5th Grade Math student-ebook-course-11

* 25. Verify The numbers 2, 3, 5, 7, and 11 are prime numbers. The
(19) numbers 4, 6, 8, 9, 10, and 12 are not prime numbers, but they can be
formed by multiplying prime numbers.

4=2∙2
6=2∙3
8=2∙2∙2
Show how to form 9, 10, and 12 by multiplying prime numbers.

26. Write 75% as an unreduced fraction. Then write the fraction as a
(33, 35) decimal number.

1 1 2 122(574). Reduce: 22233
2 22355

28. Analyze Find the missing distance d in the equation below.

(43)

16.6 mi + d = 26.2 mi

3  5  15  3 3 Refer to the do1u705b0 le-line graph26b5elow to answer problems 29 and 30.
2 2 4 4

Daily High and Low Temperatures
16

12 high
low
Temper ature ( °C)
8

4

0

–4

–8 Mon. Tues. Wed. Thu. Fri. Sat.
Sun.

* 29. a. The difference between Tuesday’s high and low temperatures was
(18) how many degrees?

b. The difference between the lowest temperature of the week and the
highest temperature of the week was how many degrees?

* 30. Predict If the daily high temperature dropped 5 degrees the day after
(18) this graph was completed, what probably happened to the daily low
temperature? Explain.

336 Saxon Math Course 1

LESSON Prime Factorization
Division by Primes
65 Factor Trees

Power Up Building Power

facts Power Up H
mental
a. Number Sense: 5 × 60
math
b. Number Sense: 586 − 50

c. Calculation: 3 × 65

d. Calculation: $20.00 − $2.50

e. Number Sense: Double 75¢.

f. Number Sense: $75 1 1
100 10

g. Primes and Composites: Name the prime numbers between 10

and 20.

h. Calculation: 9 × 9, − 1, ÷ 2, + 2, ÷ 6, + 3, ÷ 10

problem Use the digits 6, 7, and 8 to complete this multiplication 23_
solving problem:
×_
166_

New Concepts Increasing Knowledge

prime Every whole number greater than 1 is either a prime number or a composite
factorization number. A prime number has only two factors (1 and itself ), while a
composite number has more than two factors. As we studied in Lesson 19,
Thinking Skill the numbers 2, 3, 5, and 7 are prime numbers. The numbers 4, 6, 8, and
9 are composite numbers. All composite numbers can be formed by
List multiplying prime numbers together.

What are all the 4=2∙2
factors of 4, 6, 8,
and 9? 6=2∙3

8=2∙2∙2

9=3∙3

When we write a composite number as a product of its prime factors,
we have written the prime factorization of the number. The prime
factorizations of 4, 6, 8, and 9 are shown above. Notice that if we had
written 8 as 2 ∙ 4 instead of 2 ∙ 2 ∙ 2, we would not have completed the
prime factorization of 8. Since the number 4 is not prime, we would complete
prime factorization by “breaking” 4 into its prime factors of 2 and 2.

Lesson 65 337

In this lesson we will show two methods for factoring a composite number,
division by primes and factor trees. We will use both methods to factor the
number 60.

division by To factor a number using division by primes, we write the number in a
primes division box and begin dividing by the smallest prime number that is a factor.
The smallest prime number is 2. Since 60 is divisible by 2, we divide 60 by 2
to get 30.

30 15 5 1
2 60 2 30 3 15 5 5
qu2ot6ie0nt Notic22e 30 3 15
Since 30 is also divisible by 2, we divide 30 by 2. The is 15. 60 2 30
how we “stack” the divisions. 2 60

30 22231350 5 1
2 60 3 15 5 5
2 60 2 30 3 15
is divisible by the n2ex6t-0smallest p22rim36e00
Although 15 is not divisible by 2, it by 3 produces the quotient 5.
number, which is 3. Fifteen divided

30 2 2 15 5 1
2 60 3 3 15 5 5
2 30 2 30 3 15
2 60 2 60 2 30

Five is a prime number. The only prime number tha2td6i0vides 5 is 5.

30 2 2 15 5 1
2 60 3 2 30 3 15 5 5
2 30 3 15
2 60 2 60 2 30
2 60

2 2 By dividing by prime numbers, we have found the prime factorization of 60.
3
60 = 2 ∙ 2 ∙ 3 ∙ 5

Example 1
Use division by primes to find the prime factorization of 36.

Solution

We begin by dividing 36 by its smallest prime-number factor, which is 2. We
continue dividing by prime numbers until the quotient is 1. 1

1
3 3
3 9
2 18
2 36

36 = 2 ∙ 2 ∙ 3 ∙ 3

1 Some people prefer to divide only until the quotient is a prime number. When using that
procedure, the final quotient is included in the prime factorization of the number.

338 Saxon Math Course 1

factor trees To make a factor tree for 60, we simply think of any two whole numbers
whose product is 60. Since 6 × 10 equals 60, we can use 6 and 10 as
the first two “branches” of the factor tree.

60

6 10

The numbers 6 and 10 are not prime numbers, so we continue the process
by factoring 6 into 2 ∙ 3 and by factoring 10 into 2 ∙ 5.

60

6 10

2 32 5

The circled numbers at the ends of the branches are all prime numbers. We
have completed the factor tree. We will arrange the factors in order from least
to greatest and write the prime factorization of 60.

60 = 2 ∙ 2 ∙ 3 ∙ 5

Example 2

Use a factor tree to find the prime factorization of 60. Use 4 and 15 as
the first branches.

Solution

Thinking Skill Some composite numbers can be divided into many different factor trees.
However, when the factor tree is completed, the same prime numbers appear
Connect at the ends of the branches.

What other whole 60
number pairs
could we use 4 15
as the first two
branches of a 2 23 5
factor tree for 60?
60 = 2 ∙ 2 ∙ 3 ∙ 5

Practice Set a. Classify Which of these numbers are composite numbers?
19, 20, 21, 22, 23

b. Write the prime factorization of each composite number in
problem a.

c. Represent Use a factor tree to find the prime factorization of 36.

d. Use division by primes to find the prime factorization of 48.

e. Write 125 as a product of prime factors.

6 1 6 1 2 2 3 Lesson 65 339
2 2 3 8

f. Generalize Write the prime factorization of 10, 100, 1000, and

10,000. What patterns do you see in the prime factorizations of

these numbers? 1

Written Practice Strengthening1Concepts 3 3
3 3 2 6
ar2e2a1 26of 2 12
1. The total land the world is about fifty-seven million2,f2iv4e hundred

(12) six thousand sq2ua2re4 miles. Use digits to write that numbe2r o4f8square

miles. 2 48

2. The African white rhinoceros can reach a height of about 56 1 feet. How 6 1 2
1 1 2 2 2
(15) many inches is 56 2 feet? 6 2 2 3 3 3
8 5

3. Jenny shot 10 free throws and made 6. What fraction of her shots did
(29, 42)
she make? What percent of her shots 1Tdhidenshwerim535teatkhee?prime35 fa1ctorization 8  3  1
* 4. oRf e4p0r.e2se n36t00 3 8
3 f38or 3840.
(65) a factor tr1e5e
Mak5e

2 30 3 15 5 5
n2u m60bers com22po36s00ite number32? 15
* 5. Classify Which of these is a 30

(65) A 21 B 31 C 41 2 60

1 2 * 6. Write 2 2 as an improper fraction. Then multiply the improper fraction
2 3 by 83. 3
6 2 (62) What is the product?

7. Four of the ten marbles in the bag are red. If one marble is drawn from
(58)
the bag, wh8a21t rati1o13exp2re61sses the probabili1ty tha61t the21mar1b5le34will mnot b2e18 4
red? 12 2
8  3  1 3
3 8 5

* 8. 8 1  811213  121361  2 1 11*2(691). 161122161  1215 3 15m342m81  2 1 4  2145n00 1
(61) 2 6 4 8 25

Find each unkno3wn number: 13 5 1 3138y 31
12316 1 1 61112211(61403). 1215 3 15m344 2m18 1 8 2451(412). 124n050 3
 2 6 12  4  2 8 8n   y
100 8

1  1  1 15 3 12m. 4312w2 81=43 0.0144 13 5 1243585 n 1 13. 183  1  y
12 6 2 4 (45) 8 100 8 8 3
(29)

13 5 13 5 1 1 14. Compare: 1  1  2  1 3 4 1
8 8 8 8 2 3 3 2 7 5 5
(56)
5 25
1 15. 11 − (31021.2+3120.4821)32  1 3 4 3 4 1 5 1 5 50
8 2  2 7 7 5 5 5
(38)

16. Explain What is the total cost of two dozen era5se2rs5 t5ha2t5are priced
(15, 41) at 50¢1 each1 if 8% sales tax is added? Describe 5aw50ay5to50perform the
cal5cu5latio5n 5mentally.
2132  1 3 4 3 4
2 7 7

3 4 117. 5 25 5 25
7 5 5(15) C5on5n0ec5t  5T0he store manager put $20.00 worth of quarters in the
5 25 change drawer. How many quarters are in $20.00?
5 *5018.
25 4

A pyramid w7ith a square ba25se has how many
(Inv. 6) 2a5. fac2e5s?
b7 . edg7es? 44
25 25

44 c. vertices?
25 25

340 Saxon Math Course 1

* 19. Use division by primes to find the prime factorization of 50.
(65) What is th12ena31me of32asi21x-sided polygon3?74How many vertices
Connect
* 20.
(60) does it have?

1  1 2  1 * 21. Write 3 4 as an improper fraction.
2 3 3 2 (62) 7

22. The area of a square is 36 square inches.
(38) a. What is the length of each side?

b. What is the perimeter of the square?

23. Write 16% as a reduced fraction.

(33)

24. How many millimeters long is the line segment below?
(7)

cm 1 2 3 4 5 6 7

25. Estimate A1$m0705eter is about 1 1 ya3rds5. A b5ou5t how many meters long is
(7) an automobile? 10 22 55 5

2

* 26. Write the prime factorization of 375 and of 1000. What method did
(65) you use?

27. Reduce: 3555
222555
(54)

28. Estimate The radius of the carousel is 15 feet. If the carousel turns
(47) around once, a person riding on the outer edge will travel how far?

Round the answer to the nearest foot. (Use 3.14 for π.) Describe how to
mentally check whether the answer2i1s0reasonabl1e0. 5 35
2 420 2 210 3 105 7
5 35
29. Eighty percent of the 20 answers were correct2. H4o2w0 many2a 2n1sw0 ers wer3e 105
(29, 33) correct? 2 420 2 210
2 420

30. Verify The pre2f1ix0“rect-” in1r0e5ctangle me3a5ns “right.” A r7ectangle is a1
“right-angle”2sh4a2p0e. Why2is 2e1v0ery squ3ar1e0a5lso a rec5ta ng35le? 7 7
(54)

2 420 2 210 3 105 5 35
2 420 2 210 3 105
2 420 2 210
2 420

Lesson 65 341

LESSON Multiplying Mixed Numbers

66

Power Up Build2in32g Power 2 2 2 2 10 2 yd 2 2 10 2
Power Up J 3 3 3 3 3
facts
mental 2 2 10 2 yd 2 2 10 2 2 1
3 3 3 3 2
math
a. Number Sense: 5 × 160
problem
solving b. Number Sense: 376 + 99

c. Calculation: 8 × 23

d. Calculation: $1.75 + $1.75

e. Fractional Parts: 1 of $60.00 $30
3 10
$30
f. Nu31mber Sense: 10

g. Measurement: Which is greater, 5 years or a decade?

Inh.thCisa12flicguulr12aetaiosnq: u8ar×e1a8120n, 32d−a124r,e÷gu2la, r+pe31n, 0t÷a32g3o,n+sh1a, r÷e 6, ÷ 2
a common

side. The area of the square is 25 square centimeters. What is

the perimeter of the pentagon?

New Concept Increasing Knowledge

Thinking Skill Recall from Lesson 57 the three steps to solving an arithmetic problem with
fractions.
Verify
Step 1: Put the problem into the correct shape (if it is not already).
How do we
write a mixed Step 2: Perform the operation indicated.
number as a
fraction? Step 3: Simplify the answer if possible.

Remember that putting fractions into the correct shape for adding and
subtracting means writing the fractions with common denominators. To
multiply or divide fractions, we do not need to use common denominators.
However, we must write the fractions in fraction form. This means we will
write mixed numbers and whole numbers as improper fractions. We write
a whole number as an improper fraction by making the whole number the
numerator of a fraction with a denominator of 1.

Example 1

A length of fabric was cut into 4 equal sections. Each of 4 students
2 2 fabric.1H0o32 wydmuch fab2r23ic 1b0e32fore c2u12t? 1
2 3 received 2 3 yd of was there it was 3 2

342 Saxon Math Course 1

2 2 2 2 10 2 yd 2 2
3 3 3 3

Solution

This is an equal groups problem. To find the original length of the fabric we
2 mult2ip32ly 2 4.1F0ir32syt2,d32we 2 234yind frac1ti0on32 2fo32rm. 1 2 1
2 3 2 3 yd by write 2 3 an1d0 2 2 10 3 3 2

2 2  4 2 2 2 2 8  4 8  4  32 32  10 2
3 3 3 3 1 3 1 3 3 3

Second, we multiply the numerators to find the numerator of the product,

and we multiply the denominators to find the denominator of the product.

2 2  4 2 2 2 2 8  4 1 8  4 $1300332 32  10 2
3 3 3 3 1 3 3 1 3 3

Third, we simplify the product by converting the improper fraction to a

1 mB2eixf3283oe$1rd3520e0nt14hu31em342fb32aebrr.ic42w2338as52c14u$112t334020it233w3212a26s010332322y60d 1023323262 8  4 8  4  32
long. 3 1 3 1 3
2 23322
4 2 3 1 1 1  3 1
2 3 2 23

3
10 2 2 1
3 2

121123421 reEav52as1lou01ant2332a34eb21leH?4326o012w ca2n60w21e3212u31s260e4123e32s3ti13matio21n2323toc3heck whe2th32er our answe8r is 4 8 
3  1 3
1 1 5 3
2 2  1 3 2 2 2 1  2 2 1 2
3 2 3 3
321522343443Exa2S6m0olpMFu2li31teru3221iso2lt231262t,0nipwlye41:3w23262ri12tet3h1213e$131332210n03223umb13e12r52sin234f32r83ac22t2321io14n 2f2o32r2325m. 234 83260 14111230030023620771553213326238231321410131523 32 32
1 152213432 3 3  1
 1 3 8 314  322132  2 1
3 3
2

 2 1 2  43RReecaadllinthga1Mt123a13th1 231 2 1STSpg5210rh21rkeio32212die32cr1dd2211to2ytcu32,hn234d1232hcwad34433itnt,1e31221ogiw30sf13s131a32emi2a0m3112ytrmi32expdlecueli2atdlf312at521ys132inp23nt215210t2glhu323y321l21eme212340bthpb2211y134o2321ere2n23434o2rt3232dsae122s632.032121uro243321g21mTc13rottishd. ia1lo432li21t0us6f032521as23ta3th212rwea52112ta323f334ebr211y126a1yt230cht3432o213te3243i21212o621cp30nrhre31seo3c2.cd2112t21kau2312218nc6t032h34gt3e521lo12e12f2rafe23323i12ta21s2634sb1a1oo2238nnn2334da32t216bh30133l3ee122,ngw21e21ris21de16s0.2323u218o32s43fe21322a33a212162128233432313212
3 3 3

the terms of a 1
2
fraction are the 7

numerator and
1 2the den2o122m43ina1to312r.
3 3  1 3

1 2
3

 123223 2 2 224323222310 2 y2d132122130322332y12231d24332
3 3

3 1  1 2 2 3  2 2  3 1
3 32 12 4 2
3
3  1 4

1d43$30 11 $30 $30 W5 he3a13slfkesqtc1uh23a3rtehse,1rae34nc2dta43angqlue2aarntedr estim2 ate3t12h3e12 area. There are 6 full squares,
square. Since 2 half squares equal a whole
10 3 2 32$1300 3 13013032 210 s2q243ua12re2, the area2is3a21 b3o21ut 3
1 3 8 4 square units.

1 11 1 2 2 3  1 3 Lesson 66 343
2 2 3 3 4
  10 10
1 10 2 2 22

10

2 3 2 322 3 32 3 2 23 32 6 32 263633 6466 33 664 2 3 6 3 23 3 3

 1 15  4 5  4 5  4 52260 4 2602601 12326260321 213133 6232 133231 431 2  3 1 1  112312  1 2 1 2  31 2  3 2 1  222312  2 2 3  1 233 
32 3 2 3 2 3 3 3 4 2 3 3 3 2 3
Practice Set
Multiply: 2 313321 12323231b3432. 113232 234431 43431 321 2c1. 3213123221 31332121 322 2 3232 121 232 233
1 3 1 12 1 2 21 3212 1
a. 1 2  1 2 32 2  3  3  23 2   1

 2 1 2  3 1 2  3 1 1  1 321 1 d1. 231 2  3 1 2  3 2 1 e2. 322 1  2 323  1 2 3  1f32. 3  1 3
3 3 4 3 4 2 2 3 3 2 2 3 4

g. 3 1  1 323 1 rea1s32o23n4313ablhe21.n322es34sof2th2e343p31r3o212d1u2c32ts3 313ini12.e2a12n3234d3h12 2by s2k34etch2ing 3 1 2  3 1
j. 3 3 2 2

Check the 3
rect3a13ngle1s33213ona1g23ri2d.43 4 3 122 1
 22  2 2   3 2

k. 3nFu13omrmbue1lra233tae31nd3Wa1rmi23t231ei433143xaendd21n1su23432om43lvbeear.2w2o43rd3p212ro2blem3 21ab2out 3m12ultiplying a whole

 1 232 3  2W2 34ritt2e2nP3r21a2ctic3e21 Strengthening Concepts
4

1. 3tFhifetyn1pu34emr3cbeenr to1of34fm3thuelti6p10l34e-qcuheositcioenqsu3oenstti1ohne34steo3snttahr1ee43mtesutlt.iple choice. Find

(29, 33)

2. An3alyze 1 i343sTwtheel1vr34eatoiof the 30 students in the class are boys.
a. What of boys to girls in the class?
(58)

3b.wIf1he34aat3cihsstht1ue34dpe3rnotb’sa1nb43ailmityethisapt liat cweidll in a hat and one name is drawn,
be the name of a girl?

1 3 3. Analyze Some railroad rails weigh 155 po2u32nds per 21yard2. 2H3223ow mu2c23h 10 2 yd 100  72
4 33-foot-long rail weigh? 1 2 3 100  7
(15) would a


1 1  2 231 1 122123213211211222123222232223132*231((1261(64721685)))2... 2231nT112u00h1222322m00e322321322sb3221ue2mr77232s25511?2o002f2320023f32iv11e0012177002n1223115521u1100m112000000(03277b52810029355e)23.2121rs7717725511i157755s11005520020023100030251113121.*2300(1776W1005776551111)51.553h1610051a21221200t77323i553s312113211t227721h15155232e51*6131(a619111v121)3.1300e551313r00212113161a14213112g2251e11323613277261001o1121556123002f233t512312h121131114e21127713255261513132615412411532323521331511114612125214110031241220012154561211541112321237751232215551412121125424111310031154005540015421141002543612112521127731154521412155177212155145212455461321145122
2 2

02  1772515  3 21111510000 331127755 1  311*1121(5160361). 3352111412 1233125 146154122111211(219).45543521142154122121 4 311(52214). 4  1 $30
03 6 5 5 1 2 10
2  1 1 1 a12 2
13. 0.25 ÷ 5 14. 5 ÷ 0.25 2 2  2
b

721 21212121%2121212121217*21212121111(((1(%36548657945521))))21.... 212121WI21aAfRV2112the12e21hbpr12a2rir21fteeye21iss21ep21ntWathe21721enh21b12ciUpc2%ilrhasso21e21o21dc2121bafoua2atsc21fha2112att21be211221cbao221b2tffoto2ot21Brlhl21totaera21wlea12aoei21nbnf2121b2tsg7o221wa75isf12e21¢(21i4n21rb21e%9,s21ad)2q21h2112tuot12ob21haw212epl21217tmrpoo212112rub21i%12mcleh7em2121a21w21f21C12s21%21a?o7cb17u2121t2721321ol%1221d12%21raai%szn12aid21xb21t2i1po747en112?n21%0oc%2132fi21l73s21210%.21721a12212121%b2 1 a21ab212b212 721%21
2

1
2

1  1 1  1 7 1 %
2 2 2 2 2

2 11  1 21a21b212
22 2
b

(15) cost?

344 Saxon Math Course 1

1 1 1 1 1(491).a21pS0b.ue20rv7ce5hn.aaIsfnet?dheosn21aelehsa-21ltfapxerracteenitsis7 equivalent to the decimal number
2 2 2 2 1 on a $10.00
  2 %, what is the sales tax

* 20. Analyze One side of a regular pentagon measures 0.8 meter. What is
(60) the perimeter of the regular pentagon?

21. Twenty minutes is what fraction of an hour?

(29)

22. The temperature dropped from 12°C to −8°C. This was a drop of how
(14) many degrees?

The bar graph below shows the weights of different types of cerealsWeight (in ounces)
packaged in the same size boxes. Refer to the graph to answer
problems 23–25.

Weight of Cereal
20

5557
15 2  2  2  5  5  5

10

5

0 Fruit and Flakes Puffed
Flakes

Type of Cereal

23. What is the range of the weights?

(Inv. 5)

24. What is the mean weight of the three types of cereal?

(Inv. 5)

* 25. Formulate Write a comparison word problem that relates to the graph,
(13) and then answer the problem.

* 26. Connect Use division by primes to find the prime factorization of 400.
(65)
27. Analyze Simon covered the floor of a square room with 144 square
(38) floor tiles. How many floor tiles were along each wall of the room?

28. Estimate The weight of a 1-kilogram object is about 2.2 pounds.
(46) A large man may weigh 100 kilograms. About how many pounds is

that?

29. Reduce: 5557
222555
(54)

* 30. Classify Which of these polygons is not a regular polygon?
(60)
ABCD

5557 Lesson 66 345
222555

LESSON $30 125
1000
67 Using Prime Factorization 100
to Reduce Fractions
Power Up
125  2  2 5  5  5 5  5
1000  2  5 
Building Power

facts Power Up J
mental
a. Number Sense: 5 × 260 111
math b. Number Sense: 341 − 50 5  5  5 1
c. Calculation: 3 × 48 2  2  2  5  5  5  8 125
1000
111 1
1
d. Calculation: $9.25 − 75¢ 375 5
5
e. Number Sense: Double $1.25. 1000

f. Number Sense: $30 125
100 1000

g. Measurement: Which is greater, 3 yards or 5 1f2e5e12t?5
h. Calculation: 6 × 6, − 1, + 1, ÷ 3, 1÷00120000
$30$30

÷ 5,1×001200,

problem Copy this problem and110f20il5l0inth2em2is5s2in5g5d5ig5its :5 _ _ _,_ _ _
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8 8

1 3
8 8

111 36
81
346 Saxon Math Course 1 111 875 48 125
3  5  5  5 130783050 1030705 4030 500
2  2  5  5
2   5 10005 81
1 1 5 1
1

2  3  521180705515018055710505  3 4403280 452410801551307050551  55102058351020583 36 36 3
2  28 130708501 81 8

48 P5152102r05a551cti55c1 e 5Set2833861 111 111 111
400 3  11 32eWar52cithe155f13tr0h7a05e0c551tpiorin5m1. eThf83aecntore38ridzuactieo13n0e705ao0cfhbofrtahctthioenn. 38umerator
2  2  1 and the denominator of

a. 875 48 875 5102b05. 48 36 125 36
1000 400 1000 400 81 500 81

875 48 875 c. 125 48 36 125 d. 36
1000 400 1000 500 S4t0re0ngthe1n780i1ng Cw5o0n0c21epts35 81
n 1 7 2
Written Practice  100 4 4  2 8 2 3  29

* 1. bAoflluligseroerniebnibsormibnabfkooirnn3tgfh13oearotlahc2reeg43aegnrca,os12lslya.agR1redi31boboffoayn2eb41clelooaswct1243hsri$sbc2b16e0o2a0n5n0eyfa.o12rSdrh.tehHenoe43swuendm,sua2cnhdyam34rdoysanreodyf

(66)

will Allis1on n1eed for ribb3on?3
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3 2.
4
(13)
1
2 7  w  1 35(433). n Ins4te41ad3o2f87div1iding2$321.502b9y 3$0.05, Marcus formed an
10 2 1V0e0rify

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42 proble4m. What is the equivalent division problem Marcus formed, and
3 the16q020u50o1t12ient? 3
3 1  2 4 1 1 w2h41at is 4
3 3

Find each unknown number:

4. 6 cm + k = 11 cm 5. 8g = 9.6
(3) 7 421((1444732)).
7 1 1n0 w 3 n 4241 9 7 2
6. 10  w  2 3 100  52 7 100 2 2 8 2 3  29
5 8 3
(43)  2 

* 8. lTehnegtph1e21orifmeeatcehr of a qu3adrilateral is 172 inches. What is the average
side? 4Can we know for certain what type of quadrilateral
(60, 64)

1 1 3 111t$n0377hA001031ins0a0ilsy.w0zw?2e034W−4h2121y(41$o4r65353w1.2713h785y+11n1n03n0o27$00031t149?.628w322) 344162101(142500530). 53(121378×10n02.3041) 625 7 2 2 29
2 4 9. (3*482,1416269). 2A78nalyze 8 3
−2 32(0.2412×0410090.32) 

7 1 (5) 2
10 2 3
 w  *35 11. 2  29

(63)

13. 3 1  2 3 1 1  323114  2 3 *1601(2605460). 1 1  2 1 625
3 4 3 4 3 4 1000
(59)

3 1  2 3 1113(455). 312.131444÷2 34601602050 1 1  2 1 16012(045690). $6.00 ÷ $0.15
3 4 3 4

17. Five dollars was divid1e12d evenly amon3g 4 people. How much money did
3
(15) e1a12ch receive? 4 4

1 1 3 1 1 3
2 4 2 4

1 1 3 1 1 3
2 4 2 4

Lesson 67 347

5 100 48 3

7  w  1 3 1(6180n0). 0isCiotnscplued4reim41 eTthee2r3?78a31rWeah3ao231tf43ias2rt32eh2ge34unla2a1rm139qeuoa1df213tr41hilaeteq2ru41aal dis1r6i0l12a0500te01r6a0s20ql5?0uare
10 2 5
inches. What

1 3 * 19. 41rWWedrh4iutae41ct etish1e6t02h201p578e700r.iamreeawfaoc2ftt23oh21reizrae2t35ciot9nans1gon0lef06s2h5owanndb4oe41flo1w02?0087. Then
3 4 1 (67)2
7 3  2 1 3 2
10  1 3
w 2 3 1n0(*3012, 606). 2  29
5 

1 1 in.
2

1 3 1 1 625 3 1 1212 3 1 1 3 2 1 625
3 4 3 4 1000 3 4 3 4 10003
3  2 1  2 4 4 in.

1 1 3
2 4

1 1 3 21. Thirty-six of the 88 piano1k12eys are black. What fraction of the piano
2 4 keys are black?
(29)

* 22. Represent Draw a rectangular prism. Begin by drawing two congruent
(Inv. 6) rectangles.

1 1 3 * 23. Analyze 1 1 × =1 3
2 4 2 4
(30, 62)

24. There are 1000 meters in a kilometer. How many meters are in
(15) 2.5 kilometers?

25. Connect Which arrow could be pointing to 0.1 on the number line?

(50)

A BC D

–1 0 1

26. Estimate If the tip of the minute hand is 6 inches from the center of the
(47)
clock, how far does the tip travel in one hour? Round the answer to the
1 1 nearest inch. (Use 3.14 for π.)
2

27. Connect A basketball is an example of what geometric solid?

(Inv. 6)

1 1 28. Write 51% as a fraction. Then write the fraction as a decimal
2 (33, 35) number.

* 29. Represent What is the probability of rolling
(19, 58) a prime number with one toss of a number

cube?

* 30. Conclude This quadrilateral has one pair
(64) of parallel sides. What kind of quadrilateral
is it?

348 Saxon Math Course 1

LESSON Dividing Mixed Numbers

68

Power Up Building Power

facts Power Up I
mental
a. Number Sense: 5 × 80
math
b. Number Sense: 275 + 1500
problem
solving c. Calculation: 7 × 42

d. Calculation: $5.75 + 50¢

e. Fractional Parts: 1 of $48.00 $120
4 10

f. Nu14mber Sense: $120
10

g. Measurement: Which is greater, 1 meter or 100 millimeters?

h. Calculation: g7r×ay388s2,o23–c14k1s, ,4÷w5h,it×e s2o,83c–ks1,,14a÷nd3,b−lac8k socks in a drawer. In
Megan2h32as m4 any
the dark she pulled out two socks that did not match. How many more socks

does Megan need to pull from the drawer to be certain to have a matching

pair?

New Concept Increasing Knowledge

Recall the three steps to solving an arithmetic problem with fractions.

Step 1: Put the problem into the correct shape (if it is not already).

Step 2: Perform the operation indicated.

Step 3: Simplify the answer if possible.

In this lesson we will practice dividing mixed numbers. Recall from Lesson 66
that the correct shape for multiplying and dividing fractions is fraction form.
So when dividing, we first write any mixed numbers or whole numbers as
improper fractions.

Example 1

Shaw2n23a is pouring 2 2 cups of plan14t food into equ2a14l amounts to feed
3
4 plants. How much plant food is there for each plant?

Lesson 68 349

1 $120
4 10
Solution

Shawna is dividing 2 2 cups of plan2t f32ood into four 41equal groups. W2e14 divide 2 2 2 2
3 3 3
by 4. We write the numbers as improper fractions.

2 2  4 8  4
3 3 1

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3

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1 of 2 2 31e.o31fG2oe52fne2r25alize Wh31yoisf 2d52iv13idoifn2g52b31y2o324ft2he25 same as2m23 ultiplying by 14? 2 1
3 5 4

1 of 325250 S31aoxfo2n25Math Course 1
3

23 22 4

24 m 12 5 3  1 3 1 1 1 8 1 1 1  2 2
200 8 16 4 2 4 2 2 3

131121702241312111381453335w01121224533234312131s73800211217n031211423125332241117n1121220173n03261242224204312111211475124231211021210n351333241874212313350031211n1242315332011124213420024223431412111232420nW1211232112742270012423121120r742112135340043311121i3221322t23531433ntn3212431me13112n14221238112341m124222n320353413w010412113212424212700142200212110P1324m45217w0001114231m385r024311211w012111211a38n13413325302312213711c05n14321mw1((0*311t325w3821012F01**i*,5,11111422183((((((((22402c3i666545161112014n22836540611876488935555721h1n0211ef31j))))))))))d..........714756...50w10121243118m13e3111212eBuTaiI2WWwpG387415W14321m100s1n214a3qns5he212113034352313181i1121ia6lrh13241mhdt3cudsdlueri121b6h23nta145aeh21iaragexar1431ga=117145t1tS?l18il5a5lwtuel1242?w0n311211a1021yt21gi4221i234118y1?tsm0s38h31311nl830u4r,021033254331a65121232211012a214weeh0k71431353gtwt.em0384175h3h1n43a0nh1ef12phe7ede81sego341a123r113421ma1oe51si242wtila212ddmft31h112tf421s233112nr3121111Y13ni411m6f7ea83ef6s1e0rfwv4333235171431043mhnahaen0174532131124283i11475ro26fl0521o0creiauewa0184121on1132i1n18e0n7145tui38mc0lfa*ginni1212rcon38rn18t422ov1aecsbon111h83(1n5C1123w6e112a0ste13421me3111213r1422e7634121r1ts1w2311341283ri0d0ooe10o2)1rz.s1234253133ca42b21212312:1200o—fcna4431.1oge0f833ta5tciH1612remtnai1ten2113owe18115h?21nn3oiw17450sd1242i1np12ene138hgw31081h3s2111223t1242ue6oal72d13se00tnt4m12ou1501ihet83123114321m1338stfro*12tr81sah211t11231((211(31124313121hes62t54ca83gna591a8921fee12i213112114ann313i)))yt1312..1...l6fn1212c1353143233tpsoi3211a523iys311121w14175124231121112341m0en12321u12312121321rnfh-03843mo3112123534331021481c21321335344m2112f21d0e12231b12i1jh343351ve311121013ei4223s212en12eoc81t4523133313211p12121130scw52123sft83117w4220s3411224*1s0e5p02312hw311211833121110ie13211e024.112s12sn2321112.13241mo31e38(70143523337ec6343323156aI0d104Tsi242812ft17n3no1n131475h)013h.h211oltn2321n31d21ao71ts123118es12131e0nhd1311tn.224n12425211242?nwens0321312d11gHe06112211833124n21.r0a70i76a21te0v12421o3813241m012427415aH21wn234132122cn0di05w1244n12213211124d1281d221320s21o0h3122o0u1218d4e14220w11c32mtpt22130shn31112114n121re1230135r3aaw13me0h1o13251334316141c142238n1242021311i2j232p21a2132210s1475ie0ky421n412012n0rcs181tc3o1.p38yi—t22423mhd?3121o1311212sse121u1iie7111ens12321234ms03c3416c32t321412ts21o14321m113417512431m831on31234m1212231181121213f211nd315sw14321m01s38112421012112255w0w01014121243111058312341m38w13421m001021s32122112121838321501221w1011213s38130112131111132165235ww011011114753

1 3 1 3 16. (3.2 + 1) − (0.6 × 7) 17. 12.5 ÷ 0.4
4 4 (53) s
1 3 (49)
4
* 18. Analyze The product 3.2 × 10 equals which of the following?
(52)
A 32 ÷ 10 B 320 ÷ 10 C 0.32 ÷ 10

19. Estimate Find the sum of 6416, 5734, and 4912 to the nearest
(16) thousand.
s

s 20. Verify Instead of dividing 800 by 24, Arturo formed an equivalent s
(43) division problem by dividing both the dividend and the divisor by 8.

Then he quickly fosund thesquotientsof the equivalent problem. What is

the equivalent problem Arturo forsmed, and what is the quotient? Write

the quotient as a mixed number.

1  4 1 4 1  3
3 2 2
Lesson 68 351

21. The perimeter of a square is 2.4 meters.
(38) a. How long is each side of the square?

b. What is the area of the square?

22. What is the tax on an $18,000 car if the tax rate is 8%?

(41)

23. Analyze If the probability of an event occurring is 1 chance in a million,
(58) then what is the probability of the event not occurring?

24. Classify Why is a circle not a polygon?
(60)

* 25. Analyze Compa31re: 31421 4 1 4 1 4 213  3
2 2
(66, 68) Estimate Use a ruler to find the length of31this 4lin12e segme4nt12to t3he
nearest eighth of an inch.
26.

(17)

27. Conclude Which angle in this figure is an obtuse angle?

(28)

1  4 1 4 1  3 X
3 2 2

 4 1 4 1  3 WM Y
2 2
28. Write 3% as a fraction. Then write the fraction as a decimal
(33, 35) number.

29. Connect A shoe box is an example of what geometric solid?

(Inv. 6)

30. Sunrise occurred at 6:20 a.m., and sunset occurred at 5:45 p.m.
(32) How many hours and minutes were there from sunrise to sunset?

Early Finishers Each 4 by 4 grid below is divided into 2 congruent sections.

Choose A Strategy

Find four ways to divide a 4 by 4 grid into 4 congruent sections.

352 Saxon Math Course 1

LESSON Lengths of Segments
Complementary and
69 Supplementary Angles

Power Up Building Power

facts Power Up J
mental
a. Number Sense: 5 × 180
math
b. Number Sense: 530 − 50

c. Calculation: 6 × 44

d. Calculation: $6.00 − $1.75

e. Number Sense: Double $1.75.

f. Number Sense: $120 7 1
100 2

g. Measurement: Which is greater, 36 inches or 1 yard?

h. Calculation: 6 × 5, + 2, ÷ 4, × 3, ÷ 4, − 2, ÷ 2, ÷ 2

problem Nathan used a one-yard length of string to form a rectangle that was
solving twice as long as it was wide. What was the area that was enclosed by the
string?

New Concepts Increasing Knowledge

lengths of Letters are often us$e12d0 toordaesseiggnmaete7n12tp.oBinetlos.wRweceasllhtohwat we may use two points
segments to identify a line, a r1a00y, a line that passes

through points A and B. This line may be referred to as line AB or line BA. We
may abbreviate line AB as A·B. A¡B A·B A·ABB
Reading Math
AB
We can use
symbols to

designate The ray that begins at point A and passes through point B is ray AB, which may

lines, rays, and baA·neBdaBbbisresveiagtmedenA¡tBAA·.BBT(hoer speoBgrtAmioennA·otBfBA¡lAiBn)e, wAhBicbhectwaAneBebA·neBaanbdbrienvcilautdeWidnXgApBo(ionrtsBAA). XY
In thA·eBA¡fiBguWrA·eXBbelow wABeA·BcanXAYiBdentifyWthAXreBe sWWeYgXmentsX: YWX, XY, and WXYY. ThWeY WX
segments: leAnBgth of WAABBX pluWs Xthe lenXWWgYtXXh of XY equaWlXXsYYYthe leWnYgth of WWYY.
WY
A¡B A·B A·¡A¡A·A·BBBB== lineA¡ABA·BB AAA·A·A¡BBBBB
A¡·A·BB A¡B rA·ayBAB
A·B
AB = segment AWBX BA XY WY
W BA X Y

BA BA BA
BBAA

Lesson 69 353

Example 1

In this figure the length of LM is 4 cm, and the length of LN is 9 cm. What

is theLMlength oLMf MN?LN LN MN MLMN LN MN

LM N

Solution

The leLnMgth of LM pluLsNthe lenLgNtLhMof MN equaMlLsLMNtNhe length of LMNN. With the MN
information in the problem, we can write the equation shown below, where
the letter l stands for the unknown length:

4 cm + l = 9 cm
Since 4 cm plus 5 cm equals 9LcMm, we find thaLtNthe length of MN is 5 cm.

complementary Complementary angles are two angles whose measures total 90º. In the
and
figure on the left below, ∠PQR and ∠RQS are complementary angles. In the
supplementary figure on the right, ∠A and ∠B are complementary angles.
angles

SA

Thinking Skill R 60°

Verify P QB 30°

Can an angle that C
is complementary
be an obtuse We say that ∠A is the complement of ∠B and that ∠B is the complement
angle? Explain. of ∠A.

Supplementary angles are two angles whose measures total 180º. Below,

∠1 and ∠2 are supplementary, and ∠A and ∠B are supplementary. So ∠A
is the supplement of ∠B, and ∠B is the supplement of ∠A.

21 B A
75°
105 ° 105 °
75°
C D

Example 2 R

In the figure at right, ∠RWT is a right angle. QW S
a. Which angle is the supplement of ∠RWS?
b. Which angle is the complement of ∠RWS?

T

Solution

a. Supplementary angles total 180º. Angle QWS is 180º because it forms a
line. So the angle that is the supplement of ∠RWS is ∠QWR (or ∠RWQ).

b. Complementary angles total 90º. Angle RWT is 90º because it is a right
angle. So the complement of ∠RWS is ∠SWT (or ∠TWS).

354 Saxon Math Course 1

Practice Set a. In this figure the length of AC is 60 mm anBAdCCthe length of ABBC is 26 mm. AB
FinBdCthe length of AB.
AC

A BC

b. The complement of a 60º a1ngle is an angl1e1 that measures1how many
8 28 2
1 deg1rees?
82

c. The supplement of a 60º angle is an angle that measures how many

degrees?

d. Conclude If two angles are supplementary, can they both be acute?
Why or why not?

e. Name two angles in the figure at right that 3
appear to be supplementary.
1
f. Name two angles that appear to be 2
complementary.

Written Practice Strengthening Concepts

45
* 1. Model Draw a pair of parallel lAinCes. Then d7r2awBaCsecond pair AofBpAaCrallel
(28, 64) lines that are perpendicular to the first pair. Trace the quadrilateral that is

formed by the intersecting pairs of lines. What kind of quadrilateral did
you trace?

2. Connect What is the quotient if18the dividendRSis 1 and the divisor is 18?
2
(54)

3. The highest weather temperature recorded was 136ºF in Africa. The
(14) lowest was −129°F in Antarctica. How many degrees difference is there

between45these te4m5peratures?
4. Estimate72 A dolla7r2bill is about 6 inches long. Placed end to end, about
(15) how many feet would 1000 dollar bills reach?

* 5. Write the prime factorization of both the numerator and the denominator
(67) frRaSc74ti52on.
of this ThReSn reduce the fraction.
45
72

* 6. Conclude In quadrilateral QRST, which segment appears to be
(64) parallel to RS? 12345 1
12345 3 2  2

Q RS R

2 w  1 8  n 1 2  2
5 25 100 3
T S

7. In 10 days Juana saved $27.50. On average, how much did she save
(13) per day?
1  2  31  42  53  4  5 312158 3 5
1  2  31  42  53  4  5 3 1  2 3 2 4  1 8 m  1 3 m
2 4 4

Lesson 69 355

5 1 2 3331244234 55 5 523w21  1243m11584328552w5183n010 1m2328512341n04305 3 43
5 1 2 8 8f 2
 1 2311 321 152 0342.20.4328 f1315 2.4
 0.08

w1 8  n 1*32(85). 21111  222211333322232444433115555544 11 55 0222.0.48 3333(2112691).44 32212343455211348585 1 5 3 1  2 3 mm158 11m3443155433883 5 3 m1
25 100 8 2 4 8

 11133n05212210w223222134431331322113448585 228155585111n02022F3211((i36n2003))d.. 3313e52m52ma11512wwc23h4411u52m211n4343w243k55n02o.150.5w411438383885nn2288u2555m3238be2352118r5n0n0121w:0015121n0340m431143011((232325413.1620.))584..8ff11342228435323131f 583 1 m  1 3 43 538 f  1 3  f 
3 4 3 4

2n 22 3232 211123321551 1251 0022..0.0.4488 022.230.48 1 1 2.4
100 5 0.08

n 5211w3223 12123  2 22853223  152211n0w2351510*11((1641648915)).. 1022.230..448 202825.0.48 n 2 2  1 21  2 *02.1(0.65468). 2 2  1 1 2.4
100 2  0.08 100 3 35 3 5 0.08

17. a. What is the perimeter of this square? 2.5 m

(38)

b. What is the area of this square?

* 18. Explain How can you determine whether a counting number is a
(65) composite number?

* 19. Represent Make a factor tree to find the prime factorization of 250.
(65)
20. A stop sign has the shape of an eight-sided polygon. What is the name
(60) of an eight-sided polygon?

21. There were 15 boys and 12 girls in the class.
(29) a. What fraction of the class was made up of girls?

b. What was the ratio of boys to girls in the class?

22. Verify Instead of4d21ividing 4 1 by 1 12, Carla 1do21 uble2d21 both n2um12 bers before
2
(43) dividing mentally. What was Carla’s mental division pro4b21lem and its
quotient?
1 1 2 1
2 2

(3402,21632). What is th1e21reciprocal of 2 21? 4 1 1 1 2 1
WX WX 2 2 2

XY XY WY WY
24. There are 1000 grams in 1 kilogram. How many grams are in 2.25
(15) kilograms?
WX XY WY

4 1 W2X(57). H14 2112ow manyXYmilli21m211241eters 4loW12nYg is 2th12e lin4eW12b1Xe12low? 1X21Y2 1 2W21Y
2 2
1
4
cm 1 2 3 4
1
4

*1 26. WCXonnect The leXnYgth of WX is 5W3YmmW.41 TXXhYe length of XYWisY35 mm. WWhaYt
iXsYthe length of WY?
WX 4 (69)

W XY

1 11
14 44
4

356 Saxon Math Course 1

27. Represent Draw a cylinder. WX XY WY

(Inv. 6)

28. Arrange these numbers in order from least to greatest:

(50)

0.1, 1, –1, 0

29. Represent Draw a circle and shade 1 of it. What percent of the circle is
(33) shaded? 4

30. How many smaller cubes are in the large cube shown below?

(Inv. 6)

Early Finishers Taylor and her friends at school decided to make ribbons for their classmates

Real-World to wear for spirit week. Taylor’s mother offered to buy two rolls of ribbon. If
Application r$1i1b020b0on 1
each roll of ribbon is 25 yards in length and each is cut to 7 2 inches

long, how many ribbons can Taylor and her friends make to give away at

school? Show your work. Hint: 1 yard = 36 inches.

$120 $120$120 7 1 7 1 7 1
100 100 100 2 2 2

Lesson 69 357

LESSON Reducing Fractions
Before Multiplying
70

Power Up Building Power

facts Power Up G
mental
a. Number Sense: 5 × 280
math
b. Number Sense: 476 + 99
1
3 c. Calculation: 3 × 54

d. Calculation: $4.50 + $1.75

e. Fractional Parts: 1 of $90.00 $250
3 10

f. Number Sense: $250 $250
10 10

g. Geometry: A square has a perimeter of 24 cm. What is the length

of the sides of the square?

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

problem The Crunch-O’s cereal company makes two Top 2 in.
solving different cereal boxes. One is family size (12 in.
high, 9 in. long, 2 in. wide) and the other is Left Side
single-serving size (5 in. high, 3 in. long, 1 in. 12 in. Right SideFront1B2aicnk. 12 in.
wide). Each of their boxes is made out of one
piece of cardboard. To the right is a net of the Bottom 9 in.
family size box. Use this diagram to draw a net 9 in.
for the sin2gle-serving box.
3  2  6 6 3 2 6 6
5 3 15 15 5 5 3 15 15
 

 6 6 New Con25cept Increasing Knowledge
15 15

1 Before two or more fractions are multiplied, we might be able to reduce the

T53hin32k1 ing52Skill fraction terms, even if the reducing involves different fractions. For example1,
numerat53or 2 2
in the multiplication below we see that the number 3 appears as a 3  5
and as a denominator in different fractions. 22 2
 2 Connect 55 5 1
5 5353323216156553  13261565r1e6d5uces165to
Sometimes we
c3an reduce the
n3umerators and We may reduce the common terms (the 3s) before multiplying. We reduce 3
both 3s by 3. Then we multiply the remaining terms. 3
5 1 the deno5minators to 1 by dividing
6  5 of both fr5actions. 1

Reduce the 1
11 3 2 2
following: 5  3  5
535332325252
4  3 11 1
9 8
1 1 1 By reducing before we multiply, we avoid the need to reduce after we 4  3
5 1 1 1 9 1 5 9 8
6  5  6  multiply. Reducing before multiply3ing is also known as canceling.

1 33 3
33

10  56358 S1a50xon Math Cour21se 1 6 2
9 9 3

43

Example 1

Simplify: 5  1 5 1
6 5 5 1

Solution 5  1 5 1
6 5 5 1

5 dWreemen51roaeimndiiunncgae56t56t1oebrr,emwf5551o51ser.erewd61eucmeu55lt1itp19oly11. Sb1yin15dceivi5dianp11gpbeoatrhs as a numerator and as a the
6 5s by 5. Then we multiply

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3 9

6 6
9 9

66
99

2
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9
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Lesson 70 359

2 1  4 2 1  4 12211424123 12  2 32313112223143213  2 1 3 1  2 1
4 4 4 3 4

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360 Saxon Math Course 1

15. Verify The division problem 1.5 ÷ 0.06 is equivalent to which of the
(49) following?

A 15 ÷ 6 B 150 ÷ 6 C 150 ÷ 60

16. There are 1000 milliliters in 1 liter. How many milliliters are in 3.8 liters?

(39)

Find each unknown number: 32m431ƒ65
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100 2101200  n  1ƒ  4  6

20. A pyramid with a triangular base has how many
(60,
Inv. 6) a. faces?

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 1

Write the numbers in fraction form. Then reduce before multiplying.

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3 5 9 9 to 5 9 3 2
1   1 2 (70)
23–25.
grap12h below answer problems

John’s Waking Pulse

70 2 5 1 1 2 2
3 6 8 2 3 3
2100  102 683  4 7  2  n  1 m  1 ƒ
Beats per Minute
66

64

1 2  1 1 6298  2 2 1
3 5 3 2

0
Sun. Mon. Tues. Wed. Thu. Fri. Sat.

23. When John woke on Saturday, his pulse was how many beats per
(18) minute more than it was on Tuesday?

24. On Monday John took his pulse for 3 minutes before marking the graph.
(18) How many times did his heart beat in those 3 minutes?

25. Formulate Write a question that relates to the graph and answer the
(18) question.

* 26. Analyze Write the prime factorization of both the numerator and the
(67) denominator of this fraction. Then reduce the fraction.
72
300

72
300 AB BC DC BD

AB BC DC BD
Lesson 70 361

Analyze In rectangle ABCD the length of AB is 2.5 cm, aBnAdCBthe length ofDBCC BDDC

is 1.5 cm. Use this information and the figure below to answer

problems 27–30. 72 72 72 72

300A 300 300 B 300

72 ABD AB BACB C BACB DBC DBC BDDC BDDC BD
300
27. What is the perimeter of this rectangle? 11
(8) 11
3 a49  83b
28. What is the area of this rectangle? 4  3 a94  8 b 32
9 8
(31) 32

* 29. Name twAoBsegments peBrpCendicular to DC. BD
(64)

BC DC * 30. If BD were drawn on the figure to divide the rectangle into two equal
(31) parts, what would be the area of each part?

Early Finishers 1 1 1 11 1 1 1

Real-World Roland went to the local S94uper83Sto94reye83sta94e49rda83y83. bHa94e49bo83u83gabh49t an83ebwap49aint83rboller
Application and roller pan for $8.97, a gallon of milk for3$2.829, a3 mag2 az3ine 2for $31.592, and

11 two identical gallons of paint without marked prices. He paid a total of $47.83

a49  83b before tax. Find the price for each gallon of paint.
32 11
4  3
9 8 a49  83b
32

362 Saxon Math Course 1

INVESTIGATION 7

Focus on
The Coordinate Plane

By drawing two number lines perpendicular to each other and by extending
the unit marks, we can create a grid called a coordinate plane.

y

(–3, 2) 6 (3, 2)
5
4 123456 x
3
2 (3, –2)
1 origin
(0, 0)
–6 –5 –4 –3 –2 –1–1

(–3, –2) –2
–3

–4

–5

–6

Thinking Skill The point at which the number lines intersect is called the origin. The
horizontal number line is called the x-axis, and the vertical number line is
Explain called the y-axis. We graph a point by marking a dot at the location of the
point. We can name the location of any point on this coordinate plane with
On the coordinate two numbers. The numbers that tell the location of a point are called the
plane, where will coordinates of the point.
a point whose
ordered pair The coordinates of a point are written as an ordered pair of numbers in
contains two parentheses; for example, (3, −2). The first number is the x-coordinate. It
negative numbers
be located? shows the horizontal �( )� direction and distance from the origin. The second
number, the y-coordinate, shows the vertical �( )� direction and distance

from the origin. The sign of the coordinate shows the direction. Positive
coordinates are to the right or up, and negative coordinates are to the left or
down.

Look at the coordinate plane above. To graph (3, −2), we begin at the origin
and move three units to the right along the x-axis. From there we move down
two units and mark a dot. We may label the point we graphed (3, −2).

On the coordinate plane, we also have graphed three other points and
identified their coordinates. Notice that each pair of coordinates is different
and designates a unique point:

(3, −2)

(3, 2)

(−3, 2)

(−3, −2)

Investigation 7 363

Thinking Skill Refer to the coordinate plane below to answer problems 1–6.

Conclude y

If you connected 6
the points in
alphabetical 5
order (start with
AB and end C4 B
with HA), what
type of polygon 3
would you
make? D2 A

1

–6 –5 –4 –3 –2 –1–10 1 2 3 4 5 6 x

E –2 H

F –4 G

–5
–6

Visit www. 1. What are the coordinates of point A?
SaxonPublishers.
com/ActivitiesC1 2. Which point has the coordinates (−1, 3)?
for a graphing
calculator activity. 3. What are the coordinates of point E?

4. Which point has the coordinates (1, −3)?

5. What are the coordinates of point D?

6. Which point has the coordinates (3, −1)?

The coordinate plane is useful in many fields of mathematics, including
algebra and geometry.

In the next section of this investigation we will designate points on the plane
as vertices of rectangles. Then we will calculate the perimeter and area of
each rectangle.

Suppose we are told that the vertices of a rectangle are located at (3, 2),
(−1, 2), (−1, −1), and (3, −1). We graph the points and then draw segments
between the points to draw the rectangle.

y

(–1, 2) 6 (3, 2)
5
4
3

1

–6 –5 –4 –3 –2 0 12 456 x

(–1, –1) –2 (3, –1)

–3
–4
–5
–6

364 Saxon Math Course 1

We see that the rectangle is four units long and three units wide. Adding
the lengths of the four sides, we find that the perimeter is 14 units. To find
the area, we can count the unit squares within the rectangle. There are
three rows of four squares, so the area of the rectangle is 3 × 4, which is
12 square units.

Use graph paper or Investigation Activity 15 to create a coordinate plane.
Use the coordinate plane for the exercises that follow.

7. Represent The vertices of a rectangle are located at (−2, −1), (2, −1),
(2, 3), and (−2, 3).
a. Graph the rectangle. What do we call this special type of rectangle?

b. What is the perimeter of the rectangle?

c. What is the area of the rectangle?

8. Represent The vertices of a rectangle are located at (−4, 2), (0, 2),
(0, 0), and (−4, 0).
a. Graph the rectangle. Notice that one vertex is located at (0, 0). What
is the name for this point on the coordinate plane?

b. What is the perimeter of the rectangle?

c. What is the area of the rectangle?

9. Three vertices of a rectangle are located at (3, 1), (−2, 1), and (−2, −3).
a. Graph the rectangle. What are the coordinates of the fourth vertex?

b. What is the perimeter of the rectangle?

c. What is the area of the rectangle?

As the following activity illustrates, we can use coordinates to give directions
for making a drawing.
Activity

Drawing on the Coordinate Plane

Materials needed:
• 4 copies of Investigation Activity 15

10. Verify Christy made a drawing on a coordinate plane as shown on the
next page. Then she wrote directions for making the drawing. Follow
Christy’s directions to make a similar drawing on your coordinate plane.
The coordinates of the vertices are listed in order, as in a “dot-to-dot”
drawing.

Investigation 7 365

y
x

Christy’s Directions
On your coordinate plane, draw segments to connect the following points in
order:

a. (−1, −2) b. (−1, −3) c. (−112, −5) d. (−121, −6)
g. (−2, −9 21) h. (−2, −10)
e. (−1, −8) f. (−1, −8 21) k. (1, −8 12) l. (1, −8)
i. (2, −10) j. (2, −9 12) p. (1, −2)
m. (112, −6) n. (121, −5) o. (1, −3)

Lift your pencil and restart:

a. (−2 12, 4) b. (2 12, 4) c. (5, −2)

d. (−5, −2) e. (−2 12, 4)

11. Conclude Carlos wrote the following directions for a drawing. Follow
his directions to make the drawing on your own paper. Draw segments
to connect the following points in order:

a. (−9, 0) b. (6, −1) c. (8, 0)
e. (6, 12) f. (6, −1)
d. (7, 1) h. (10, −2) i. (7, 1)
k. (−10 21, 3) l. (−11, 2)
g. (9, −2 12) n. (−10, −121) o. (9, −2 12)
j. (6, 121) q. (−7, −8) r. (−10, −8)
m. (−10 12, 0)
p. (−3, −3 12)
s. (−9, −121)

366 Saxon Math Course 1

Lift your pencil and restart:

a. (−10 21, 0) b. (−11, −12) c. (−12, 12)
d. (−1121, 1) e. (−12, 112) f. (−1121, 2)
g. (−12, 2 21) h. (−11, 3 21) i. (−10 21, 3)
j. (−1121, 8) k. (−9 12, 8) l. (−7, 3)
m. (−6, 2 12) n. (−7, 3)
o. (−6, 5)
p. (−4, 5) q. (−1, 2)

12. Model On a coordinate plane, make a straight-segment drawing.
Then write directions for making the drawing by listing the coordinates
of the vertices in “dot-to-dot” order. Trade directions with another
student, and try to make each other’s drawings.

extensions a. Represent Use whole numbers, y C
fractions, and mixed numbers to write D
the coordinates for each point. 4
E
3
B
2

1 F

A

0 1 2 3 4x

b. Represent Use the given coordinates y D
to identify the point at each location. 6C A
Express the coordinates as whole
numbers or decimal numbers. 5 E

4

3

2B

1

0 F
1 2 3 4 5 6x

c. Generalize Graph these points on a coordinate graph. Then connect the
points.

(4, 2), (6, 2), (2, 4), (8, 4), (4, 6), (6, 6)

• What polygon did you form?

• Name a set of points that when connected would form a hexagon
inside the hexagon you drew.

Investigation 7 367

LESSON Parallelograms

71

Power Up Building Power 120  1.2 64
Power Up D f 224
facts
mental a. Number Sense: 5 × 480

math b. Number Sense: 367 − 99

c. Calculation: 8 × 43

d. Calculation: $10.00 − $8.75

e. Number Sense: Double $2.25.

f. Number Sense: $250
100

g. Geometry: A square has an area of 25 in.2. What is the length of the

sides of the square?

h. Calculation: 8 × 9, + 3, ÷ 3, × 2, − 10, ÷ 5, + 3, ÷ 11

problem Griffin used 14 blocks to build this
solving three-layer pyramid. How many blocks
would he need to build a six-layer
pyramid? How many blocks would he
need for the bottom layer of a nine-layer
pyramid?

New Concept Increasing Knowledge

In this lesson we will learn about various properties of parallelograms. The
following example describes some angle properties of parallelograms.

Example 1

In parallelogram ABCD, the measure of angle A is 60∙.

Reading Math a. What is the measure of C? A B
C
Give two other b. What is the measure of B?
ways to name
∠C. D

Solution

a. Angles A and C are opposite angles in that they are opposite to each
other in the parallelogram. The opposite angles of a parallelogram have
equal measures. So the measure of angle C equals the measure of
angle A. Thus the measure of ∠C is 60∙.

368 Saxon Math Course 1

Math Language b. Angles A and B are adjacent angles in that they share a side. (Side AB is
a side of ∠A and a side of ∠B.) The adjacent angles of a parallelogram
Remember that are supplementary. So ∠A and ∠B are supplementary, which means
supplementary their measures total 180°. Since ∠A measures 60°, ∠B must measure
angles have a 120∙ for their sum to be 180°.
sum of 180°.
Model A flexible model of a parallelogram is useful for illustrating some
properties of a parallelogram. A model can be constructed of brads and stiff
tagboard or cardboard.

Lay two 8-in. strips of tagboard or cardboard over two parallel 10-in. strips as
shown. Punch a hole at the center of the overlapping ends. Then fasten the
corners with brads to hold the strips together.

10 in.

8 in.

If we move the sides of the parallelogram back and forth, we see that
opposite sides always remain parallel and equal in length. Though the angles
change size, opposite angles remain equal and adjacent angles remain
supplementary.

With this model we also can observe how the area of a parallelogram
changes as the angles change. We hold the model with two hands and slide
opposite sides in opposite directions. The maximum area occurs when the
angles are 90°. The area reduces to zero as opposite sides come together.

heightDiscuss The area of a parallelogram changes as the angles change. Does
the perimeter change?
The flexible model shows that parallelograms may have sides that are equal
in length but areas that are different. To find the area of a parallelogram, we
multiply two perpendicular measurements. We multiply the base by the
height of the parallelogram.

base

Lesson 71 369

The base of a parallelogram is the length of one of the sides. The height of
a parallelogram is the perpendicular distance from the base to the opposite
side. The following activity will illustrate why the area of a parallelogram
equals the base times the height.
Activity

Area of a Parallelogram

Materials needed:
• graph paper
• ruler
• pencil
• scissors

Represent Tracing over the lines on the graph paper, draw two parallel
segments the same number of units long but shifted slightly as shown.

Then draw segments between the endpoints of the pair of parallel segments
to complete the parallelogram.

4 units
high

5 units long

The base of the parallelogram we drew has a length of 5 units. The height of
the parallelogram is 4 units. Your parallelogram might be different. How many
units long and high is your parallelogram? Can you easily count the number
of square units in the area of your parallelogram?
Model Use scissors to cut out your parallelogram.
Then select a line on the graph paper that is perpendicular to the first pair of
parallel sides that you drew. Cut the parallelogram into two pieces along
this line.

We will cut here.

370 Saxon Math Course 1

Rearrange the two pieces of the parallelogram to form a rectangle. What is
the length and width of the rectangle? How many square units is the area of
the rectangle?

Our rectangle is 5 units long and 4 units wide. The area of the rectangle is
20 square units. So the area of the parallelogram is also 20 square units.

By making a perpendicular cut across the parallelogram and rearranging the
pieces, we formed a rectangle having the same area as the parallelogram.
The length and width of the rectangle equaled the base and height of
the parallelogram. Therefore, by multiplying the base and height of a
parallelogram, we can find its area.

Example 2
Find the area of this parallelogram:

5.2 cm 5 cm

6 cm

Solution

We multiply two perpendicular measurements, the base and the height.
The height is often shown as a dashed line segment. The base is 6 cm.
The height is 5 cm.

6 cm × 5 cm = 30 sq. cm
The area of the parallelogram is 30 sq. cm.

Practice Set Conclude Refer to parallelogram QRST to answer problems a–d.

a. Which angle is opposite ∠Q? T Q
R
b. Which angle is opposite ∠T?

c. Name two angles that are supplements S
of ∠T.

d. If the measure of ∠R is 100°, what is the measure of ∠Q?

Calculate the perimeter and area of each parallelogram:

ee. . 12 m ff.. 5 in.

10 m 6 in.

8 m 8 in.

Lesson 71 371

g. Analyze A formula for finding the area of a parallelogram is A = bh.
This formula means

Area = base × height

The base is the length of one side. The height is the perpendicular
distance to the opposite side. Here we show the same parallelogram in
two different positions, so the area of the parallelogram is the same in
both drawings. What is the height in the figure on the right?

9 cm 6 cm 12 cm
h

12 cm 9 cm

Written Practice Strengthening Concepts

1. What is the least common multiple of 6 and 10?

(30)

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8 4
(14)

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4 2

3  3 42132 683 (332)32. 6Ttimh83e1e14m3d34oid52vii23et 2ela3n12sd18t?e14d14320325 m835i41nute143s78.5If t834h21e3 18m1o56vi$e7s54t.a1205r0t14e6d6a1t378713412:15 p26.m121.5,3a$43t7w5h.02a0t12 1
4 8 2
7

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2 23232 1 2
2
2 3 1
3  8 1 4 

3  3 4 1  6 8. 6((15315.+5 )$23307554381.5641.32)0÷03283811(12178−5704112.6)(6559131).5148715$41378115278.3032180115(522).$75175351421.430815$0147158387.1(060310)7.87125 1 17512411$1278575$.07605.01057$217657.012 03 3 722112
4 8 2 4 4
(59)

5  3 1 5 1  51 78 311(813319)..
8 4

15 $75.00 7 1 (53) Quan or5dere3d81a $4.50 b5o14wl o1f s78oup. Th1e5ta$x75ra.0te0was 7 12% (which
2 equals 0.075). He paid for the soup with a $20 bill.
14.

(41)

a. What was the tax on the bowl of soup?

b. What was the total price including tax?

c. How much money should Quan get back from his payment?

* 15. What is the name for the point on the coordinate plane that has the
(Inv. 7) coordinates (0, 0)?

372 Saxon Math Course 1

* 16. Represent Refer to the coordinate plane below to locate the points
(Inv. 7) indicated.

y

6

5

D 4C B

3

2

E1 A x

–6 –5 – 4 –3 –2 –1–10 1 2 3 4 5 6

F –2 G H

–3

–4

–5

–6

Name the points that have the following coordinates:

a. (−3, 3) b. (0, −3)

Identify the coordinates of the following points:

c. H d. E 120 64
f 224
Find each unknown number:  1.2
17. 1.2f = 120
18. 120  1.2 64
(49) f 224
(49)

* 19. Write the prime factorization of both the numerator and the denominator
(67) of this fraction. Then reduce the fraction.

120  1.2 64 120  1.2 64
f 224 f 224

20. The perimeter of a square is 6.4 meters. What is its area?
(38) $250

21. Analyze What fraction of this circle is not 100
(Inv. 2) shaded?
$250
100

$250 22. Explain If the radius of this circle is 1 cm,
100 (47) what is the circumference of the circle? (Use

3.14 for π.) How did you find your answer?

$250

23. Estimate A centi1m00eter is about as long as this segment:
(7)

About how many centimeters long is your little finger?

Lesson 71 373

24. Connect Water freezes at 32° 50° F
(10) Fahrenheit. The temperature shown on 40° F
30° F
the thermometer is how many degrees
Fahrenheit above the freezing point of
water?

64
224

25. Ray watched TV for one hour. He determined that commercials were
(29, 33) shown 20% of that hour. Write 20% as a reduced fraction. Then find

the number of minutes that commercials were shown during the hour.

26. Name the geometric solid shown
(Inv. 6) at right.

* 27. Analyze This square and regular triangle
(60) share a common side. The perimeter of the
square is 24 cm. What is the perimeter of the
triangle?

28. Choose the appropriate unit for the area of your state.
(31) A square inches
B square yards C square miles

* 29. a. What is the perimeter of this 7 cm 8 cm
(71) parallelogram? 10 cm

b. What is the area of this
parallelogram?

* 30. Conclude In this figure ∠BMD is a right angle. B
(69) Name two angles that are AM
a. supplementary.
C
b. complementary.
D

374 Saxon Math Course 1

LESSON Fractions Chart
Multiplying Three Fractions
72

Power Up Building Power 72 2 3 8 3
120 3 4 5 4
facts
mental Power Up H

math a. Number Sense: 3 × 125

b. Number Sense: 275 + 50

c. Number Sense: 3 × $0.99

d. Calculation: $20.00 − $9.99

e. Fractional Parts: 1 of $6.60
3

f. Decimals: $2.50 × 10

g. Statistics: Find the average 45, 33, and 60.

h. Calculation: 2 × 2, × 2, × 2, × 2, − 2, ÷ 2

problem Kioko was thinking of two numbers whose average was 24. If one of the
solving numbers was half of 24, what was the other number?

New Concepts Increasing Knowledge

fractions We have learned three steps to take when performing pencil-and-paper
chart arithmetic with fractions and mixed numbers:

Step 1: Write the problem in the correct shape.

Step 2: Perform the operation.

Step 3: Simplify the answer.

The letters S.O.S. can help us remember the steps as “shape,” “operate,”
and “simplify.” We summarize the S.O.S. rules we have learned in the
following fractions chart.

Fractions Chart

+− × ÷

1. Shape Write fractions Write numbers in fraction form.
with common
denominators.

Add or subtract the × ÷
numerators. Cancel. Find reciprocal of divisor,
2. Operate then cancel.

Multiply numerators.
Multiply denominators.

3. Simplify Reduce fractions. Convert improper fractions.

Lesson 72 375

Math Language • Below the + and − symbols we list the steps for adding or subtracting
Recall that fractions.
canceling means
reducing before • Below the × and ÷ symbols, we list the steps for multiplying or dividing
multiplying. fractions.

multiplying The “shape” step for addition and subtraction is the same; we write
three the fractions with common denominators. Likewise, the “shape” step
for multiplication and division is the same; we write both numbers in
fractions fraction form.

At the “operate” step, however, we separate multiplication and division.
When multiplying fractions, we may reduce (cancel) before we multiply.
Then we multiply the numerators to find the numerator of the product, and
we multiply the denominators to find the denominator of the product. When
dividing fractions, we first replace the divisor of the division problem with its
reciprocal and change the division problem to a multiplication problem. We
cancel terms, if possible, and then multiply.

The “simplify” step is the same for all four operations. We reduce answers
when possible and convert answers that are improper fractions to mixed
numbers.

To multiply three or more fractions, we follow the same steps we take when
multiplying two fractions:

Step 1: We write the numbers in fraction form.

Step 2: We cancel terms by reducing numerator-denominator pairs that
have common factors. Then we multiply the remaining terms.

Step 3: We simplify if possible.

Example

Multiply: 2  1 3  3 1 3 8
3 5 4 5 5
2 3 3
Solution 3  1 5  4 1 3 8
5 5

Practice Set 2 Fbiersf5812ot35rweem431w43u231lrt3322iit54pely1582i51853n223g53a.s4311M5443t1hu43el83t54iip54mlyp1irn35og85pteh2231re12frraec582mt1iao1i1nn04311i58n.gT4t54heernmws,ewreedfiuncdetwheheprreodpuocsts.ible
3
2
3
1 a. Dra1 w 1the fractio1 ns chart from this lesson.

b. Describe th1e three steps fo12r ad65din53g fractio3ns. 1 1  2 2 3  2 1 1  1 2
2 3 4 2 3
4

c. Describe the steps for dividing fractions.

Multiply: 4 3 1 23111540 83 4
2 5 8 2 1 1
d. 3   2 e. 2 2  1 10  4

1 1  5 41 3 3  11212 65 25323 3  23  1 1  212312 43123 2 1 1  1
4 2 6 5 4 2 2

376 Saxon Math Course 1

2  4  3 2 1  1 1  4
3 5 8 2 10
Written Practice Strengthening Concepts

32(1218).. 54WCho83nanteicst theF2oa21uvretraa1bg1lee1032sopfo454o4.2n,s832e.6q1u,aalsn2d14 21c3u.6p?.1H11o0wm4an12yta65ble53spoons 3  1 1  2 2
would equal one full cup? 2 3
(54)

3. The temperature on the moon ranges from a high of about 130°C
(14) 12abo65ut 2−532111410°1C11.03This41is12a12d2iff2365ere43n5ce ho3wm1an211y12 2321 2 3
to a low of o2f 3 4  2
1 de32gre54es?83
4

4. Four of the 12 marbles in the bag are blue. If one marble is taken from
(58)
tah.ebbluaeg?, whant is t21hep53robabi1lity twhatntbh1.7e2n21motarbwb53lulee?is22113w31 7 1 1
  12 w  2 2  3 3

n  1  3 1c.14Wwhat w17o2rd nwam12e s265t12he53 re3l31ation3ship1b12etwe2e32n th43eev2ents in a a1nd21 b?1 2
2 5 3

5. The diameter of a circle is 1 meter. The circumference is how many
(7, 47) centimeters?(6(Use130.)14 fao4r π.)110b (6a3 101) 100ba4  110b  a3  1100b

(6  10) 6. eCaoc11nh0nbeucntknaWo3whnat1nf10ura0mcbbtieorn: of a dollar is a nickel?
(2a9)4
Find 1 3 1 nwn 21 1217253 53w(4831). 2121ww331172172 2 21212 1
2 5 3
7. n   w w 3 133

(56)

n  1  3 1  w  172(599). w  2 1  3 1 10. 1 − w = 0.23
2 5 2 3
(43)

11. Write the standard decimal number for the following:
(46) (6  10)  a4  11(06b(61a031)0) 1a104a04b 1101b10b a3a3 1101010b0b
(6  10)  a4  110b  a312. 110E0stbimate Which of these numbers is closest to 1?
(50) A −1
B 0.1 C 10

13. What is the largest prime number that is less than 100?

(19)

* 14 Classify Which of these figures is not a parallelogram?
(64)
AC

BD

15. Connect A loop of string two feet around is formed to make a square.
(38) a. How many inches long is each side of the square?

b. What is the area of the square in square inches?

Lesson 72 377

* 16. Conclude Figure ABCD is a rectangle. A MB
(69) a. Name an angle complementary to ∠DCM.
b. Name an angle supplementary to ∠AMC.

D C

Refer to this menu and the information that follows to answer
problems 17–19.

Menu

Grilled Chicken Sandwich $3.49 Juice: Small $0.89
Green Salad $3.29 Medium $1.09
Pasta Salad $2.89 Large $1.29

From this menu the Johnsons ordered two grilled chicken sandwiches, one
green salad, one small juice, and two medium juices.

17. What was the total price of the Johnsons’ order?
(1)

18. If 7% tax is added to the bill, and if the Johnsons pay for the food with a
(41) $20 bill, how much money should they get back?

19. Formulate Make up an order from the menu. Then calculate the bill,
(1) not including tax.

20. If A = lw, and if l equals 2.5 and w equals 0.4, what does A equal?

(47)

* 21. Write the prime factorization of both the numerator and the denominator
(66) of this fraction. Then reduce the fraction.

72 2 3 8
120 3 4 5

Refer to the coordinate plane below to answer problems 22 and 23.

y 72 2 3
120 3 4

6

K 5 A
J B
4 L
3

2

–6 –5 –4I–331 –2 1 C x
–1–10
1 234 56

–2

H –3 F D
G –4 E1

–5 3

–6

* 22. Identify the coordinates of the following points:
(Inv. 7) a. K
b. F

* 23. Name the points that have the following coordinates:
(Inv. 7) a. (3, −4)
b. (−3, 0)

378 Saxon Math Course 1

5 48 22  110  4

1  5  3 3 13322154212211283231*212(4312644123)1.01al2i2343nM2pea21o4sdrtep.223l Te1rraDp1541c0erean1wd83t12hic4aeupq1la1au12ri23artdoo2rfit121lhpa23etaerfrai1arlsll1e1tt0lhplaiantieri4sso.ffoTlirhnmeenesddarnbadywtahabeosiuentcteothrnsedescpataimnirgeoldifnipseatsar.naIlcsleel
2 6 5
4 3  21212265232315314315408324
 5  83 1 1
2
the quadrilateral a rectangle?

1 * 25. 1  6541 3 3  112 21 6525323 * 243(762). 23  1 1  213212 43 132 2 1 1  1 2
2 5 2 2 3
1 5 3 4 (72) 3 1 212321 43123 1 2
2  6 14 5 4  23  1 2  2 * 28. 1 2  1 3
3  11221 65 2(5537432). (68)

29. (0.12)(0.24) 30. 0.6 ÷ 0.25

(39) (49)

Early Finishers LaDonna had errands to run and decided to park 15 30 45
her car in front of a parking meter rather than drive
Real-World from store to store. She calculated that she would 60
Application spend about 20 minutes in the post office and 10
minutes at the hardware store. Then she would
spend 5 minutes picking up her clothes from the 0
cleaner’s and another 30 minutes eating lunch.

The sign on the meter read

$0.25 = 15 minutes

$0.10 = 6 minutes

$0.05 = 3 minutes

a. How much time will LaDonna spend to finish
doing her errands?

b. If the meter has ten minutes left, how much
money will she need to put into the meter?

Lesson 72 379