100 100 5 5 1 5 5

3 60 14000pIannetrehc4qie0sun3%lite0v. s50aS0sl%ei.on4nncte35wn1u6e00m053.w40%b0%ilel rp1.e6r0Hq0a104uec00art0eilcsew65310ea4,53%n530wmo%e1uth0lcte110ia6pr0%n0lm0yme35utbhl63tyoi00pd150%l3y0o%000af50.%c4f%rh:aacnt0gio.6i453nn00gb%ay1f110r040a010.00c40%t%iont04ot.03o4f0%o0a50rm%1400530  40% 3
5 100 5
  60%

3
0.4  0.540 

300% Then we simplify and find that 3 equals 60%. 300%  60%
5 5 5 to percents.
3
5  60% 3 300%  60%
5 5
% 60T%hinking

Skill We can use the same procedure to change decimals Here we

Discuss multiply 0.375 by 100%.

How can you use 0.375 × 100% = 37.5%
mental math to To change a number to a percent, multiply the number by 100%.
change a decimal
to a percent?

488 Saxon Math Course 1

Example 1

Change 1 to a percent. 1 1  100%  100%
3 3 3 1 3

Solution

1 We multiply 1 by 100%. 1  100%  100% 33 13%
3 3 3 1 3 3 139030%31%
3 100%
1 2 1 1 2 1 1  100% 2101430% 2  1
3 4 3 4 3 1 4

To simplify, we divide 100% by 3 and write the quotient as a mixed number. 9
110
1 1  100% 2214114030% 2 1 2  1 132903203149%%4141 9
3 3 1 4 4 1

1 1 3 25
2 4 2  4 9 100%
2 1 9 4  1  225%
4 4

10 1
9 25
4914911102010510%%222255%%
2 1 2  1 2 2 1441 9 9
4 4 4 4

Exam2 41ple 2 9 9
4 4

1

Write 1.2 as a percent.

25
9 So1lu0t10io%n
9 9 4  225%
4 4

1 We multiply 1.2 by 100%.

1.2 × 100% = 120%

In some applications a percent may be greater than 100%. If the number
great13erth1a0n101%, then10th30e%percent
we are1changing to a p1 ercent is is greater
than 1300%.
3

Example 3

1 1 SolWWuteriiotsenho2w141313at31ws oa10mp10ee%rtcheond2ts1.410b3130e1331l%ow13. 2  1 2  1 1 1
3 3 4 4 3
3 33 13%

1 100% 13113030%131010%  103013%33111019010001%%010%10301%0330%1303013%%
3 1

2 1 1 2 1 Mmee31athnos2d“4121:W41.e” sWpel312itcthh94ae141n20wg214102eh14%oel2ae14cnh1up0m30abr%2te94rto2a2n41ad14p14fe2rra14cce49t1niot2na.1nT20d5h4110et%2h2me14nix2a14e2dd2d91n514. u%2mb3e2411r31903209013441%% 9
4 3 4 10

2 1 2 412 1 9
4 4 1

2 1 Mnuem2th41boerd249214:94eWqueaclsh2at491hnegei14m194t20hp251094er41o%mp22ei14xr2ef0d2r410a2n%c5ut49%imo+nb492e9415.r205%Wt10o94%e=atnh2eim249n25p2c%r5ho%a1p2n0e549g102re%41fr94actotio2an2p.549eT%rhce49e1nm20945t101.ix1%e205d10%225%22
4
1 9
2 4 4

2 1
4

25 1 1 11

2 1 9 9 9  100%  225%
4 4 4 4 1

1

Lesson 94 489

Example 4

Write 2 1 as a percen2t.16 13 13  100%  1300% 1300%  2
6 6 6 1 6 6

Solution

Method 1 shown in example 3 is quick, if we can recall the percent equivalent

2 1 cnoouf mma febr2ea23tor16c00t2amio61onirna.d23sMb.tWehteehiomwdip2ll223r6100uoi1ssp63eeermafsreiaetchrtoiifod1tn6h23e1632i3npaet1nhr0cdis10emn%etxuael1t6m32qi3p300up1liyv3leab0.16l01yeW010%n1010e0t0%%dw0o%reit.se12nt3h0o0e630t0%rm%eaixd1ei3dl6y066023%% 21163232306%0%100%2
6

2 1 2 1 13 13  100%  1300% 1300%  216 32 %
6 6 6 6 1 6 6

Now w6e6d32%ivide 1300%23 by 6 and write61the quotie81nt as a mixed numb1er41. 2 4
5

13 2310063aor 321b010%2300a231o003r02360b% 20 2 32001306103210%3000023%121001026%03230%%32300 20301%1000% 66 232%030% 3266231%00% 23 20301%00% 6
6 30 3  6623%  6623%

20 aor 2 b 20 2 2  100%  200%
30 3 30 3 3 3

Example 5 3

� 15230,305213, � 2 6616233252573%,,�2552,6,83121263x00013210%S5273%2o,16�1l52bsGfsTWu1r0hw,ty0ati232eu0roixcel1o11d%swftn0i3iner52o733w6t0s0bn,ny636t%e0�et5231rsfo32t%23l,eio2o,%nf2�o0xwwda2231tn30h00.h116tp%23eh1ita0Q6ceh33161eo0thre31h14rcfirie6123bs�ranbR6tuctyt6hos1t.523i23es32f0o,3wtt%0n25puh131e,6116eedo3r�3rfeec223s0tn006et8116g1h0u252tn0ei%s1,dr61322t0025lesosn45,10nt?anu%tmsd811t2he0eo2255123261ne0n,00,6f16to%25bs521a23t,rh,uo3%t1ehs0r3126.6a0b233wWt152b2%u63we,0se1r3520.232e8113ec00,N%r161aegaon41ogiwrur25i232l132rs00s6,l23w3166300s.eb521.6e61W,3eT2341mihht%11heau100entl101t100ri3p0pw%%223010el600ey1602%roc%ct45hreoen132121n63,t30vf141ar300eoa2263sr0%fc145t0w%6tt60tihohe32%een%61231326663330012331%2114510001001 1
3 3
13
6 1520, 052, 1300%
26116 %16361130

1300
%32230012610010

3

�2 �3 �2442 �Pr2263a0064ca32%otirc8312233e002b3S�e1t102002%22333005CW��heaa223.fni0n02�g30d.35e5%4�2te�1232h216a00a1461�26c3tah6o6263�2263123200rd665%23232ea2342300�232bc%16o2%00ai16rm�3oa23oraob�f2lr23tnb32h428312u223be22323232000061m001654b61s�23ab.toue2233012rd001r.00e1232230t040600bon023216%00t%16as op6ne6ro2tc2132hr022361312e%0600e30316n133061%tb%bu32611sy1412366wm331266636euc62316rl6.132%e32t36323i3000p%2381g%.l1iyr38122il13231ns60053110.g31216003100301320b61003030%y223%%110451023110010011%0011110000%1320036100%%33000061%%:6300%060%2%%0111230100130012%10023003041616%%010300%663014013%%61832%%6%61263230663%00666230%623%1%32312%3%3810260065460223%16%4501322303231%%1

2
3
1
6

640 640 d. 0611242.040 566 23%112 66 23%16112 6236e32.%116 .3 2 1 21 1 1 32fi..8130000143..06226115510810081 1 28103310%114 66 231%114 14 32124145 2
20 20 3 64 36 4 6 3
1 1
46 20 ao1r 2 b 20 2 6 %  100%
3 3
11 1 1 g. 10.0390 3 66 32%31 30 h. 1.225 2 4
612 6 4 5
34 3

Change each fraction or mixed number to a percent by multiplying by 100%:

112, 16, 14,11132, 16,j.14,1321132,6166,2314%,3213, 12 2 k. 1 1 1 1l. 181 1 1 1 21 14 1 1 2 4 12 14 2 4 1 1
63 6 86 1 8 4 4 45 4 5 35 5 3
3 68
12 1 1 1 118 1 1 41 4 14 1 1
63 6 86 8 m. 4 1 4 21 54 n. 2 5 12 35 1 3 o. 1 3

p. What percent of this rectangle is shaded?

q. Connect What percent of a yard is a foot?

490 Saxon Math Course 1 1 1 2 1 2
3 3 3

Written Practice Strengthening Concepts

* 1. Analyze Ten of the thirty students on the bus were boys. What percent
(94) of the students on the bus were boys?

2. Connect On the Celsius scale water freezes at 0°C and boils at
(18) 100°C. What temperature is halfway between the freezing and boiling

temperatures of water?

3. Connect 1 the length of 1se32gment AB is 11 2 length of s1e32gment AC, 1 2
3
(69) 3If 3 3the

a31nd if segm13ent 1A23C is 12 cm1l32on1g32, then how1l32ong is segment BC?

1A B 1 2 C 1 2 1 1 2
3 3 3 3 3

4. What percent of this group is shaded?

(94)

1 * 5. Change311 2 to a percent11b3223y multiplying 1 2 by 100%.
3 3 3
(94)
C6.h4ang6e411.(65B.6e4to.g4ian66pb411341e6yr14wcerintitnbg6y146m41 ua43lsti1p13al32ydiencgim1.436a35.l34124bnyum1160b134410e23%r.3).12342158 6114341 341904185432586 134909 5 8
* 6.  8 10 6  9
9  5 
(94) 6

7.

(74)

* 8. 104 − 103 6.4  6 1 9.6 14How much is 3 of63.460? 634121  1 43641 4 5
4 4 8
(92) (70)

1 11332 113232 Tommy pla1ce23d a cylindrical can of spaghetti sauce
3 on the counter. He measured the diameter of the

can and found that it was about 180camn.dU31s121e.t34h1is43  4 58 3 1 U11s90e343.16544fo5898r π. 9  5  8
6.4infor6m14ation to66.a441nsw6e14r proble6m3414s 2 10 6 9
1910
10. The label wraps around the clairbceul6mn.14f4eeerden6tco14eboef? 346 1 3 1 341 3  4 5 3 1
the can. How long6.d4oes6t14he 4 2 4 8 2
(47)

* 11. Analyze How many square centimeters of countertop does the can
(86) occupy?

6.4  6 1 6614.4  6 1 436 1 12. 3 1  341 3  4 5 3 1 1901 34 6549885 13. 9  5  8 3 � 21 33 1 � 100
4 4 4 2 4 8 2 10 6 9 7 x 3
(61) (72)

* 14. Write 250,000 in expanded notation using exponents.
(92)

15. $8.47 + 95¢ + $12 16. 37.5 ÷ 100
(1) (51)
3 �73 1�002x1 1 52, 25, 52,
17. 7 � 21 33 1 52,1(65288,). 33 3 � 10052, 25, 25,
x 3
(85)

19. If ninety percent of the answers were correct, then wh73at�pe2xr1cent were 1
incorrect? 33 3
(41) � 100

20. Write the decimal number one hundred twenty and23th�re2e 25 � 3 � 42 � 24
hundredths.
(35)

3 � 21 21. Arrange these numbers in order from least to greatest:
7 x
(76)

2333�31 2� 21500� 3 �25,4252, �23 2�−422.255, 52�, 523, �−54.22� 24

23 � 225 � 3 � 42 � 24
Lesson 94 491

640 1

22. Conclude A pyramid with a square base has how many edges?

(Inv. 6)

23. What is the area of this parallelogram?

(71)

8 in.

10 in.

* 24. Classify The parallelogram in problem 23 is divided into two
(93) congruent triangles. Both triangles may be described as which of the

following?

A acute B right C obtuse

25. During the year, the temperature ranged from −37°F in winter to 103°F
(14) in summer. How many degrees was the range of temperature for the

26. 73ye�ar?2x1 The co3o3rd31in�at1e0s0of 25, 52, vertices 25o,f 52a, triangle are (0, 0),
(Inv. 7, the three
79) Model

27. (730,−24x1), and (−43,3013). Graph the 25t,ri52a,ngle and find its area.
 100

(Inv. 5) Margie’s first nine test scores are shown below.

21, 25, 22, 19, 22, 24, 20, 22, 24

a. What is the mode of these scores?

b. What is the median of these scores?

* 28. 23 � 225 � 3 � 42 � 24
(92)
29. Sandra filled the aquarium with 24 quarts of water. How many gallons of
(78) w23ater2di2d5San3dra p4o2 ur in2to4the aquarium?

30. A bag contains lettered tiles, two for each letter of the alphabet. What is
(58, 74) the probability of drawing a tile with the letter A? Express the probability

ratio as a fraction and as a decimal rounded to the nearest hundredth.

640 1 1 1 1
20 12 6 4 3

640 1 1 1 1
20 12 6 4 3

112, 16, 14, 13, 2 1 1 1 1 2 4
3 6 8 4 5

492 Saxon Math Course 1

LESSON Reducing Rates
Before Multiplying
95

Power Up Building Power

facts Power Up G
mental
a. Number Sense: 60 ∙ 80
math
b. Number Sense: 437 − 150
c. Percent: 25% of 80
d. Calculation: $3.99 + $4.28
e. Decimals: 17.5 ÷ 100
f. Number Sense: 30 × 55
g. Algebra: If w = 10, what does 7w equal?
h. Calculation: 6 × 8, + 1, 2 , × 5, + 1, 2 , × 3, ÷ 2, 2

problem Between the prime number 2 and its double, 4, there is a prime number
solving
1122, 61, 341, 13,4
Is there at least one prime number between every prime number and its
double?

112, 16, 41, 13,

New Concept Increasing Knowledge

Since Lesson 70 we have practiced reducing fractions before multiplying.
This is sometimes called canceling.

111
3 2 5 1 4 miles 2 hours 8 miles
4  5  6  4 1 hour  1  1  8 mile

212

We can cancel units before multiplying just as we cancel numbers.
111
3 2 5 1 4 miles 2 hours 8 miles 55 miles 6 hours
4  5  6  4 1 hour  1  1  8 miles 1 hour  1

212
Since rates are ratios of two measures, multiplying and dividing rates

involves multiplying and dividing units.

Example 1
Multiply 55 miles per hour by six hours.

Lesson 95 493

Solution

Math Language We write the rate 55 miles per hour as the ratio 55 miles over 1 hour, because

1 1 Recall that a ratio “per” indicates division. We write six hours as the ratio 6 hours over 1.

2  5  41ibosfyatdwc4i1vooimsmhniouoiplumenas.rrbiseorsn2 hours  8 miles  8 miles 55 miles  6 hours
5 6 1 1 1 hour 1

1 2

The unit “hour” appears above and below the division line, so we can

cancel hours.

55 miles  6 hours  330 miles 5 feet  12 inches  60 in
1 hour 1 1 1 foot

Connect Can you think of a word problem to fit this equation?

Example 2 in3c1dhhoeolsluarrpser fo8ohto1. urs 6 baskets  100 shots 10 cents 
Multiply 10 shots 1 1 kwh
5 feet by 12

Solution

We write ratios of 5 feet over 1 and 12 inches over 1 foot. We then cancel

55 miles 6 h6o1huo1rsurs  3u3n0itsma5i1ln5edhsmomiuleursltiply6. ho15urf1s5eef1et e3t132011im2nf1ociiolnhfeotcesohstes 5 feet  12 inches  60 inches
330 miles  60 inches1 1 foot
60 inches
55 hm1oihuleorsur
1
mnfocilohete3s1sd3ho1odllh6uaoPo0rrllrsuaairrnsccth8iceh8seo15huSfo11reseuertts
121Winfhobaceo..hnte361sp1d0bo6h1oasso0lbsslh6uakiabso0rreshstlektsiosne,tctcssh8aen1hsc0o1e10ul0r1sn0shu1somhtsboetsrs and units before multiplying: 121016h210cko6ewhku0nomrhstkusmrs1021h601o.3hu11orksuwrhs
611010b1acks01sewhkcnkoheewttstsnshts21602.3061.k1s3w1hkohwtsh

610basTRshhkeoeeattsdasbinbgre1Mv0i0aatt1isohhnots c. 10 cents  26.3 kwh 160 km  10 hours
1 kwh 1 2 hours 1

10 ck“kewkilnowhtwhsa”tstth2aon6ud.3rs1sk,fowrh d. 160 km  10 hours
1 2 hours 1

a rate used to e. Multiply 18 teachers by 29 students per teacher.

measure energy.

f. Multiply 2.3 meters by 100 centimeters per meter.

g. Solve this problem by multiplying two ratios: How far will the train travel
in 6 hours at 45 miles per hour?

Written Practice Strengthening Concepts

1. What is the total price of a $45.79 item when 7% sales tax is added to
(41) the price?

* 2. Jeff is 1.67 meters tall. How many centimeters tall is Jeff ? (Multiply
(95) 1.67 meters by 100 centimeters per meter.)

3. Analyze If 5 of the 40 seed(s5spro1u0t0e)d, h(o6wm1a0n)yseae7dsd1i1d0bnot a3  1100b 1
(77) sprout? 8 6

494 Saxon Math Course 1

4. Write this number in standard notation: 5 (5
8

(46)

5 (5  100)  (6  10)  a7  110b  a3  1100b 1
8 6

a857  110b  a3 (511001b00)  (6  1016) *(954a).7Cha11n0gbe16 ato3 its 1p10e0rcbent equivalent16by multiplying 1 by 100%.
6

* 6. Analyze What is the percent equivalent of 2.5?
(94)
How 5 money is 30%(5 of 1$0102.)0085 ?(6  10)  a7(511100b0) a3(6110100b)  a7 
7.
mu8ch
(41)

* 8. Connect The minute hand of a clock turns 180° in how many m43inut53es? 18

(90)

3 (297).53 658Efveaeluta.tHe o1wT8h18meacn(i51ryc2cu12omm581f0epr0lee3)nt43ec58et(u6or2fn32tshd1e0of(1e)r5os1n10tthat1e7i(r05ef0roo)n1n1t01Ew0b(l0i6hz)eaebale31mt(220h635a)’sk1eb101iaa0k07seb) is 1a107b22111a03b 16 1a
4 

43 111053 5 185818 225312 1 )(53a4371(5002)2112110321(800b2()0.6)1CbEaol1hi13zx0a1(ae6d0bs)eb.1tWuh104316il0hat0r25iab7td)hte53iisss0as1dt.1h7t80oaebwc22vkn53o1o1hl0aufeb3mo1r 8n163ee180o-a1-cff310out0hob1beti2cd1s21-210rt43fiao210vcoebktw?353a4316y? 1 6 2516  0.8 1 1
b  a3 8 2 6 6 6

(5  100)  (6  10 2 11811810 1 3 22352 2 1
 3 2 4 3 10
2 12 3  1

1100b 5 (5  100)  (6  10)  a7  110b  a3  1100b 6 1 1
81 4 6
1
66

6 1 3  3 18 1 43 12532143  353134(23).1282381 111812811012 1231234  233234 22351212310 1 1 2 1
4 5 8 10 2
411.
(57)

6 1 3  33  3 18 1 181182 121(7321).2 321 3  324323  2123110 1 1 22153(942). 25 2 1 102012) 61520) 6052.a870.1810b
4 4 54 8 4 10 23 2
5
5 (5   (6 
1 1 3 2 1 53H162o25w+m80.a7.8n65y14221(+d538foe186uc.ri8mtha1sl2aa21rnesiwn e23r)1243?8(382,132379).641(11.1510)26 2
18 8  12 2 3 4  2 3  1 10 15. 5  0.8 25
23
(68)

25 2 1 4311(3868).. 2 1
23 2 (74) 2

19. t6oE41stthimeanteearFeisntdwthhoelesu6nmu14 mobf e6r14,b4e.f9o5re, and 8.21 by rounding each number
adding. Explain how you arrived at
(51)

6 1 6 1 your answer.
4 4
Analyze The diameter of a ro43und53tabletop is168081 inc1h2es12. 3 2 1
* 20. a. What is the radius of the tabletop? 3 4  2 3  1 10
(86)

6 1 b. What is the area of the tabletop? (Use 3.14 for π.)
4

21. Arrange these numbers in order from least to greatest:
(75)
41, 4%, 0.4 4 x
8  12 AB AC

Find each unknown number. x
41, 4 12
22. y + 3.4 = 5 6 1 23. 8  AB AC
4
(43) (85)

24. A cube has edges that are 6 6c2mlo2ng9.  2  23  2400
(Inv. 6,
82) a. What is the area of each face of the cube?

b. What is the volum6e2of th2e 9cube2? 23  2400
c. What is the surface area of the cube?

Lesson 95 495

482(659).8414141x2,C, o1nxn2ect iAs8448B24 x41, 4  x AB AC BC
m11x22m 8 12 AC 2 2400
AB BC
41, 41, AB lonAgC. AACBis 42 mmBCloBnAgCC. How lon6g2 is BC?
 29  23 

A BC

62  29  2  23  2400
* 26. 62  29  2  23  2400
62 6229 292(89,22923) 62232420209400 2  23  2400

27. What is the ratio of a pint of water to a quart of water?

(78)

* 28. The formula for the area of a parallelogram is A = bh. If the base of a
(91) ppaarraalllleellooggrraamm?isH1o.2wmcaannedstthimeahteioignhhtei41slp,0y.9oumc,hwehcaktyiso48uthr ea1nax2srewaero?f theAB
AC

* 29. Multiply 2.5 liters by 1000 milliliters per liter. 2.5 liters  1000 milliliters
1 1 liter
(95)
2.5 1l2it.e5rs1liters100013100ml0i.ti0el1l2I2irflm.i.l5tit5tehiel1lr1liiirsstltieetserrspsrsinn1e1r000i0s0011smmplliitutiielellnli2rirllii.ott5eenrr1lcsistee,rswhat1i0s0t0h1em6li2tiellirlit2ers9  2  23  2400
(58, 74) probability that the arrow will end up pointing
41
to an even number? Express the probability

ratio as a fraction and as a decimal. 32

Early Finishers The local university football sista4d8iu,5m00s.eIat thsa6s20.b5,0e1l0eit0nerfdsaentse,r1ma0ni0nd0e1admvliteihellriraalitgteaerns
attendance at home games
Real-World
Application average fan consumes 2.25 beverages per game.

a. If each beverage is served in a cup, about how many cups are
used during an average game? Express your answer in scientific
notation.

b. Next week is the homecoming game, which is always sold out. A box of
cups contains 1 × 103 cups. How many boxes of cups will be needed

for the game?

496 Saxon Math Course 1

2 4 RT RS ST
RT
LESSON 2 3 RS ST
4
96
Functions

Graphing Functions

Power Up Building Power 4 hours
Power96Up 36 1 6 dollars
facts Dw  1 hours 32  23  24  5  62  216
mental
a. Number Sense: 70 ∙ 90 6  36 4 hours  6 dollars 32 
math 9 w 1 1 hours

problem b. Number Sense: 364 + 250
solving
c. Percent: 50% of 60

d. Calculation: $5.00 − $0.89

e. Decimals: 100 × 0.015

f. Nu11m6 ber Sense: 750 2
30

g. Measurement: How many pints are in 2 quarts?

h. Calculation: 6 × 6, − 1, ÷ 5, ×116 8, − 1, ÷ 11,73×500 8, × 2, + 1, 2

Copy t25his factor tree a25nd fill in the 2
missing numbers: 5

2
5

55

33 22

New Concepts Increasing Knowledge

functions We know that the surface area of a rectangular prism is the sum of the areas
of its sides. A cube is a special rectangular prism with six square faces. If we
know the area of one side of a cube, then we can find the surface area of that
cube. We can make a table to show the surface areas of cubes based on the
area of one side of the cube.

Area of Each Surface Area

Side of a Cube of the Cube

(cm2) (cm2)

4 24

9 54

16 96

25 150

Lesson 96 497

Discuss Use the data in the table to help you create a formula for the
surface area of a cube. Let A be the area of each side of the cube and
S be the surface area of the cube.

(S = 6A)

Your formula is an example of a function. A function is a rule for using one
number (an input) to calculate another number (an output). In this function,
side area is the input and surface area is the output. Because the surface
area of a cube depends on the area of each side, we say that the surface
area of a cube is a function of the area of a side. If we know the area of
one side of a cube, we can apply the function’s rule (formula) to find the
surface area of the cube.

Example 1 lm
5 20
Find the rule for this function. Then use the rule 7
to find the value of m when l is 7. 10 25
15 30

Solution

We study the table to discover the function rule. We see that when l is 5,

m is 20. We might guess that the rule is to multiply l by 4. However, when l
is 10, m is 25. Since 10 × 4 does not equal 25, we know that this guess is
incorrect. So we look for another rule.

We notice that 20 is 15 more than 5 and that 25 is 15 more than 10. Perhaps
the rule is to add 15 to l. We see that the values in the bottom row of the
table (l = 15 and m = 30) fit this rule. So the rule is, to find m, add 15 to l.
To find m when l is 7, we add 15 to 7.

7 + 15 = 22

The missing number in the table is 22.

Instead of using the letter m at the top of the l I + 15
5 20
table, we could have written the rule. In the table 7
at right, l + 15 has replaced m. This means we 10 25
add 15 to the value of l. We show this type of table

in the next example.

15 30

498 Saxon Math Course 1

Example 2
Find the missing number in this function table:

x 234
3x ∙ 2 4 7

Solution

This table is arranged horizontally. The rule of the function is stated in the
table: multiply the value of x by 3, then subtract 2. To find the missing
number in the table, we apply the rule of the function when x is 4.

3x – 2
3(4) – 2 = 10
We find that the missing number is 10.

graphing Many functions can be graphed on a coordinate plane. Here we show a
functions function table that relates the perimeter of a square to the length of one of
its sides. On the coordinate plane we have graphed the number pairs that
appear in the table. The coordinate plane’s horizontal axis shows the length
of a side, and its vertical axis shows the perimeter.

sP Perimeter (P ) of Square 24
14 20
28 16
3 12 12
4 16
8
4

0 123456
Length of Side (s )

We have used different scales on the two axes so that the graph is not
too steep. The graphed points show the side length and perimeter of four
squares with side lengths of 1, 2, 3, and 4 units. Notice that the graphed
points are aligned. Of course, we could graph many more points and
represent squares with side lengths of 100 units or more. We could also
graph points for squares with side lengths of 0.01 or less. In fact, we can
graph points for any side length whatsoever! Such a graph would look like a
ray, as shown on the next page.

Lesson 96 499

Perimeter (P ) of Square 24
20
16
12

8
4

0 123456
Length of Side (s )

Example 3

The perimeter of an equilateral triangle is a function of the length of its
sides. Make a table for this function using side lengths of 1, 2, 3, and 4
units. Then graph the ordered pairs on a coordinate plane. Extend a ray
through the points to represent the function for all equilateral triangles.

Solution

Thinking Skill We create a table of ordered pairs. The letter s sP
stands for the length of a side, and P stands for 13
Generalize the perimeter. 26
39
What is the rule 4 12
for this table?

Now we graph these points on a coordinate plane with one axis for perimeter
and the other axis for side length. Then we draw a ray from the origin through
these points.

Perimeter (P ) of Triangle 15
10

5

0 123456
Length of Side (s)

Every point along the ray represents the side length and perimeter of an
equilateral triangle.

500 Saxon Math Course 1

Practice Set Generalize Find the missing number in each function table:

a. x y b. a b

31 38

53 5 10

64 7 12

10 15

c. x 368 d. x 3 4 7

3x + 1 10 19 3x ∙ 1 8 20

e. Model The chemist mixed a solution that weighed 2 pounds per quart.
Create a table of ordered pairs for this function for 1, 2, 3, and 4 quarts.
Then graph the points on a coordinate plane, using the horizontal axis
for quarts and the vertical axis for pounds. Would it be appropriate to
draw a ray through the points? Why or why not?

Written Practice Strengthening Concepts

1. When the sum of 2.0 and 2.0 is subtracted from the product of 2.0 and
(12, 53) 2.0, what is the difference?

2. A 4.2-kilogram object weighs the same as how many objects that each
(49) weigh 0.42 kilogram?

3. If the average of 8 numbers is 12, what is the sum of the 8 numbers?

(18)

4. Conclude What is the name of a quadrilateral that has on65e pair of sides
that are parallel and on65e pair of sides that are not parallel?
(64)

* 5. a. Write 0.15 as a percent. 5
6
(94)

b. Write 1.5 as a percent.

* 6. Write 5 as a percent.
6
(94)

7. Classify Three of the numbers below are equivalent. Which one is not
(41, 76) equivalent to the others?

A1 B 100% C 0.1 D 100 5
8. 113 100 6
100 5 289
(73) 100 9. is 5 of 360?
Ho6 w much 6
(70)

* 10. Estimate Between which two 11c00o00nsecutive wh65ole numbers is 289?
(89)

100 5 289
100 6

(45) (54) 1 1
2
(45) (54) 1 1 1 3 81
81 2 100 4
100 5
6 501
Lesson 96
(45) (54)
81 1 1 1 3
2 4

100 5 289
100 the field,
* 11. Analyze Silvest6er ran around
(90) turning at each of the three backstops.

What was the average number of degrees

he turned at each of the three corners? 289

100 5
100 6

6  36 4 hours  6 dollars 32  23  24  5  62  216
9 w 1 1 hours

* 12. (4G5en) (e5ra4li)ze Find1t12he missing nu1m34ber in this function table.
(96) x 4 7 13 15
5 81
6

2x ∙ 1 7 13 29 30 16 2  100 2 1  3 1
0.08 3 2 3

13. Factor and reduce: (453) (054) 1 2116 2  100 1 432 1  3 1  4 1 65
08.108 3 2 3 6
(67)

1 1611623011032002111((((004267864094211))))....01052725006353.0.012323o000f8$2103103322.123013.03400.021008856(0d3e4331c16i231m12126a4l23461an3610013s1.313.06w1006080238e2302r4)86119100620011((1(21637597892)))...511602313266.621311123322583×5313431131$31610310660025.8358304425166134132225212152 83 30313.00856.3461556313.3435831331643325283 6 5 1
16 10520 3

30 30 2 2
0.08 0.08 3
6  53103.00883 16

2 1 4 16RT 6 5 1  3 2 1
5 3 5.3 3 8 3
3  RS63534 5
32 0  3534.3
05.08 2
5

21. What is the ratio of the2n34umber of centRsTin a dime to tRheSnumber of30ST 16 2  1
3 R
(23) e3Rc42aen1343Scn=htsuR624innS3416∙ka1n4oqwuanrtnSReurTT?mb2eSRr43TT: 5 31RS 3RT ST RS 0.S0T8
0 16 2  100 6 8RS 2 12 ST 5.3243 3 3
08 3 RT 2F21ind  5 4 RT
* 22.
2 3 2 3 RT * 23. 0.3n =
4 4
42(58(4877))).1(5T4Mh) oednefl2in34dD1raa21nwd (87)
2 3 2 3 ( RtThe lengRtShs of  6 dollars
4 4 RT aRmsSaeragknmtd2heR43eSnTtTm1?id34 pinocSinhTteosfloRnRTgS..LLaabbeelltthhee96meRniSdSdp3Twp6ooininttsS.RWahn4adhSt To1aT.urers 1 hours

* 25. Solve this proportion: 6  36 4 hours  6 dollars 32  23  24  5 
(85) 9 w 1 1 hours RT
2 3
4
ho1u4rsho1*Ru62Sr(19s65dh).oolM96ula61rursdslhtoi3owpl696ullayrrss4S3hwT6ours342bhyo16u2963r4ds32ohlo1la3uw622r61rs3sdh4pooelulra26r1hr5ssdo4houo4lrul:a6rh5r2sos1urs2621366212dhoo1l2u3l6a3r2rss
RT 24  5 32622321624  5  6
2963  32w64  5 462ho1ur2s 1661dhool
6  36  36 4
9 w9 w

 69623w26 9616 36 4 h(o1In22uv78.71r7)s.., 4(6hCE,soo16t1n0uimnd)rh,esaooc(96t4lteula,rr4sT6sT1)3h,whd6heaeoonclsuldoaarrosy(s–rind2g,in964“a4)3At.eh2Wpso13wiuh6noratf2s’ts3th3isae2 tp6vh12oeedhu2r4ot4aon3ilcruldheaero1arstss5hu2ooerfsf4wtah6oep2r6al1p5drdaah1aro12lo6alreloul6all13uero2rs62nlsgodrga”rm22arem31afe?6rers2(0t7o3,450030th2),e5  62  216  6
w 23  242 5

24  5

(78) fact that a pint of water116weighs about 7o35n00e pound. Abo2ut how man6y
29
pounds does a gallon of water weigh? 5  36 4 hours
1 750 1 750 w 1
2 22 of a
 36 4 hours  6175dh0ool*ula2r(r9ss92). 16 32  2330 2176540  5  3220 16 1 750 2
w 1 Analyz1e  62 prim2e number 5 16 30

1 1 750 W2hat 12is6 the 30 with one roll
16
16 30 30 30. probability2of rolling a

(58, 74) numbe1r cube? Expres7s550the ratio as a f5raction and as a decimal.
72520
2 16 2 21 30 530 2 2
M2at7h3500Cours73e55001 5 156 5
502116 Sa11x62on 22 2
2 2 5
2 5 5
2
55 55

1 750

LESSON Transversals

97

Power Up Building Power

facts Power Up L
mental
a. Number Sense: 20 ∙ 50
math b. Number Sense: 517 − 250
c. Percent: 25% of 60
d. Calculation: $7.99 + $7.58
e. Decimals: 0.1 ÷ 100
f. Number Sense: 20 × 75
g. Measurement: How many liters are in 1000 milliliters?
h. Calculation: 5 × 9, − 1, ÷ 2, − 1, ÷ 3, × 10, + 2, ÷ 9, − 2, ÷ 2

problem Chad and his friends played three games that are scored from 1–100. His
solving lowest score was 70 and his highest score is 100. What is Chad’s lowest
possible three-game average? What is his highest possible three-game
average?

New Concept Increasing Knowledge

A line that intersects two or more other lines is a transversal. In this drawing,
line r is a transversal of lines s and t.

r

s

t

Math Language In the drawing, lines s and t are not parallel. However, in this lesson we will
focus on the effects of a transversal intersecting parallel lines.
Parallel lines are
lines in the same Below we show parallel lines m and n intersected by transversal p. Notice
plane that do not that eight angles are formed. In this figure there are four obtuse angles
intersect and are (numbered 1, 3, 5, and 7) and four acute angles (numbered 2, 4, 6, and 8).
always the same
distance apart. p

exterior 12 m
interior 43 n
exterior 56
87

Lesson 97 503

Thinking Skill Notice that obtuse angle 1, and acute angle 2, together form a straight line.
These angles are supplementary, which means their measures total 180°.
Verify So if ∠1 measures 110°, then ∠2 measures 70°. Also notice that ∠2 and ∠3
are supplementary. If ∠2 measures 70°, then ∠3 measures 110°. Likewise,
Why does ∠3 and ∠4 are supplementary, so ∠4 would measure 70°.
every pair of
supplementary There are names to describe some of the angle pairs. For example, we say
angles in the that ∠1 and ∠5 are corresponding angles because they are in the same
diagram contain relative positions. Notice that ∠1 is the “upper left angle” from line m, while
one obtuse and ∠5 is the “upper left angle” from line n.
one acute angle?
p

exterior 12 m
interior 43 n
exterior 56
87

Which angle corresponds to 2?

Which angle corresponds to 7?

Since lines m and n are parallel, line p intersects line m at the same angle as
it intersects line n. So the corresponding angles are congruent. Thus, if we
know that ∠1 measures 110°, we can conclude that ∠5 also measures 110°.

The angles between the parallel lines (numbered 3, 4, 5, and 6 in the figure
on previous page) are interior angles. Angle 3 and ∠5 are on opposite sides
of the transversal and are called alternate interior angles.

Name another pair of alternate interior angles.

Alternate interior angles are congruent if the lines intersected by the
transversal are parallel. So if ∠5 measures 110°, then ∠3 also measures
110°.

Angles not between the parallel lines are exterior angles. Angle 1
and ∠7, which are on opposite sides of the transversal, are alternate
exterior angles.

Name another pair of alternate exterior angles.

Alternate exterior angles formed by a transversal intersecting parallel lines
are congruent. So if the measure of ∠1 is 110°, then the measure of ∠7 is
also 110°.

While we practice the terms for describing angle pairs, it is useful to
remember the following.

When a transversal intersects parallel lines, all acute
angles formed are equal in measure, and all obtuse
angles formed are equal in measure.

Thus any acute angle formed will be supplementary to any obtuse angle
formed.

504 Saxon Math Course 1

Example

Transversal w intersects parallel lines x and y.

w

ab x
dc y
ef
hg

a. Name the pairs of corresponding angles.
b. Name the pairs of alternate interior angles.
c. Name the pairs of alternate exterior angles.
d. If the measure of a is 115∙, then what are the measures of e

and f?

Solution

a. a and e, b and f, c and g, d and h
b. d and f, c and e
c. a and g, b and h
d. If ∠a measures 115°, then ∠e also measures 115∙ and ∠f measures 65°.

Practice Set a. Which line in the figure at right is a c
transversal?
41 f
b. Which angle is an alternate interior angle 32 g
to ∠3? 85

c. Which angle corresponds to ∠8? 76

d. Which angle is an alternate exterior angle
to ∠7?

e. Conclude If the measure of ∠1 is 105°, what is the measure of each of
the other angles in the figure?

Written Practice Strengthening Concepts

1. How many quarter-pound hamburgers can be made from 100 pounds of
(49) ground beef ?

2. Connect On the Fahrenheit scale water freezes at 32°F and boils at
(18) 212°F. What temperature is halfway between the freezing and boiling

temperatures of water?

Lesson 97 505

* 3. This function table shows the relationship between temperatures
(96) measured in degrees Celsius and degrees Fahrenheit. (To find the

Fahrenheit temperature, multiply the temperature in Celsius by 1.8,
then add 32.) Find the missing number in the table.

C 0 10 20 30
1.8C + 32 32 50 68

Predict What is special about the result when C = 100? (Hint: You

may want to refer to problem 2.) 5 0.675 2 1
8 4
5 1 2 7
4. Compare: 8 00.6.67755 2 4 1 5 8

5 (76) as58a
8
* 05..67W5rite 2 1 perc0e.6n7t1.525 2 1 * 6. W78 rite 1 2 as a percent78.
4 4 5
(94) (94)
*(58974).
9. Wr0it.6e705.7 as2a14 percent. 1 2 th*(e984p). riWmreitefa78ctaosrsa58opfe3r2ce00n. .tT6.h7e5n wr2it41e 1 2
Use division by primes 5 5

to find the
(73) prime factorization of 320 using exponents.

* 10. dIneognreeems dinouetes85 the ms0ei.cn6ou7nt5edhhaan2nd41dooffaacclolocckkttuur1rnn25sin3o6n0e°.mHionwutem78?any
(90) the

* 11. Analyze Jason likes to ride his skateboard around Parallelogram
(90) Park. If he made four turns on each trip around the park, what was the
average number of degrees in each turn?

6104325287 49  (61310  2821)  32 2 1  100
2
3 876243 49567813 (61340212 6581378) 32222112 613100222121 1
6 4 1052   1002 2  100

12. 6 3 5 876 3 5687136341(6332).12567831 221221613 102021221 1(66481).3400221587 100 6 1  2 1 2 1  100
4 4 3 2 2
(59)   

663443557887 6116(1((1337785783413)))...46J232o...13229512v213ictau+b87b8ioc(.du4y2eg24a2c12h9.r12i2dtm+s3a331f1l1o131870ac2r0n0ut04sbhw.ie22c.ef5ylro)awr873de13srb4oe.21f2d12(m5s6.35u.).331lH87c(131ohw−fom0r21321..tu15hc)e(3h12131g31m÷arud0l21ce.21hn.13)5.isS31hle21eftwfo21i13lrl74nJeo31ev214dwit4a 1 4721 1 7  w1
44.2.28787 3 2 4 442
to
w
44

use for her vegetable garden? Write your answer as a fraction.

19. 4dA.id2nanlyozt87e p4aIf.s28s?0%873o314f .t2he2.35873031stud2e21.n5t3s1331pas2s21.e513dt31h4e21.2te12s13t,87h31o21w ma13n3y4731s21tu4d2w4e.5nt47s 4w214217431 1 
w13
(41)  442

323(1350031).C2o2.5.m5pare:12213131 13132121 47744w44w4 11
22

21. Predict What is the next number in this sequence?

(10)

. . ., 1000, 100, 10, 1, . . .

506 Saxon Math Course 1

7 Find each unknown number: w
8 1 6021 7310 11380 1 7 44
4.2  3 3 222.5. a + + = 2 23. 4  1
(3) 2
(85)

1  2 1 2 1  100 24. The perimeter of this square is 48 in. What is
3 2 2 (79) the area of one of the triangles?

2 1  100 Refer to the table below to answer problems 25–27.
2 Mark’s Personal Running Records

Distance Time (minutes:seconds)

5 0.675 2 1 mile 1 2 0:58 7
8 4 5 8
1 1 1 1 1 7 w
3  2.5 2  3 3  2 4  44 1 mile 2:12
2

1 mile 5:00

1  1 1  1 7  w 25. If Mark set his 1-mile record by keeping a steady pace, then what was
2 3 3 2 4 44 his 12-mile time during the 1-mile run?
(32)

26. Conclude What is a reasonable expectation for the time it would take
(32) Mark to run 2 miles?

A 9:30 B 11:00 C 15:00

27. Formulate Write a question that relates to this table and answer the
(32) question.

* 28. Transversal t intersects parallel lines r and s. Angle 2 measures 78°.
(97)
t

12 r
43 s

56
87

a. Analyze Which angle corresponds to ∠2?
b. Find the meas1u0r2eso2f ∠459and(1∠08. 8)  32

* 29. 102  249  (10  8)  32
(92)
30. What is the probability of rolling a composite number with one roll of a
(58) number cube?

3 1
3

3 1
3

Lesson 97 507

LESSON Sum of the Angle Measures of
Triangles and Quadrilaterals
98

Power Up Building Power 23  281  32  a21 2 120 in.  1 ft
Power Up J 1 12 in.
facts b
mental
a. Number Sense: 40 ∙ 50 23  223 8128312  3a221b2 a21 2 120 in1.201 in1.12fint .112 ft
math 1 in.
b. Number Sense: 293 + 450 b

c. Percent: 50% of 48

d. Calculation: $20.00 − $18.72

e. Decimals: 12.5 × 100

f. Number Sense: 360 2
40

g. Measurement: How many cups are in 2 pints?

h. Calculation: 8 × 8, − 1, ÷ 9, × 4,34+600 2,34÷600 2, + 1, 2 , 2

problem If two people shake hands, there is one handshake. If three people shake
solving hands, there are three handshakes. If four people shake hands with one
another, we can picture the number of handshakes by drawing four dots
(for people) and connecting the dots with segments (for handshakes).
Then we count the segments (six). Use this method to count the number of
handshakes that will take place between Bill, Phil, Jill, Lil, and Wil.

New Concept Increasing Knowledge

If we extend a side of a polygon, we form an exterior angle. In this figure ∠1
is an exterior angle, and ∠2 is an interior angle. Notice that these angles are
supplementary. That is, the sum of their measures is 180º.

Thinking Skill 21

Verify Recall from Lesson 90 that a full turn measures 360º. So if Elizabeth makes
three turns to get around a park, she has turned a total of 360º. Likewise, if
Act out the turns she makes four turns to get around a park, she has also turned 360º.
Elizabeth made to
verify the number 2
of degrees. 2

1 31

3 4
The sum of the measures of The sum of the measures of
angles 1, 2, and 3 is 360°. angles 1, 2, 3, and 4 is 360°.

508 Saxon Math Course 1

If Elizabeth makes three turns to get around the park, then each turn
averages 120º.

360°  120° per turn 360°  90° per turn
3 turns 4 turns

If she makes four turns to get around the park, then each turn averages 90º.

360°  120° per turn 360°  90° per turn
3 turns 4 turns

Recall that these turns correspond to exterior angles of the polygons and
that the exterior and interior angles at a turn are supplementary. Since the
exterior angles of a triangle average 120º, the interior angles must average
60º. A triangle has three interior angles, so the sum of the interior angles is
180º (3 × 60º = 180º).

The sum of the interior angles of a triangle is 180º.

3

12

The sum of angles
1, 2, and 3 is 180°.

Since the exterior angles of a quadrilateral average 90º, the interior angles
must average 90º. So the sum of the four interior angles of a quadrilateral is
360º (4 × 90º = 360º).

The sum of the interior angles of a quadrilateral is 360º.

2 A B
3 60°

4 70°
1 C

The sum of angles
1, 2, 3, and 4 is 360°.

Example 1

What is mA in  ABC?

Solution

The measures of the interior angles of a triangle
total 180º.

m∠A + 60º + 70º = 180º
Since the measures of ∠B and ∠C total 130º,
m∠A is 50º.

Lesson 98 509

Example 2

What is mT in quadrilateral QRST? R Q
80°
Solution 80°
T
The measures of the interior angles of a 110 °
quadrilateral total 360º. S

m∠T + 80º + 80º + 110º = 360º

The measures of ∠Q, ∠R, and ∠S total 270º. So m∠T is 90º.

Practice Set Quadrilateral ABCD is divided into two triangles by segment AC. Use for
problems a–c.

B

2 A
16

34 5
C D

a. What is the sum of m∠1, m∠2, and m∠3?

b. What is the sum of m∠4, m∠5, and m∠6?

c. Generalize What is the sum of the measures of the four interior angles

of the quadrilateral? R

d. What is m∠P in △PQR?

e. What is the measure of each interior angle of 30°
a regular quadrilateral?
75°
Q P

f. Model Elizabeth made five left turns as she ran around the park. Draw
a sketch that shows the turns in her run around the park. Then find the
average number of degrees in each turn.

Written Practice Strengthening Concepts

1. When th12e sum of 1 and 1 is divide14d by t12he pr12oduc12t of 1 14and 14, wh14at is 14th5e21 1 5 1 14
2 4 2 2 2 25
(12, 72) quotient?

1 1 * 2. An14alyze Jenny is 5 1 feet tall. She54is how many inches tall?
4 2 2
(95)
1 1 4
4 5 2 3. If 5 of the 200 runners finished the race, how many runners did not finish

(77) the race?

510 Saxon Math Course 1

* 4. Lines p and q are parallel. p q
(97)

12 5 6 m
43 87

a. Which angle is an alternate interior angle to ∠2?

1 1 b. If ∠122 measures 85º14, what are the m5e21asures of ∠654and ∠7?
2 4

* 5. Analyze The circumference of the earth is about 25,000 miles. Write that
(92) distance in expanded notation using exponents.

6. Estimate Use a ruler to measure the
(17, 27) diameter of a quarter to the nearest sixteenth

of an inch. How can you use that information
to find the radius and the circumference of
the quarter?

7. Connect Which of these bicycle wheel parts is the best model of the
(27) circumference of the wheel?

A spoke B axle C tire

8.1 Predict As th1is sequence con1 tinues, teearmchinte41trhmisesqeuqaulsenthcee?s5u21m of the 4
two previous t4erms. What is t2he next 5
(10)2

11, 11, 2, 3, 5, 8, 113,. . .0.001 3 1
3
3 1  0.0
is th0e.0p3robability1t0h0a1t31it 0.03
9. If there is a 20% chance of rain, what will not
(58)
rain? 113103100.000.310.000101.00.3001130331013 3 1
* 10. 1W1A31rni0tae.l0y011z.30e13130a10s.0a8pwe11r3=0c310e0$n.00t111..3.016310031001..0000..313001300111310(631308). 3
(94)
100
* 11.
1 (87) 3 1 0.03 100
3 12. 3
1 (49)
100
sm6a12ll 1 1, 6121,0,412.,95 21
14. If the volume of each blo4c.9k5is one2 6  1.5 2 1 1.
6
(82) cubic inch, what is the volume of this 

rectangular prism?
6Ip2fr1261aicseh6i641inr1212..tc95lc5uods(44idnt..seg99c55$t21i1am,61x9a?.7l)1E9622,1x6a0126161.p521n,lad12i,nt4116h4..h.12e955.21o95sw15a1,(7l4y6e3o.)s.91u-5,211ta2c0,,61xa61,n12r11a,c,,t12eh100.61e5.21,,i5sc1212(k6,,fr%y1ao.c21215,utiw1ro1,ahn,na)st1w1i,s1,e0,t0r,h,12ue121,st,,ion0tg21a,21l12, 21
15.

(74)

6 1  4.95 17.
2
(41)

estimation.

* 18. What fraction of a foot is 3 inches?
(95)
19. What percent of a meter is 3 centimeters?
(75)

Lesson 98 511

6 1  4.95 2 1  1.5 1, 1, 0, 12, 21
2 6

20. The ratio of children to adults in the theater was 5 to 3. If there were
(88) 45 children, how many adults were there?

21. Arrange these numbers in order from least to greatest:
(14, 17)
1 1 1, 1, 0, 12, 21
6 2  4.95 2 6  1.5

22. Classify These two triangles together
(64) form a quadrilateral with only one pair of

parallel sides. What type of quadrilateral is
formed?

23. Conclude Do the triangles in this quadrilateral appear to be congruent
(60) or not congruent?

* 24. a. Analyze What is the measure of ∠A A
(98) in △ABC? 40°110° x
CB
b. Analyze What is the measure of the
exterior angle marked x?

25. Write 40% as a
(33, 74) a. simplified fraction.

b. simplified decimal number.

26. The diameter of this circle is 20 mm. What is
(86)
the area of the circle? (Use 3.14 for π.)
23  281  32 a21 2 12200 imn.m 1 ft
 1 12 in.
b

* 27. 23  281  32  a21b2 120 in.  1 ft
(92) 1 12 in.

* 28. Multiply 120 inches by 1 foot per 12 inches.
(95)
281  32  a21b2 120 in.  1 ft
23  1 12 in.

29. A bag con2ta3ins 2208r1edm334a6200rbleas21abn2d 15 b2lu1e20m1 ianr.bles1.12 ft
in.
(23, 58)
a. What is the ratio of red marbles to blue marbles?

b. If one marble is drawn from the bag, what is the probability that the
360
40 marble will b2e blue?

* 30. Conclude An architect drew a set of 21b2 120 in.  1 ft
(93) plans for a house. In the2p3 lans2, t8h1ero3o2f is a 1 12 in.
360 supported 2by a triangular framework. When
40

23  281  32  a21twhbi2ell house f13i4es620e00b1t uilnoil.nt,gtwa1no12dsfintitdh.ee2sboafstehewiflrlabmee3w3ork
be 19

feet long. Classified by side length, what type

of triangle will be formed?

512 Saxon Math Course 1

360 2
40

LESSON 3
10
99
Fraction-Decimal-Percent
Equivalents

Power Up Building Power

facts Power Up K
mental
a. Number SenseA: C60 ∙ 50 1 1 AC AB BC
math 4

b. Number Sense: 741 − 450

c. Percent: 25% of 48

d. Calculation: $12.99 + $4.75

e. Decimals: 37.5 ÷ 100

f. Number Sense: 30 × 15

g. Measurement: Which is greater 1 liter or 1000 milliliters?
h. Calculation: 713× 7, + 1, ÷ 2, 2 , × 4, − 2, ÷ 3, × 5, + 3, ÷ 3

problem If the last page of a section of large newspaper is page 36, what is the fewest
solving number of sheets of paper that could be in that section?

New Concept Increasing Knowledge

Fractions, decimals, and percents are three ways to express parts of a whole.
An important skill is being able to change from one form to another. This
lesson asks you to complete tables that show equivalent fractions, decimals,
and percents.

Example
Complete the table.

Fraction Decimal Percent
a. b.
1 d.
2 0.3
f. 40%
c.

e.

Solution bfreace21tqiouniv2aanl01ed..n50ta.

The numbers in each row should For 1 we Fworrite40a%dewc12eimwarl1it0e10a%  50%
and a percent. For 0.3 we write a 2
percent.

fraction and a decimal.

a. 1  221 01..502 0.5 1 1 b. 112010%1010%5043% 50% 0.3 01.330  3 40%
2 1.012 2 235 10

33 33 Lesson 99 513
55 44

1  100%  50% 0C121o..ce50n..n0e42c.03t%01.1232514321.C5012o13m01124p0002l00e11012.t.0%150e21..50t524h0eFce%52r..taa01312122435c0b1%321521.t.l5e0io1.214n0021020011012..0%1535120Da12.f.502..e521c0010.i2d8m..5f1050..0013242101%a%.40..234112l350.03%1Pdb×02151e1..=3100021r0%%10c024130012e%%0.4n%0t15==005412010%00.30123%%.0%4%132150121113000051%10.1242030%01%0010..1015015%30052054010%00.0%3%%.35342101%3540113004000%%0.03524011430.004030%0.03%12013.52031
2 1

 50% 0.3  3
10

Pra0c.5tice S21et 2
 2 1.0 1
1 2
2

3
5
33
54

3 3 g. h.
5 4
3 3
3 3 35 i. 1 1 3 4 0.123 3j. 3
8 5 4 k. 2 4 5% 8
5 l. 8
1 1 3 3
2 8 8

Written Practice 1 Strengthening 3C1o12ncepts 3 3
1 2 8 8
3
88 cut many
3 1. A foot-long ribbon 1c21an be into3how 1 1 -in3ch 3 3
1 1 8 (68) Ana3lyze 2 8 8
2 8 8
leng8ths?

2. A can1o21f 3 3
g8 eometr3ic solid?
(Inv. 6) Analyze bIef a38no1sf21itshethger8oshuapp1ve2138oot38efdwyheast 8
and 3 no, then83 what fraction
(173721). 8 voted

of the group did not vote?

4. Connect Nine months is

(29, 75)

a. what fraction of a year?
b. what percent of a year?

5. One-cubic-foot boxes were stacked as
(82) shown. What was the volume of the stack of

boxes?

1 * 6. 11 Tom was fa71cing 1 Then he 1 counterclockwise 270°.
5 7Analy5ze
eas5t. turne7d
(90) After the turn, what direction was Tom facing?

7. If 1 of the pie was17eaten, what percent of the pie was left?
5
(75)

* 8. Write the p15ercent form of 17.

(94) 3
4
 225  (2  3) 9. 6  6.2 (decimal answer)

(74)

10. 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 ∙ 0
(5)
15 4.5 15 24 2160040.1.58 21*0521(8296).42n42 156200 204.1.2585 2(2643)522 1602025  (2 2663434)65.22 
20  24 11. 0.18 20  n
n
(49)

514 Saxon Math Course 12105  24 4.5 21600 264  52  225  (2  3)
n 0.18
121 1513 245 4.512 1  1 3 251600
121  13  5 264  52  225  (2  3)

24 4.5 2120564 24 4.5 21600 623464  52  225  (2  3)
n 0.18 n 52 202.158× (22 + 33)) 6.2
 21600 13. 
(92)

14. Analyze Solve this proportion: 15  24 4.5 21600 2
20 n 0.18
(85)

1 3 15. 12 1  1 3  5 16. (4.2 × 0.05) ÷ 7
2 5 2 5
 1  5 (72) (53)

17. If the sales-tax rate is 7%, twhheapte1isr2cte21hnet toa1fx35thoen a $111.11 purchase?
Analyze The table shows 5
(41) population aged 25–64

18.
(Inv. 5) with some senior high school education. The figures are for the year

2001. Use the table to answer a–c.

Country Percent
Peru 44%
57%
Iceland 46%
Poland 43%
51%
Italy 46%
Greece 53%
Chile
Luxembourg

a. Find the mode of the data.
b. If the data were arranged from least to greatest, which country or

countries would have the middle score?
c. What is the term used for the answer to problem b? Will this quantity

always be the same as the mode in every set of data? Explain.

19. Write the prime factorization of 900 using exponents.

(73)

20. Think of two different prime numbers, and write them on your paper.
(20) Then write the greatest common factor (GCF) of the two prime

numbers.

21. Explain The perimeter of a square is 2 meters. How many centimeters
(7, 8) long is each side? Explain your thinking.

* 22. a. What is the area of this triangle?

(79, 93)

10 cm 5 cm

8 cm

b. Classify Is this an acute, right, or obtuse triangle?

Lesson 99 515

* 23. a. What is the measure of ∠B in D A
(98) quadrilateral ABCD? 110° 90°

b. What is the measure of the13e0 xterior angle 75°
at D? C

3 B
3 10
3 3
3 Com3ple1t0e the table1t0o answer problems1024–26.
3
10 10 10

Fraction Decimal Percent

* 24. a. 0.6 b.
(99)

* 25. a. b. 15%
(99)
b. AC 1 1 AC AB
* 26. 3 a. 4 BC AB
(99) 10

27. AlaCMbAoedC1Alet14Clhe1D41mraiwdpAo1Ci14nt1B141A.i14CnWcAhhCaets lo1n14g. AC and maArCk tA1hB14eABmidpoinAt oBf BC
AFACiCnd BACC, and
(17)
AC AC areAtChe lAeBngAthBs of AB aBndCBC? BC

28. There are 32 cards in a bag. Eight of the cards have letters written
(58) on them. What is the chance of drawing a card with a letter written

on it?

29. Compare: 1 gallon 1 14 liters 1 AC 2 AB BC
AC 3
(78) 4
31ttahhGnee31ednri132nederpliaaaultim2zitoeeantnseTdhrhi31(tpidhs2e)bfueod2ntfiwac2amteicoeeinnrtcettlraehb.iesTlert2hahsedehiruoo13aswudt(isrpu)usti.s
* 30. rd

(27, 96) 2 1.2 2.4
0.7 1.4
1 1 5
3 3 15 30

Describe the rule and find the missing

number.

Early Finishers oJensesaecdhissph31lealyf sarterofpohr iseoscocn2er4. shelves in the family room. Two of the 6 trophies
How many trophies are NOT for soccer?
Real-World
Application Write one equation and use it to solve the problem.

516 Saxon Math Course 1

LESSON Algebraic Addition of Integers

100

Power Up Building Power

facts Power Up I
mental
a. Number Sense: 50 ∙ 80
math
b. Number Sense: 3980 + 550
c. Percent: 50% of11000

d. Calculation: $40.00 − $21.89

e. Decimals: 0.8 × 100

f. Number Sense: 750
25

g. Measurement: How many pints are in 2 quarts?

h. Calculation: 5 + 5, × 10, − 1, ÷ 9, + 1, ÷ 3, × 7, + 2, ÷ 2

problem How many different triangles of any size are in this figure?
solving

New Concept Increasing Knowledge

Math Language In this lesson we will practice adding integers.

Integers consist The dots on this number line mark the integers from negative five to positive
of the counting five (−5 to +5).
numbers (1, 2,
3, ...), the negative –5 0 5
counting numbers
(−1, −2, −3, ...), If we consider a rise in temperature of five degrees as a positive five (+5) and
and 0. All numbers a fall in temperature of five degrees as a negative five (−5), we can use the
that fall between scale on a thermometer to keep track of the addition.
these numbers are
not integers. Imagine that the temperature is 0°F. If the 0°F –5
temperature falls five degrees (−5) and then –5°F –5
Thinking Skill falls another five degrees (−5), the resulting – 10 ° F
temperature is ten degrees below zero (−10°F).
Analyze When we add two negative numbers, the sum
is negative.
How is a
thermometer like a −5 + −5 = −10
number line? How
is it different?

Lesson 100 517

Math Language Imagine a different situation. We will again start 5°F –5 +5
with a temperature of 0°F. First the temperature 0°F
Opposites are falls five degrees (−5). Then the temperature rises –5 °F +5
numbers that five degrees (+5). This brings the temperature –10
can be written back to 0°F. The numbers −5 and +5 are 5°F
with the same opposites. When we add opposites, the sum 0°F
digits but with is zero. –5 °F
opposite signs.
They are the −5 + +5 = 0
same distance,
in opposite Starting from 0°F, if the temperature rises five
directions, from degrees (+5) and then falls ten degrees (−10), the
zero on the temperature will fall through zero to −5°F. The sum
number line. is less than zero because the temperature fell
more than it rose.

+5 + −10 = −5

Example 1
Add: +8 + ∙5

Solution
We will illustrate this addition on a number line. We begin at zero and move
eight units in the positive direction (to the right). From +8 we move five units
in the negative direction (to the left) to +3.

–5

+8

–1 0 1 2 3 4 5 6 7 8 9

+8 + −5 = +3
The sum is +3, which we write as 3.

Example 2
Add: ∙5 + ∙3

518 Saxon Math Course 1

Solution

Thinking Skill Again using a number line, we start at zero and move in the negative
direction, or to the left, five units to −5. From −5 we continue moving left
Generalize three units to −8.

When two –3
negative integers
are added, is the –5
sum negative or
positive? –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1

−5 + −3 = −8

The sum is ∙8.

Example 3
Add: ∙6 + +6

Solution
We start at zero and move six units to the left. Then we move six units to the
right, returning to zero.

+6

–6

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2

−6 + +6 = 0

Example 4

Add: (+6) + (∙6)

Solution

Sometimes positive and negative numbers are written with parentheses. The
parentheses help us see that the positive or negative sign is the sign of the
number and not an addition or subtraction operation.

(+6) + (−6) = 0
Negative 6 and positive 6 are opposites. Opposites are numbers that can be
written with the same digits but with opposite signs. The opposite of 3 is −3,
and the opposite of −5 is 5 (which can be written as +5).
On a number line, we can see that any two opposites lie equal distances
from zero. However, they lie on opposite sides of zero from each other.

opposites

–5 –3 0 3 5
opposites

Lesson 100 519

If opposites are added, the sum is zero.
−3 + +3 = 0 −5 + +5 = 0

Example 5

Find the opposite of each number:

a. ∙7 b. 10

Solution

The opposite of a number is written with the same digits but with the
opposite sign.

a. The opposite of −7 is +7, which is usually written as 7.
b. The opposite of 10 (which is positive) is ∙10.

Using opposites allows us to change any subtraction problem into an
addition problem. Consider this subtraction problem:

10 − 6
Instead of subtracting 6 from 10, we can add the opposite of 6 to 10. The
opposite of 6 is −6.

10 + −6
In both problems the answer is 4. Adding the opposite of a number to
subtract is called algebraic addition. We change subtraction to addition by
adding the opposite of the subtrahend.

Subtraction: minuend — subtrahend = difference

(sign change)

Addition: addend + opposite of = sum
subtrahend

Example 6
Simplify: ∙10 ∙ ∙6

Solution

This problem directs us to subtract a negative six from negative ten. Instead,
we may add the opposite of negative six to negative ten.

–10 – –6

–10 + +6 = −4

Example 7
Simplify: (∙3) ∙ (+5)

520 Saxon Math Course 1

Solution

Instead of subtracting a positive five, we add a negative five.
(–3) – (+5)

(–3) + (–5) = −8

Practice Set Model Find each sum. Draw a number line to show the addition for
problems a and b. Solve problems c–h mentally.

a. −3 + +4 b. −3 + −4

c. −3 + +3 d. +4 + −3

e. (+3) + (−4) f. (+10) + (−5)

g. (−10) + (−5) h. (−10) + (+5)

Find the opposite of each number:

i. −8 j. 4 k. 0

Solve each subtraction problem using algebraic addition:

l. −3 − −4 m. −4 − +2

n. (+3) − (−6) o. (−2) − (−4)

Written Practice Strengthening Concepts

1. If 0.6 is the divisor and 1.2 is the quotient, what is the dividend?

(39)

2. If a number is twelve less than fifty, then it is how much more than
(12) twenty?

3. If the sum of four numbers is 14.8, what is the average of the four
(18) numbers?

* 4. Model Illustrate this problem on a number line:

(100)

−3 + +5

* 5. Find each sum mentally: b. −2 + −3
(100) a. −4 + +4 d. +5 + −10

c. −5 + +3

* 6. Solve each subtraction problem using algebraic addition:
(100) a. −2 − −5
b. −3 − −3

c. +2 − −3 d. −2 − +3

* 7. Analyze What is the measure of each angle of an equilateral
(93, 98) triangle?

Lesson 100 521

8. Quadrilateral ABCD is a parallelogram. DA
(71) If angle A measures 70°, what are the

measures of angles B, C, and D?

CB

9. a. If the spinner is spun once, what is the 3
(58) probability that it will stop in a sector 22

with a number 2? How do you know your 1
answer is correct?

102  (52  11)  24b9. aEbsot3ium3 tatheowIfmthaenysptiimnnee23sr is spun 30 times,
would it be

expected to stop in the sector with the

number 3?

10. Find the volume of the rectangular prism at
(82) right.
102  (52102 11)(52 21419) 323 496in. 33 2
3

5 in.

42 5 7  413402  (51210122 112()51221022 1419)(52 323 1419)  323 49 1b20o24y39s323. W( 53h2 3at 72in. 2 2
24 8 Twelve of the 27 studen1t0s2 in t(h5e2 cla1ss1)are 3
11. is131th) era2tio439ofg2i3rl3s
(23)
to boys in the class? 3

* 12. Analyze 102  (52  11)  249  31302  (52  11) 2 249  33 2
(92) 3
3

102  (52  11)  249  3*313. The fraction 2 is equal to what perc24e42nt? 42 5 7  4 3 5 7  413412  2 1 1 1  2 1
(94) 3 24 8 4 8 2 2 2

14. If 20% o1f0t2he s(t5u2den1ts1)brou2gh4t9thei3r 3lunch to school, 2 what fraction
(33) of the students did not bring their lunch to school?
th3 en

9  15 * 15. 42 42 5 8724421(5694).43425 7  4143125 7825124871341224244(1678432).211 1 1212215 78212
12 x (92) 24 24 8 2
18. 3 1 1
(38) 5− + 4 4 1 2  2 2

(3.2 0.4) 24

19. RthEEosextup2nimlna12tdaihnteet24o42aW24trIhfe24eeathunoesefedatshiraeqemsubteaostreetq5trsuo875oamtof78reaom4ffcoe43ti4ohract34se.uu(plrUa1e9or2sotp24ehl124laei321s1s1.a1xat125ir4bce1o2a9fs2ou21wo2rtfiπ12mha.o1)mxrw5eincm5gta78apnngoyloe4sl.q43isWua6hryefedfeeote1, wt21?e 2 1
use cubes instead of squares to measure the volume of a rectangular 2
(80)

42 5 7  4 3 1 1
24 8 4 2

20.

(82)

p19r2ism?1x5 9  15 9  15 9  15
12 x 12 9x 12 x
12 15
21. Solve this proportion:  x

(85)

RSeegctmanengtleAACBiCs19D120isc8m1x5clmonlgo.nUgsaentdhi6s cinmfowrmid1a9e2ti.on 15 D A
x C B

9  15 to answer problems 22 and 23.
12 x
22. What is1t92hear1ex5a of triangle ABC?

(79)

23. What is the perimeter of triangle ABC?
(8)

522 Saxon Math Course 1

24. Measure the diameter of a nickel to the
(27) nearest millimeter.

* 25. Estimate Calculate the circumference of a
(47) nickel. Round to the nearest millimeter. (Use
3.14 for π.)

26. A bag contains 12 marbles. Eight of the marbles are red and 4 are
(58, 74) blue. If you draw a marble from the bag without looking, what is the

probability that the marble will be blue? Express the probability ratio as
a frac31tion and as a d1e21cimal rounded215to the nearest hundredth.

Connect Complete the table to answer problems 27–29.

Fraction Decimal Percent

* 27. 9 a. b.
(99) 10

* 28. a. 1.5 b.
(99)

* 29. a. b. 4%
(99)
750
30. A full2o5ne-gallon container of milk was used to fill two one-pint
(78) containers. How many quarts of milk were left in the one-gallon

container?

1 2  1  1
3 3 2 3
Early Finishers These three prime factorizations represent numbers that are powers of 10.

Choose A Strategy Simplify each prime factorization.

22 × 52 24 × 54 25 × 55

Use exponents to write the prime factorization of another number that is a
power of 10.

Lesson 100 523

INVESTIGATION 10

Focus on
Compound Experiments

Some experiments whose outcomes are determined by chance contain
more than one part. Such experiments are called compound experiments.
In this investigation we will consider compound experiments that consist of
two parts performed in order. Here are three experiments:

1. A spinner with sectors A, B, and C is spun; then a marble is drawn from
a bag that contains 4 blue marbles and 2 white marbles.

2. A marble is drawn from a bag with 4 blue marbles and 2 white marbles;
then, without the first marble being replaced, a second marble is drawn.

3. A number cube is rolled; then a coin is flipped.

The second experiment is actually a way to look at drawing two marbles
from the bag at once. We estimated probabilities for this compound
experiment in Investigation 9.

A tree diagram can help us visualize the sample space for a compound
experiment. Here is a tree diagram for compound experiment 1:

Math Language Spinner Marble Compound
A blue Outcome
Recall that the
list of all possible A, blue
outcomes in an
experiment is white A, white
called a sample
space. A tree blue B, blue
diagram is one
way to represent B
the sample
space for an white B, white
experiment.
blue C, blue
C

white C, white

Each branch of the tree corresponds to a possible outcome. There are
three possible spinner outcomes. For each spinner outcome, there are
two possible marble outcomes. To find the total number of compound
outcomes, we multiply the number of branches in the first part of the
experiment by the number of branches in the second part of the experiment.
There are 3 × 2 = 6 branches, so there are six possible compound
outcomes. In the column titled “Compound Outcome,” we list the outcome
for each branch. “A, blue” means that the spinner stopped on A, then the
marble drawn was blue. Although there are six different outcomes, not all the
outcomes are equally likely. We need to determine the probability of each
part of the experiment in order to find the probability for each compound
outcome. To do this, we will use the multiplication principle for compound
probability.

524 Saxon Math Course 1

The probability of a compound outcome is the
product of the probabilities of each part of the
outcome.

We will use this principle to calculate the probability of the first branch of

experiment 1, the spinner-marble experiment, which corresponds to the

1 compound o2utcome “A, blue.” 4
236

The first part of the outcome is that the spinner

stops in sector A. The probability of this outcome BC

is 21, since sector A occupies half the area o32f the 4
circle. 1A 6
6
1 � 2 1
2 3 3

The second part of the outcome is that a blue

mthae21rsb� il32xe is drawn from the bag. Since four of1 2 1
marbles are bl1ue, the probability of t31his 3 62
1 2 1 1 outcome is 64, which s2implifies to 32. 2 2 43
2 � 3 � 3 2 3 6

2 To find the probability of the compoun64d outcome, we multiply the
3

3 1 � 2 Nproo21tbi�cae32b�tilhitai31etsa23lotT�hfh53oee�uapgc25rhhop“b21Aaa�,rbt23bi.lliutye”ofis“Ao31,nbeluoef ”siixs1p6421o�s23s,ibwlheico64hu�tec53qo�umae52lss,31.the 1 2
5 2 3 6 31
3
1 probability of “A, blue” is greater than 16. Th2is is because “A” is the most likely 2
3 of the three possible spinner outcomes, and “blue” is the more likely of the 3

tw53o possible marble o21u�tc32o�me31 s. 2 � 3 � 2 4 4
31 � 52 � 51 6 64
1 2 1 4 2 3 3 2 6
2 � 3 � 1
3For problems 1–6, copy the table6below tahn12ed�sc23uamlcouflattheetpheropbraobbilaitbieilsityofotfheea3ch 3
4
� 1 Thinking Skill 6 possible outcome. For the last row, fin23d
3 six possible outcomes.
Predict

What do you 3 OAu,tcbolume23 e� P2 ro53bability 2 � 3 � 2 2
5 A, white 3 5 5
expect the sum3 of 3 � 4 � 3 � 2 3
the probabilitie5s 5 �15.5312�� 2 � 1 6 5 5 4
4 32 3
to be? 2 � 3 � 2 6 5 6
3 5 5

B, blue 2.

B, white 3.3 2 �
C, blue 3
5

4.

C, white 5.

sum of 6.
probabilities

Investigation 10 525

For problems 7–9 we will consider compound
experiment 2, which involves two draws from a
bag of marbles that contains four blue marbles
and two white marbles. The first part of the
experiment is that one marble is drawn from the
bag and is not replaced. The second part is that
a second marble is drawn from the marbles
remaining in the bag.

7. Model Copy and complete this tree diagram showing all possible
outcomes of the compound experiment:

Compound

4 1st Draw 1 2nd Draw Outcome 2
3
6 2B B, B

24

3 B6

1 1 � 2 1
6 2 3 3

1 W1
W3 e will calculate the probability of the ou6tcome blue, blue (B, B). On the first
1 marb32les 64,
2 draw four of the six are blue, so the probability of blue is which 4
eq32 uals 32. 1 2 4631 6
2 � 3 �

I4f the first marble drawn is blue, then thre2e blue
m6 arbles and two white marbles remain (s3ee

1 � 2 pbth31iluceteupmrreoab46aratb�brl53eiigl�iothynt52)o.tfhSteohsetehoceuoptnc31rdoobmdareabwbililtuiyseo,53f.bdTluhreaewirse16infogrea, 1
2 3 6
2 2 � 3 � 2
� 5 3 5 5

2 � 3 � 25. 4 � 3 � 2
3 5 6 5 5

1 � 2 � 1 8. Represent Copy an4d complete this table to show the probab2ility of
2 3 3 4 each remaining pos6sible outcome and2 the sum of the probab3ilties of
6 all outcomes. Remember that the firs3t draw changes the collection of

marbles in the bag for the second draw.

3 2 O� u35 t�co52me Probability 4 � 3 � 2
5 3 6 5 5
2 3 2 4 3 2
3 � 5 � 5 blue, blue 6 � 5 � 5

sum of
probabilities

9. Suppose we draw three marbles from the bag, one at a time and
without replacement. What is the probability of drawing three white
marbles? What is the probability of drawing three blue marbles?

526 Saxon Math Course 1

For problems 10–14, consider a compound experiment in which a nickel is
flipped and then a quarter is flipped.

10. Represent Create a tree diagram that shows all of the possible
outcomes of the compound experiment.

11. Represent Make a table that shows the probability of each possible
outcome.

Use the table you made in problem 11 to answer problems 12–14.

12. What is the probability that one of the coins shows “heads” and the
other coin shows “tails”?

13. What is the probability that at least one of the coins shows “heads”?

14. What is the probability that the nickel shows “heads” and the quarter
shows “tails”?

extensions Analyze For extensions a and b, consider experiment 2 in which a bag
contains 4 blue marbles and 2 white marbles. One marble is drawn from
the bag and not replaced, and then a second marble is drawn.

a. Find the probability that the two marbles drawn from the bag are
different colors.

b. Find the probability that the two marbles drawn from the bag are the
same color.

Analyze For extension1s c and d, consider experiment 1 involvin2g spinning
the spinner and then dr2awing a marble. 3

1 c. The compleme2nt of “A, blue” is “not A, blue”. Find the p4robability that
2 the compound3 outcome will not be “A, blue.” 6

d. Find the probabilit21y �th32at the compound outcome will not inc31lude “A”
and will not include “blue.”

1 � 2 e. The probabiliti31es in exercises c and d are different. Exp16lain why.
2 3

For extensions f acnudbega,21nc�do23ntsh�iedn13erflitphpeincgoma pqouuanrtdere.xperiment cons64 isting of
rolling a number

1 � 2 � 1 f. eRxeppererismenetntD. ra64w a tree diagram to show the sample sp23ace for the
2 3 3

3 2 � 3 � 2
3 5 5
g. Find the probabilit5y of each compound outcome.

3 2 � 3 � 2 4 � 3 � 2
5 3 5 5 6 5 5

Investigation 10 527

LESSON Ratio Problems Involving Totals

101

Power Up Building Power

facts Power Up H
mental
a. Number Sense: 20 ∙ 300
math
b. Number Sense: 920 − 550
problem
solving c. Percent: 25% of 100

d. DCaeclcimulaatlsio: n3: .7$518÷.919108+01fe$e5t.3�0 1 yar1d8 feet � 1 yard
e. 3 feet 1 3 feet

f. Number Sense: 40 × 25

g. Measurement: Which is greater: 1 liter or 500 milliliters?
h. Calculation: Find h1a16lf of 100, − 1,1126 , × 5, + 1, 2 , × 3, + 2, ÷ 2

The numbers in these boxes form number patterns. What one 123
number should be placed in both empty boxes to complete the 24
patterns? 39

New Concept Increasing Knowledge

Thinking Skill In some ratio problems a total is used as part of the calculation. Consider this
problem:
Model
The ratio of boys to girls in a class was 5 to 4. If there were 27 students
Use red and in the class, how many girls were there?
yellow counters
or buttons to We begin by drawing a ratio box. In addition to the categories of boys and
model the girls, we make a third row for the total number of students. We will use the
problem. letters b and g to represent the actual counts of boys and girls.

Ratio Actual Count
Boys 5 b
Girls 4 g
Total 9 27

528 Saxon Math Course 1

Math Language In the ratio column we add the ratio numbers for boys and girls and get
the ratio number 9 for the total. We were given 27 as the actual count of
A proportion is students. We will use two of the three rows from the ratio box to write a
a statement that proportion. We use the row we want to complete and the row that is
shows two ratios already complete. Since we are asked to find the actual number of girls, we
are equal. will use the “girls” row. And since we know both “total” numbers, we will also
use the “total” row. We solve the proportion below.

Ratio Actual Count

Boys 5 b

Girls 4 g 4  g 2  f
Total 9 27 9 27 7 175

9g = 4 ∙ 27

g = 12

We find that there were 12 girls in the class. If we had wanted to find the
number of boys, we would have used the “boys” row along with the “total”
row to write a proportion.

Example

The ratio of football players to band members on the football field was
2 to 5. Altogether, there were 175 football players and band members on
the football field. How many football players were on the field?

Solution

We use the information in the problem to make a table. We include a row for
the total. The ratio number for the total is 7.

Ratio Actual Count
f
Football Players 2 b

Band Members 5 175

Total 7

Next we write a proportion using two rows of the table. We are asked to find
the number of football players, so we use the “football players” row. We know
both totals, so we also use the “total” row. Then we solve the proportion.

Ratio Actual Count

Football Players 2 f g
Band Members 5 27
Total 7 b94  2  f
7 175

175 7f = 2 ∙ 175

f = 50

We find that there were 50 football players on the field.

Lesson 101 529