Saxon 6/5

Supplemental Practice 641

Lesson 26 Divide: 2. 2 Ä£∞§ 3. 3 Ä™£¢
1. 2 Ä¡£§ 5. 3 Ä$á∞.§á ¶ 6. 4 Ä$á¡.™á ¢
4. 3 Ä$á¢.á∞§ 8. 4 Ä£∞§ 9. 5 Ä¡™º
7. 4 Ä™¢• 11. 6 Ä$á¢.£á ™ 12. 6 Ä$á•.ᶧ
10. 5 Ä$á™.£á º 14. 7 Ä•¢¶ 15. 7 Īº£
13. 7 Ä∞¡¡ 17. 8 Ä$á§.ᢕ 18. 9 Ä$∞á .§á ¶
16. 8 Ä$á¢.ᢺ 20. 8 ħªº 21. 7 ħ¡¡
19. 9 Ä∞§•

Lesson 28 1. What time is shown on the clock? Morning
2. What time was it 2 hours ago?
3. What time will it be in 2 hours? 11 12 1
4. What time was it half an hour ago? 10 2
5. What time will it be in a half hour? 93
84

76 5

6. What time is shown on the clock? Afternoon

7. What time will it be in 12 hours? 11 12 1
10 2
8. What time was it 2 hours ago? 93
84
9. What time was it half an hour ago?
76 5
10. How many minutes is it until
1:00 p.m.?

11. What time is shown on the clock? Morning
12. What time will it be in 24 hours?
13. What time was it half an hour ago? 11 12 1
14. What time will it be in 1A hours? 10 2
15. How many minutes is it until noon? 93
84

76 5

642 Saxon Math 6/5

16. What time is 10 minutes before noon?

17. What time is 1A hours after midnight?

18. What time is 5 minutes after two in the afternoon?

19. What time is 5 minutes before six in the morning?

20. What time is a quarter after three in the afternoon?

Lesson 29 Multiply: 2. 47 ¥ 30 3. 50 ¥ 78
1. 10 ¥ 36

4. 34 ¥ 70 5. 90 ¥ 37 6. 45 ¥ 10

7. 20 ¥ 35 8. 73 ¥ 40 9. 60 ¥ 38

10. 74 ¥ 80 11. 10 ¥ 271 12. 932 ¥ 30

13. 70 ¥ 674 14. 465 ¥ 20 15. 60 ¥ 793

16. 81 ¥ 100 17. 500 ¥ 36 18. 64 ¥ 900

19. 400 ¥ 84 20. 96 ¥ 800

Lesson 33 Round each number to the nearest ten:

1. 46 2. 37 3. 61 4. 58

5. 43 6. 79 7. 85 8. 96

Round each number to the nearest hundred:

9. 375 10. 216 11. 850 12. 781

13. 460 14. 329 15. 198 16. 748

Round each number to the nearest ten:

17. 121 18. 127 19. 358 20. 341

21. 769 22. 532 23. 477 24. 265

Supplemental Practice 643

Lesson 34 Divide: 2. 4 Ä•£ 3. 2 ħ¡
1. 3 Ä£¡

4. 3 Ä¡™™ 5. 4 Ä™¢£ 6. 5 Ä¢º¢

7. 6 Ä£§∞ 8. 6 Ä£º∞ 9. 8 Ä¢º¶

10. 3 Ä$£á .á¡∞ 11. 4 Ä$á•.ᙢ 12. 5 Ä$á∞.ᢺ

13. 2 Ä¢¡∞ 14. 3 Ī™º 15. 4 Ä¢££

16. 7 Ä$á¶.ᢙ 17. 3 Ä$§á .ầ 18. 4 Ä$ªá .§á º

Lesson 37 1. Draw a square and shade A of it.

2. Draw a square and shade A of it another way.

3. Draw a square and shade A of it another way.

4. Draw a square and shade F of it.

5. Draw a circle and shade A of it.

6. Draw a circle and shade H of it.

7. Draw a circle and shade C of it.

8. Draw a rectangle and shade A of it.

9. Draw a rectangle and shade F of it.

10. Draw a rectangle and shade C of it.

11. Draw a rectangle and shade J of it.

12. Draw a square and shade H of it.

13. Draw a circle and shade D of it.

14. Draw a rectangle and shade D of it.

644 Saxon Math 6/5

15. Draw a rectangle and shade K of it.

16. Draw a circle and shade O of it.

17. Draw a rectangle and shade O of it.

18. Draw a rectangle and shade L of it.

19. Draw a circle and shade S of it.

20. Draw a rectangle and shade S of it.

Lesson 38 Use a fraction or mixed number to name each point marked
with an arrow on these number lines:

AB CD E

01234

FG H I J

01 2 3 4
KL MN O

01 2 3 4
PQR ST

01 2 34
XY
UV W

01234

Lesson 43 Find each sum or difference: 2. 213 + 313
1. 331 + 1

3. 5 + 125 4. 1 + 3
4

Supplemental Practice 645

5. 684 + 183 6. 723 + 5

7. 4 + 3 8. 3150 + 1140
10

9. 9 + 721 10. 5 + 1
6

11. 623 – 4 12. 334 – 124

13. 721 – 1 14. 185 – 1
2

15. 834 – 243 16. 312 – 321
17. 10170 – 1140
18. 453 – 1
5

19. 945 – 4 20. 187 – 7
8

Lesson 48 Write each number in standard form:
1. (5 ¥ 1000) + (2 ¥ 100) + (8 ¥ 10)
2. (6 ¥ 100) + (4 ¥ 10) + (2 ¥ 1)
3. (4 ¥ 10,000) + (5 ¥ 1000) + (6 ¥ 10) + (7 ¥ 1)
4. (5 ¥ 1000) + (4 ¥ 100) + (9 ¥ 10) + (2 ¥ 1)
5. (7 ¥ 10,000) + (1 ¥ 1000) + (4 ¥ 100)
6. (6 ¥ 1000) + (4 ¥ 100) + (3 ¥ 1)
7. (7 ¥ 1000) + (8 ¥ 10) + (9 ¥ 1)
8. (1 ¥ 10,000) + (4 ¥ 100) + (7 ¥ 1)
9. (6 ¥ 1000) + (1 ¥ 10)
10. (1 ¥ 10,000) + (6 ¥ 1000) + (5 ¥ 1)

646 Saxon Math 6/5

Write each number in expanded notation:
11. 65

12. 742

13. 320

14. 506

15. 7500

16. 2001

17. 1040

18. 1760

19. 1492

20. 25,000

Lesson 50 Find the average of each group of numbers:

1. 3, 3, 6 2. 4, 5, 7, 8

3. 5, 6, 8, 9 4. 15, 17, 19

5. 21, 19, 26 6. 1, 2, 3, 4, 5

7. 3, 5, 7, 9 8. 36, 44

9. 65, 47, 32 10. 6, 7, 8, 9, 10

11. 112, 124 12. 47, 52, 54

13. 6, 6, 6, 10 14. 11, 12, 13, 14, 15

15. 33, 34, 35 16. 30, 40, 50, 60

17. 22, 24, 26, 28 18. 163, 197

19. 97, 101, 111 20. 43, 62, 56, 63

Supplemental Practice 647

Lesson 51 Multiply: 2. 96 3. $0.78 4. $0.52
1. 38 ¥ 97 ¥ 76 ¥ 47
¥ 49
6. 69 7. $0.58 8. $0.16
5. 63 ¥ 81 ¥ 59 ¥ 74
¥ 85
10. 27 11. $0.85 12. $0.47
9. 96 ¥ 73
¥ 36 ¥ 96 ¥ 72
14. 36
13. 74 ¥ 83 15. $0.74 16. $0.67
¥ 18
18. 63 ¥ 58 ¥ 64
17. 92 ¥ 49
¥ 47 19. $0.18 20. $0.46

¥ 85 ¥ 89

Lesson 52 Write the value of the 1 in each number:

1. 315,275,486 2. 21,987,564

3. 128,675 4. 7,351,487

5. 125,386,794 6. 97,315,248

Name the value of the place held by the zero in each number:

7. 20,675,482 8. 123,450,683

9. 5,046,912 10. 17,954,068

11. 805,423,796 12. 8,907,485

Which digit is in the millions place in each number?

13. 654,297,801 14. 37,591,846

Which digit is in the ten-millions place in each number?

15. 752,931,468 16. 246,801,357

Write the value of the 5 in each number:

17. 375,286,420 18. 17,576,284

19. 56,234,196 20. 123,456,786

648 Saxon Math 6/5

Use digits to write each number:
21. one million, two hundred fifty thousand

22. five million, three hundred twelve thousand

23. ten million, one hundred twenty-five thousand, two
hundred

24. thirteen million, two hundred ten thousand, five hundred

25. twenty-five million, one hundred ninety-six thousand,
one hundred

26. three hundred twenty-seven million

27. six hundred forty-five million, six hundred thousand,
two hundred

28. seven hundred sixteen million, nine hundred eleven
thousand

29. one hundred twenty million, six hundred fifteen thousand

30. nine hundred eighty-four million, two hundred thousand

Use words to name each number:
31. 1,500,000

32. 10,200,000

33. 15,352,000

34. 25,740,000

35. 42,164,000

36. 78,345,200

37. 120,000,000

38. 253,000,000

39. 412,520,000

40. 635,154,000

Supplemental Practice 649

Lesson 54 Divide: 2. 30 Ä¢∞º 3. 40 Ä$á¢.•á º
1. 20 Ä¢™º 5. 60 Ä•ºº 6. 70 Ä$¶á .Ẻ
4. 50 Ķºº 8. 20 Ä∞§º 9. 30 Ä$∞á .¶á º
7. 80 Īºº 11. 50 Ä•∞º 12. 60 Ä$ªá .Ẻ
10. 40 ħ∞º 14. 20 ħ¡¢ 15. 30 Ä$¶á .•á º
13. 70 Ä•ºº 17. 50 Ī•¶ 18. 60 Ä$áª.᧺
16. 40 Ä•¶§

Lesson 56 Multiply: 2. 650 3. $4.08 4. $3.54
¥ 473 ¥ 592 ¥ 260
1. 135
¥ 246

5. 625 6. 754 7. $3.47 8. $6.80
¥ 403 ¥ 365 ¥ 198 ¥ 743

9. 503 10. 418 11. $9.73 12. $3.49
¥ 936 ¥ 650
¥ 409 ¥ 156

13. 760 14. 507 15. $2.43 16. $9.53
¥ 394 ¥ 938
¥ 671 ¥ 870

17. 740 18. 486 19. $7.05 20. $5.78
¥ 698 ¥ 203
¥ 258 ¥ 369

Lesson 58 Divide. Write each quotient as a mixed number.

1. 6 Ä¡ª 2. 5 Ä£§ 3. 4 Ä™¶

4. 16 ÷ 7 5. 25 ÷ 8 6. 56 ÷ 9

7. 10 8. 50 9. 81
3 7 10

10. 2 Ä¢∞ 11. 3 Ä¢§ 12. 4 Ä¢¶

13. 56 ÷ 5 14. 79 ÷ 6 15. 61 ÷ 10

16. 33 17. 125 18. 95
8 3 6

19. 100 ÷ 7 20. 100 ÷ 9 21. 100 ÷ 3

650 Saxon Math 6/5

Lesson 62 Estimate each answer by rounding before doing the
arithmetic. Round numbers less than 100 to the nearest ten.
Round numbers more than 100 to the nearest hundred.

1. 36 + 43 2. 38 + 49 3. 73 – 31

4. 59 – 31 5. 51 ¥ 39 6. 78 ¥ 42

7. 88 ÷ 29 8. 81 ÷ 19 9. 397 + 214

10. 688 + 291 11. 687 – 304 12. 915 – 588

13. 503 ¥ 491 14. 687 ¥ 298 15. 395 ÷ 21

16. 589 ÷ 29 17. 87 + 93 18. 786 + 495

19. 893 – 514 20. 980 – 217

Lesson 63 Subtract:

1. 1 – 1 2. 2 – 2 3. 3 – 1
3 3 4

4. 4 – 3 5. 2 – 115 6. 3 – 161
4

7. 4 – 265 8. 5 – 381 9. 6 – 183

10. 8 – 585 11. 7 – 678 12. 10 – 1
2

13. 4 – 2110 14. 6 – 3130 15. 3 – 221

16. 5 – 1112 17. 10 – 1 18. 8 – 452
10

19. 1 – 11 20. 3 – 253
12

Supplemental Practice 651

Lesson 68 Use words to name each decimal number:

1. 3.4 2. 0.23

3. 12.9 4. 7.14

5. 20.5 6. 15.15

7. 10.1 8. 1.10

9. 120.8 10. 21.04

Use digits to write each decimal number:
11. twenty-three and four tenths

12. thirty-two hundredths

13. ten and five tenths

14. two and twenty-five hundredths

15. fifty-two and one tenth

16. five hundredths

17. one hundred thirty-five and nine tenths

18. seventy-six and twelve hundredths

19. one and six hundredths

20. ninety-six and five tenths

Lesson 75 Simplify:

1. 8 2. 7 3. 12 4. 7
3 2 4 4

5. 10 6. 100 7. 523 8. 663
5 100

9. 485 10. 944 11. 3181 12. 494

13. 583 14. 795 15. 873

652 Saxon Math 6/5

Add. Simplify each answer.

16. 2 + 2 17. 3 + 3 + 3 18. 2 + 2 + 2
3 3 4 4 4 3 3 3

19. 112 + 112 20. 332 + 132 21. 5 + 4
3 3

Lesson 76 Multiply:

1. 1 ¥ 1 2. 1 ¥ 3 3. 2 ¥ 2
2 2 2 4 3 3

4. 1 ¥ 1 5. 5 ¥ 1 6. 3 ¥ 1
3 3 6 2 4 2

7. 1 ¥ 1 8. 1 ¥ 2 9. 3 ¥ 2
2 3 5 3 7 5

10. 1 ¥ 1 11. 2 ¥ 1 12. 1 ¥ 1
4 4 3 3 2 5

13. 1 ¥ 1 14. 3 ¥ 3 15. 5 ¥ 1
2 4 4 4 8 2

16. 1 ¥ 1 17. 3 ¥ 1 18. 3 ¥ 3
3 4 4 4 4 5

19. 1 ¥ 1 20. 5 ¥ 3
10 10 8 4

Lesson 79 Find the fraction name for 1 used to make each equivalent

fraction:

11. 1 ¥ ? = 2 12.1 ¥ ? = 6
2 ? 4 2 ? 12

13. 2 ¥ ? = 4 14.2 ¥ ? = 8
3 ? 6 3 ? 12

Supplemental Practice 653

15. 3 ¥ ? = 6 16.3¥ ? = 9
4 ? 8 4 ? 12

17. 1 ¥ ? = 5 18.5¥ ? = 10
2 ? 10 6 ? 12

Find the numerator that completes each equivalent fraction:

9. 2 = ? 10. 1 = ? 11. 4 = ?
5 10 4 12 5 15

12. 3 = ? 13. 2 = ? 14. 1 = ?
8 16 3 15 6 12

15. 1 = ? 16. 1 = ? 17. 3 = ?
3 18 2 20 10 20

18. 3 = ? 19. 4 = ? 20. 1 = ?
4 20 5 20 10 100

Lesson 82 Find the greatest common factor (GCF) of each pair of
numbers:

1. 4 and 6 2. 4 and 8 3. 6 and 8

4. 6 and 9 5. 6 and 10 6. 6 and 12

7. 8 and 12 8. 9 and 12 9. 10 and 12

10. 5 and 10 11. 3 and 5 12. 8 and 16

Reduce each fraction by dividing the terms of the fraction by
the GCF of the terms:

13. 12 14. 12 15. 9
16 18 15

16. 8 17. 12 18. 16
16 20 24

654 Saxon Math 6/5

Lesson 86 Multiply. Simplify answers when possible.

1. 1 ¥ 2 2. 1 ¥ 3 3. 2 ¥2
3 2 3

4. 2 ¥ 3 5. 1 ¥5 6. 3 ¥3
3 4 4

7. 2 ¥ 4 8. 3¥ 3 9. 4¥ 2
5 5 3

10. What is C of 9? 11. What is D of 9?

12. What is F of 8? 13. What is H of 8?

14. What is J of 10? 15. What is L of 10?

16. What is O of 12? 17. What is S of 12?

18. What is U of 21? 19. What is X of 21?

20. What is b of 16? 21. What is f of 16?

Lesson 90 Reduce each fraction or mixed number to lowest terms:

1. 2 2. 3 3. 4 4. 4
8 9 6 10

5. 5 6. 3 7. 124 8. 386
10 12

9. 263 10. 4180 11. 162 12. 596

13. 4 14. 6 15. 8 16. 10
8 12 12 20

17. 4 18. 8 19. 12 20. 10
20 16 18 100

21. 18 22. 50 23. 16 24. 60
24 100 20 100

Supplemental Practice 655

Find each sum, difference, or product. Reduce your answers
to lowest terms.

25. 3 + 3 26. 9 – 3 27. 2 ¥ 1
8 8 10 10 3 4

28. 1 ¥3 29. 114 + 241 30. 365 – 161
6

31. 595 + 191 32. 5 + 5 33. 7 + 1
12 12 12 12

34. 15 – 3 35. 3 ¥ 2 36. 2 ¥ 3
16 16 10 3 3 8

37. 9 + 7 38. 17 – 11 39. 6 ¥ 5
24 24 18 18 10 10

40. 1 ¥ 6 41. 7 + 1
12 20 20

Write each percent as a reduced fraction:

42. 25% 43. 10% 44. 2% 45. 60%

46. 80% 47. 90% 48. 30% 49. 1%

50. 50% 51. 20% 52. 5% 53. 70%

54. 99% 55. 4% 56. 40% 57. 75%

Lesson 91 Simplify each fraction or mixed number:

1. 8 2. 9 3. 10 4. 10
6 6 6 8

5. 12 6. 12 7. 14 8. 27
8 10 4 6

9. 20 10. 15 11. 15 12. 14
8 6 10 8

13. 364 14. 41106 15. 5140

656 Saxon Math 6/5

Find each sum or product. Simplify your answers.

16. 8 + 8 + 8 17. 378 + 478
9 9 9

18. 3 ¥ 10 19. 6 ¥ 9
4 5 2

Lesson 92 Divide: 2. 24 Ä¢£™ 3. 18 Ä¢£™
1. 12 Ä¢£™

4. 27 Ä¢£™ 5. 13 Ä™£∞ 6. 29 Ä¢º¡

7. 32 Ä∞¡§ 8. 19 Ä£ªª 9. 23 Ä¢ªº

10. 14 Ä∞ºº 11. 25 Ķºº 12. 33 Ä¡ººº

13. 41 Ä¢§¢ 14. 39 Ä•ºº 15. 17 Ä¢™™

16. 22 ħ∞¶ 17. 15 Ä™¡• 18. 31 Ī¢£

Lesson 96 Divide. Remember to simplify your answers.

1. 2 ÷ 1 2. 1 ÷ 2 3. 1 ÷ 3
3 2 2 3 3 4

4. 3 ÷ 1 5. 3 ÷ 1 6. 1 ÷ 3
4 3 4 4 4 4

7. 2 ÷ 1 8. 1 ÷ 2 9. 2 ÷ 1
2 2 3

10. 1 ÷2 11. 1 ÷ 1 12. 1 ÷ 1
3 6 3 3 6

13. 3 ÷ 1 14. 1 ÷ 3 15. 3 ÷ 2
4 2 2 4 3

16. 2 ÷3 17. 3 ÷ 3 18. 3 ÷3
3 4 4

Lesson 99 Find each sum or difference: 2. 23.51 – 17
1. 3.47 + 6.4

3. 25.3 + 0.421 4. 6.57 – 0.8

5. 3.842 + 1.6 6. 20.45 – 12

7. 4.2 + 4 + 0.1 8. 5.423 – 1.4

9. 4.28 + 0.6 + 3 10. 1.00 – 0.84

11. 7.45 + 12.383 Supplemental Practice 657
13. 3 + 4.6 + 0.27
15. 14.2 + 6.4 + 5 12. 1.000 – 0.625
17. 5.2 + 3 + 0.47 14. 36.27 – 12
19. 5.36 + 12 16. 3.427 – 1
18. 32.47 – 5.8
Lesson 102 Subtract: 20. 16.25 – 15
1. 0.4 – 0.15
3. 3.5 – 0.35 2. 0.3 – 0.23
5. 0.2 – 0.12 4. 4.2 – 1.25
7. 5.0 – 1.4 6. 8.6 – 4.31
9. 0.8 – 0.75 8. 0.75 – 0.375
11. 0.6 – 0.599 10. 4.3 – 0.125
13. 4.0 – 1.25 12. 1.25 – 0.625
15. 0.25 – 0.125 14. 4.1 – 0.14
17. 0.5 – 0.425 16. 7.0 – 1.6
19. 6.0 – 0.6 18. 4.8 – 3.29
21. 3 – 2.1 20. 0.34 – 0.291
23. 1 – 0.2 22. 4 – 3.21
25. 6 – 4.7 24. 3.45 – 1
27. 3.4 – 2 26. 1 – 0.01
29. 12 – 6.4 28. 1 – 0.23
31. 4.3 – 1 30. 15 – 1.5
33. 1 – 0.9 32. 8 – 7.9
35. 25 – 12.5 34. 4 – 3.99
37. 14 – 5.6 36. 16.7 – 8
39. 4 – 2.77 38. 8 – 1.35
40. 1 – 0.211

658 Saxon Math 6/5

Lesson 104 Round each number to the nearest whole number:

1. 781 2. 3.8 3. 4.18

4. 565 5. 5.2 6. 4.93

7. 1231 8. 16.9 9. 14.23

10. 323 11. 6.7 12. 5.41

13. 1651 14. 24.4 15. 12.75

16. 9190 17. 9.6 18. 9.87

Lesson 109 Multiply: 2. 4 3. 0.7 4. 0.6
¥ 0.6 ¥ 0.8 ¥6
1. 0.3
¥5

5. 0.4 6. 0.8 7. 0.25 8. 2.5
¥ 0.4 ¥9 ¥3 ¥5

9. 2.5 10. 0.12 11. 1.2 12. 0.15
¥ 0.7 ¥6 ¥ 0.8 ¥5

13. 0.18 ¥ 3 14. 4.7 ¥ 0.5
15. 0.3 ¥ 0.8 16. 1.23 ¥ 0.7
17. 6.25 ¥ 8 18. 0.15 ¥ 1.5
19. 0.45 ¥ 0.3 20. 0.06 ¥ 8

Lesson 110 Multiply: 2. 0.2 3. 0.12 4. 0.05
¥ 0.4 ¥ 0.3 ¥ 0.07
1. 0.3
¥ 0.3

5. 0.08 6. 0.12 7. 0.12 8. 0.42
¥ 0.7 ¥ 0.12 ¥ 0.08 ¥ 0.2

9. 0.25 10. 0.23 11. 0.03 12. 1.23
¥ 0.3 ¥ 0.4 ¥ 0.07 ¥ 0.04

13. 0.4 ¥ 0.2 14. 0.25 ¥ 0.1

Supplemental Practice 659

15. 0.025 ¥ 0.7 16. 6.5 ¥ 0.01

17. 0.03 ¥ 0.03 18. 0.01 ¥ 0.1

19. 0.24 ¥ 0.3 20. 0.12 ¥ 0.06

Lesson 112 Find the least common multiple (LCM) of each pair of
numbers:

1. 3 and 4 2. 4 and 5 3. 4 and 6

4. 3 and 6 5. 4 and 8 6. 6 and 8

7. 6 and 9 8. 6 and 10 9. 6 and 12

10. 8 and 10 11. 8 and 12 12. 8 and 16

13. 10 and 15 14. 5 and 15 15. 5 and 10

16. 5 and 6 17. 10 and 20 18. 10 and 25

19. 20 and 30 20. 20 and 40

Lesson 113 Name the number of shaded circles as a mixed number and as
an improper fraction:

1. 2.

3. 4.

Change each mixed number to an improper fraction:

5. 321 6. 231 7. 323

8. 421 9. 181 10. 251

11. 512 12. 431 13. 314

14. 712 15. 313 16. 451

660 Saxon Math 6/5

Lesson 116 Find each sum or difference:

1. 1 + 1 2. 3 – 1 3. 1 + 3
2 4 4 2 2 8

4. 5 – 1 5. 1 + 1 6. 7 – 1
8 2 4 8 8 4

7. 3 + 1 8. 1 – 1 9. 1 + 1
4 8 3 9 2 10

10. 8 – 2 11. 1 + 1 12. 9 – 1
9 3 5 10 10 2

13. 2 + 3 14. 3 – 1 15. 1 + 7
5 10 10 5 6 12

16. 3A 17. 3H 18. 5d 19. 5O
+ 1F + 1b + 1A + 1C

20. 4A 21. 3D 22. 4d 23. 6u
+ 1O + 1O + 1F + 1A

24. 3u 25. 5 A 26. 4ç 27. 6 H
+ 2L + 1ç + 1C + 1â

28. 4h 29. 4H 30. 6 F 31. 5y
– 1A – 2d + 1ç – 1A

32. 8D 33. 4S 34. 6h 35. 7è
– 1O – 1A – 1H – 3A

36. 1 + 1 37. 1 – 1 38. 1 + 1
2 3 2 3 3 4

39. 1 – 1 40. 1 + 1 41. 1 – 1
3 4 2 5 2 5

42. 1 + 1 43. 1 – 1 44. 2 + 1
4 5 4 5 3 4

45. 2 – 1 46. 3 + 1 47. 3 – 1
3 4 4 3 4 3

Supplemental Practice 661

48. 1 + 1 49. 1 – 1 50. 5 + 3
4 6 4 6 6 4

51. 5 – 3 52. 3 + 2 53. 3 – 2
6 4 4 3 4 3

54. 3C 55. 5K 56. 4O 57. 4H
+ 1F + 2A + 3H – 1A

58. 5S 59. 4h 60. 9C 61. 4L
– 1F – 1H + 3K + 1F

62. 6A 63. 4S 64. 8H 65. 7f
+ 1C – 1A – 1D – 4C

66. 353 + 1130 67. 512 – 131
68. 723 + 161
70. 435 + 341 69. 723 – 135
72. 381 + 234
Lesson 117 Divide: 71. 6 1 – 661
4
1. 3 Ä£.¢á ™
4. 6 Ä¢.™á 73. 9 3 – 735
7. 2 ĺ.ᣧ 4
10. 6 ġ.ᣙ
13. 6.4 ÷ 4 2. 4 Ä∞.™á 3. 5 ĺ.á•∞
15. 6.5 ÷ 5
17. 3.24 ÷ 6 5. 7 ĺ.•á ¢ 6. 8 Ī.§á
19. 1.44 ÷ 9
8. 4 Ķ.™á 9. 5 Ķ.∞á

11. 7 Ä¡™.§á 12. 8 Ä£.ᢢ

14. 0.64 ÷ 2

16. 0.63 ÷ 3

18. 12.8 ÷ 8

20. 23.8 ÷ 7

662 Saxon Math 6/5 22. 4 ĺ.ᙕ 23. 5 Ä¡.á£∞
21. 3 ĺ.¡á ∞
24. 6 ĺ.á¡¢¢ 25. 7 ĺ.§á £ 26. 8 ĺ.á¡¢¢
27. 9 ĺ.¢á ∞
30. 4 ĺ.ᣧ 28. 3 ĺ.ºá ¡™ 29. 2 ĺ.ºá ∞¢
33. 0.18 ÷ 3
35. 0.36 ÷ 9 31. 5 ĺ.᣺ 32. 6 ĺ.¡á £•
37. 0.08 ÷ 2
39. 0.64 ÷ 8 34. 1.54 ÷ 7

Lesson 118 Divide: 36. 0.144 ÷ 6
1. 4 Ä£.á¢
4. 8 ĺ.∞á ™ 38. 0.095 ÷ 5
7. 5 ĺ.á¶
10. 2 ĺ.á∞ 40. 0.036 ÷ 4
13. 0.5 ÷ 4
15. 1.2 ÷ 8 2. 5 ĺ.á¡™ 3. 6 Ä™.á¶
17. 0.9 ÷ 2
19. 0.18 ÷ 4 5. 2 Ä£.¡á 6. 4 ĺ.á∞¢

Lesson 119 Divide: 8. 6 Ä¡.á∞ 9. 8 Ä£.§á
1. 0.3 ĺ.¡á ∞
4. 0.2 ĺ.£á ™ 11. 4 Ä¡.á∞ 12. 5 ĺ.¡á ™
7. 0.6 ĺ.¶á ™
10. 0.5 ħ.á∞ 14. 0.6 ÷ 5

16. 3.3 ÷ 6

18. 0.9 ÷ 5

20. 0.18 ÷ 8

2. 0.4 Ä™.ᢠ3. 0.5 ĺ.¡á ∞
5. 0.3 Ä¡.ᙣ 6. 0.4 ĺ.∞á §
8. 0.7 ĺ.᪕ 9. 0.8 Ä¡.á∞™
11. 0.4 ĺ.á¡£™ 12. 0.6 Ä¡.ᙧ

13. 4.6 ÷ 0.2 Supplemental Practice 663
14. 0.64 ÷ 0.4
15. 4.5 ÷ 0.3 16. 0.45 ÷ 0.5
18. 1.23 ÷ 0.3
17. 3.21 ÷ 0.3 20. 1.74 ÷ 0.6

19. 0.95 ÷ 0.5

Lesson 120 Multiply:

1. 121 ¥ 2 2. 3 ¥ 114 3. 212 ¥ 3
3 4 6. 112 ¥ 141
9. 2 ¥ 312
4. 4 ¥ 221 5. 131 ¥ 131 12. 321 ¥ 143
15. 421 ¥ 4
7. 1 ¥ 132 8. 231 ¥ 1 18. 134 ¥ 132
2 2

10. 313 ¥ 3 11. 132 ¥ 221

13. 1 ¥ 232 14. 234 ¥ 1
3 2

16. 3 ¥ 132 17. 241 ¥ 121

GLOSSARY

acute angle An angle whose measure is more than 0° and
less than 90°.

right angle obtuse angle

acute angle not acute angles

An acute angle is smaller than both a right angle and an
obtuse angle.

acute triangle A triangle whose largest angle measures less
than 90°.

right obtuse
triangle triangle

acute triangle not acute triangles

addend Any one of the numbers added in an addition
problem.

7 + 3 = 10 The addends in this problem are 7 and 3.

algorithm Any process for solving a mathematical problem.

In the addition algorithm we add the ones first, then the tens,
and then the hundreds.

a.m. The period of time from midnight to just before noon.

I get up at 7 a.m., which is 7 o’clock in the morning.

angle The opening that is formed when two lines, line
segments, or rays intersect.

These line segments form an angle.

area The number of square units needed to cover a surface.

5 in.

2 in. The area of this rectangle
is 10 square inches.

665

666 Saxon Math 6/5

arithmetic sequence A sequence in which each term is
found by adding a fixed amount to the previous term.

+3 +3 +3 +3 This arithmetic sequence
counts up by 3’s.
3, 6, 9, 12, 15, …

array A rectangular arrangement of numbers or symbols in
columns and rows.

XXX This is a 3-by-4 array of X’s.
XXX It has 3 columns and 4 rows.
XXX
XXX

associative property of addition The grouping of
addends does not affect their sum. In symbolic form,
a + (b + c) = (a + b) + c. Unlike addition, subtraction is
not associative.

(8 + 4) + 2 = 8 + (4 + 2) (8 – 4) – 2 ≠ 8 – (4 – 2)

Addition is associative. Subtraction is not associative.

associative property of multiplication The grouping of

factors does not affect their product. In symbolic form,
a ¥ (b ¥ c) = (a ¥ b) ¥ c. Unlike multiplication, division

is not associative.

(8 ¥ 4) ¥ 2 = 8 ¥ (4 ¥ 2) (8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)

Multiplication is associative. Division is not associative.

average The number found when the sum of two or more
numbers is divided by the number of addends in the sum;
also called mean.

To find the average of the numbers 5, 6, and 10, first add.
5 + 6 + 10 = 21

Then, since there were three addends, divide the sum by 3.
21 ÷ 3 = 7

The average of 5, 6, and 10 is 7.

bar graph A graph that uses rectangles (bars) to show numbersDays
or measurements.

Rainy Days
8

6
bar

4

2

Jan. Feb. Mar. Apr.

This bar graph shows how many rainy days there were in each
of these four months.

Glossary 667

base (1) The lower number in an exponential expression.

base 53 exponent
53 means 5 ¥ 5 ¥ 5 and its value is 125.

(2) A designated side or face of a geometric figure.

base base base

capacity The amount of liquid a container can hold.

Cups, gallons, and liters are units of capacity.

Celsius A scale used on some thermometers to measure
temperature.

On the Celsius scale, water freezes at 0°C and boils at 100°C.

center The point inside a circle from which all points on
the circle are equally distant.

2 in. The center of circle A is 2 inches
A from every point on the circle.

century A period of one hundred years.

The years 2001–2100 make up one century.

chance A way of expressing the likelihood of an event; the
probability of an event expressed as a percentage.

The chance of snow is 10%. It is not likely to snow.
There is an 80% chance of rain. It is likely to rain.

circle A closed, curved shape in which all points on the
shape are the same distance from its center.

circle

668 Saxon Math 6/5

circle graph A graph made of a circle divided into sectors.
Also called pie chart or pie graph.

Hair Colors of Students

Red

Brown 2

4 This circle graph displays
data on students’ hair color.
Blond Black

4 6

circumference The distance around a circle; the perimeter
of a circle.

A

If the distance from point A
around to point A is 3 inches,
then the circumference of the
circle is 3 inches.

cluster A group of data points that are very close together.

X

XXX

XXX

X XXX X

X X XX X XX

0 1 2 3 4 5 6 7 8 9 10

cluster

common denominators Denominators that are the same.

The fractions 2 and 3 have common denominators.
5 5

common fraction A fraction with whole-number terms.

154 1.2 3 π
273 2.4 4.5 2

common fractions not common fractions

common year A year with 365 days; not a leap year.

The year 2000 is a leap year, but 2001 is a common year. In a
common year February has 28 days. In a leap year it has 29 days.

Glossary 669

commutative property of addition Changing the order of
addends does not change their sum. In symbolic form,
a + b = b + a. Unlike addition, subtraction is not
commutative.

8+2=2+8 8–2≠2–8
Addition is commutative. Subtraction is not commutative.

commutative property of multiplication Changing the order

of factors does not change their product. In symbolic form,
a ¥ b = b ¥ a. Unlike multiplication, division is not

commutative.

8¥2=2¥8 8÷2≠2÷8
Multiplication is commutative. Division is not commutative.

comparative bar graph A method of displaying data, usually
used to compare two or more related sets of data.

Department Store Sales

Number Sold 500 Sweaters
400 T-shirts
300
200
100

Feb. Apr. June Aug. Oct. Dec.

This comparative bar graph compares how many sweaters
were sold with how many t-shirts were sold in each of these
six months.

composite number A counting number greater than 1 that is
divisible by a number other than itself and 1. Every
composite number has three or more factors. Every composite
number can be expressed as a product of two or more prime
numbers.

9 is divisible by 1, 3, and 9. It is composite.

11 is divisible by 1 and 11. It is not composite.

cone A three-dimensional solid with a circular base and a
single vertex.

cone

670 Saxon Math 6/5

congruent Having the same size and shape.

These polygons are congruent. They
have the same size and shape.

coordinate(s) (1) A number used to locate a point on a
number line.

A
–3 –2 –1 0 1 2 3

The coordinate of point A is –2.

(2) A pair of numbers used to locate a point on a coordinate
plane.

y

3

2B

1

–3 – 2 –1 123 x
–1
–2
–3

The coordinates of point B are (2, 3). The x-coordinate is listed
first, the y-coordinate second.

coordinate plane A grid on which any point can be
identified by its distances from the x- and y-axes.

y

3 Point A is located
at (–2, 2) on this
2 coordinate plane.

A1

–3 – 2 –1 123 x
–1
–2
–3

counting numbers The numbers used to count; the numbers
in this sequence: 1, 2, 3, 4, 5, 6, 7, 8, 9, ….

The numbers 12 and 37 are counting numbers, but 0.98 and A
are not.

Glossary 671

cube A three-dimensional solid with six square faces.
Adjacent faces are perpendicular and opposite faces are
parallel.

cube

cubic unit A cube with edges of designated length. Cubic
units are used to measure volume.

The shaded part is 1 cubic unit.
The volume of the large cube is
8 cubic units.

cylinder A three-dimensional solid with two circular bases
that are opposite and parallel to each other.

cylinder

data (Singular: datum) Information gathered from
observations or calculations.

82, 76, 95, 62, 98, 97, 93

These data are Skylar’s first 7 test scores.

decade A period of ten years.

The years 2001–2010 make up one decade.

decimal number A numeral that contains a decimal point.

23.94 is a decimal number because it contains a decimal point.

decimal places Places to the right of the decimal point.

5.47 has two decimal places.
6.3 has one decimal place.
8 has no decimal places.

decimal point A symbol used to separate the ones place
from the tenths place in decimal numbers.

34.15

decimal point

672 Saxon Math 6/5
degree (°) (1) A unit for measuring angles.

360°

There are 90 degrees There are 360 degrees
(90°) in a right angle. (360 °) in a circle.

(2) A unit for measuring temperature.

100°C Water boils.

There are 100 degrees between
the freezing and boiling points
of water on the Celsius scale.

0°C Water freezes.

denominator The bottom number of a fraction; the number
that tells how many parts are in a whole.

1 The denominator of the fraction is 4.
4 There are 4 parts in the whole circle.

diameter The distance across a circle through its center.

3 in. The diameter of this
circle is 3 inches.

difference The result of subtraction.

12 – 8 = 4 The difference in this problem is 4.

digit Any of the symbols used to write numbers: 0, 1, 2, 3,
4, 5, 6, 7, 8, 9.

The last digit in the number 7862 is 2.

distributive property A number times the sum of two
addends is equal to the sum of that same number times each
individual addend: a ¥ (b + c) = (a ¥ b) + (a ¥ c).

8 ¥ (2 + 3) = (8 ¥ 2) + (8 ¥ 3)
Multiplication is distributive over addition.

Glossary 673

dividend A number that is divided.

12 ÷ 3 = 4 4 12 = 4 The dividend is 12 in
3 12 3 each of these problems.

divisible Able to be divided by a whole number without a
remainder.

5 The number 20 is divisible by 4,
4 20 since 20 ÷ 4 has no remainder.

6R2 The number 20 is not divisible by 3,
3 20 since 20 ÷ 3 has a remainder.

division An operation that separates a number into a given
number of equal parts or into a number of parts of a given size.

21 ÷ 3 = 7 We use division to separate 21 into 3 groups of 7.

divisor A number by which another number is divided.

12 ÷ 3 = 4 4 12 = 4 The divisor is 3 in
3 12 3 each of these problems.

double-line graph A method of displaying a set of data,
often used to compare two performances over time.

Compounded Value of $1000 at 7% and 10% Interest

Dollar Value 3000 7%
2000 10%

double-line graph

1000

2 4 6 8 10 12
Years

edge A line segment formed where two faces of a solid
intersect.

One edge of this cube is colored
blue. A cube has 12 edges.

elapsed time The difference between a starting time and an
ending time.

The race started at 6:30 p.m. and finished at 9:12 p.m. The
elapsed time of the race was 2 hours 42 minutes.

674 Saxon Math 6/5

endpoint A point at which a line segment ends.

AB

Points A and B are the endpoints of line segment AB.

equation A number sentence that uses the symbol “=” to
show that two quantities are equal.

x = 3 3 + 7 = 10 4+1 x<7

equations not equations

equilateral triangle A triangle in which all sides are the
same length.

This is an equilateral triangle.
All of its sides are the same length.

equivalent fractions Different fractions that name the same
amount.

1=2
24

1 and 2 are equivalent fractions.
2 4

estimate To find an approximate value.

I estimate that the sum of 199 and 205 is about 400.

evaluate To find the value of an expression.

To evaluate a + b for a = 7 and b = 13, we replace a with
7 and b with 13:

7 + 13 = 20

even numbers Numbers that can be divided by 2 without a
remainder; the numbers in this sequence: 0, 2, 4, 6, 8, 10, ....

Even numbers have 0, 2, 4, 6, or 8 in the ones place.

event An outcome or group of outcomes in an experiment
involving probability.

The event of rolling a 4 with one roll of a standard number
cube has a probability of O.

Glossary 675

exact number A number that has not been rounded.

Corissa estimated that about 50 tickets were sold, but the exact
number of tickets sold was 49.

expanded form A way of writing a number that shows the
value of each digit.

The expanded form of 234 is 200 + 30 + 4.

expanded notation A way of writing a number as the sum of
the products of the digits and the place values of the digits.

In expanded notation 6753 is written
(6 ¥ 1000) + (7 ¥ 100) + (5 ¥ 10) + (3 ¥ 1).

experiment A test to find or illustrate a rule.

Flipping a coin and selecting an object from a collection of
objects are two experiments that involve probability.

exponent The upper number in an exponential expression;
it shows how many times the base is to be used as a factor.

base 53 exponent
53 means 5 ¥ 5 ¥ 5 and its value is 125.

exponential expression An expression that indicates that
the base is to be used as a factor the number of times shown
by the exponent.

43 = 4 ¥ 4 ¥ 4 = 64
The exponential expression 43 uses 4 as a factor 3 times. Its
value is 64.

face A flat surface of a geometric solid.

One face of the cube is shaded.
A cube has six faces.

fact family A group of three numbers related by addition
and subtraction or by multiplication and division.

The numbers 3, 4, and 7 are a fact family. They make these
four facts:

3+4=7 4+3=7 7–3=4 7–4=3

676 Saxon Math 6/5

factor (1) Noun: Any one of the numbers multiplied in a

multiplication problem.

2¥3=6 The factors in this problem are 2 and 3.

(2) Noun: A whole number that divides another whole
number without a remainder.

The numbers 2 and 3 are factors of 6.

(3) Verb: To write as a product of factors.

We can factor the number 6 by writing it as 2 ¥ 3.

Fahrenheit A scale used on some thermometers to measure
temperature.

On the Fahrenheit scale, water freezes at 32°F and boils at 212°F.

fraction A number that names part of a whole.

1 of the circle is shaded.
4

1 is a fraction.
4

frequency The number of times an event or outcome occurs.

Quiz Results

Number Correct Tally Frequency
0 0
1 1
2 4
3 7
4 10
5 3

This table shows the frequency of recent quiz scores.

frequency table A table that is used to tally and display the
number of times an event or outcome occurs.

Quiz Results

Number Correct Tally Frequency
0 0
1 1
2 4
3 7
4 10
5 3

This frequency table summarizes the class’s performance on
the most recent quiz.

Glossary 677

function A rule for changing an “in-number” to an “out-
number.”

IN F OUT This function uses the rule
“multiply by two.”
U

3N 6

C

4T 8

I

7 O 14

N

geometric sequence A sequence in which each term is
found by multiplying the previous term by a fixed amount.

¥3¥3 ¥3 ¥3 We multiply a term by 3 to find
the term that follows it in this
1, 3, 9, 27, 81, … geometric sequence.

geometric solid A shape that takes up space.

geometric solids not geometric solids

cube cylinder circle rectangle hexagon

geometry A major branch of mathematics that deals with
shapes, sizes, and other properties of figures.

Some of the figures we study in geometry are angles, circles,
and polygons.

graph (1) Noun: A diagram that shows data in an organized
way. See also bar graph, circle graph, line graph, and
pictograph.

Rainy Days Hair Colors of Students
8
6 Red
4
Days 2 Brown 2

Jan. Feb. Mar. Apr. 4
bar graph
Blond Black

4 6

circle graph

(2) Verb: To draw a point, line, or curve on a coordinate plane.

678 Saxon Math 6/5Frequency

greatest common factor (GCF) The largest whole number
that is a factor of two or more given numbers.

The factors of 20 are 1, 2, 4, 5, 10, and 20.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
The common factors of 20 and 30 are 1, 2, 5, and 10.
The greatest common factor of 20 and 30 is 10.

histogram A method of displaying a range of data. A
histogram is a special type of bar graph that displays data in
intervals of equal size with no space between bars.

Scores on Test

10
8

6 histogram

4
2
0

21–28 29–36 37–44 45–52 53–60
Score

horizontal Side to side; perpendicular to vertical.

oblique line vertical line

horizontal line not horizontal lines

icon A symbol used in a pictograph to represent data.

Consumed by Matt in One Day

Water
Soda
Milk
Juice

= 1 cup = 8 ounces

Each icon in the pictograph represents 1 cup of liquid that
Matt consumed.

identity property of addition The sum of any number and 0
is equal to the initial number. In symbolic form, a + 0 = a.
The number 0 is referred to as the additive identity.

The identity property of addition is shown by this statement:
13 + 0 = 13

Glossary 679

identity property of multiplication The product of any
number and 1 is equal to the initial number. In symbolic
form, a ¥ 1 = a. The number 1 is referred to as the
multiplicative identity.

The identity property of multiplication is shown by this
statement:

94 ¥ 1 = 94

improper fraction A fraction with a numerator greater than
or equal to the denominator.

4 2 These fractions are improper fractions.
3 2

integers The set of counting numbers, their opposites, and
zero; the members of the set {…, –2, –1, 0, 1, 2, …}.

–57 and 4 are integers. 15 and –0.98 are not integers.
8

International System of Units See metric system.

intersect To share a point or points.

These two lines intersect.
M They share the common point M.

intersecting lines Lines that cross.

intersecting lines

inverse operations Operations that “undo” one another.

a+b–b=a Addition and subtraction are
a–b+b=a inverse operations.

a ¥ b ÷ b = a (b ≠ 0) Multiplication and division are
a ÷ b ¥ b = a (b ≠ 0) inverse operations.

a2 = a (a ≥ 0) Squaring and finding square
( a )2 = a (a ≥ 0) roots are inverse operations.

680 Saxon Math 6/5

invert To switch the numerator and denominator of a
fraction.

If we invert the fraction H, we get 4 .
3

isosceles triangle A triangle with at least two sides of equal
length.

Two of the sides of
this isosceles triangle
have equal lengths.

leap year A year with 366 days; not a common year.

In a leap year February has 29 days.

least common multiple (LCM) The smallest whole number
that is a multiple of two or more given numbers.

The multiples of 4 are 4, 8, 12, 16, 20, ….
The multiples of 6 are 6, 12, 18, 24, 30, ….
The least common multiple of 4 and 6 is 12.

legend A notation on a map, graph, or diagram that
describes the meaning of the symbols and/or the scale used.

kitchen The legend of this scale

living/dining F inch = 5 feet drawing shows that 1 inch
4
bath represents 5 feet.

length A measure of the distance between any two points.

3 in.

The length of this nail is 3 inches.

line A straight collection of points extending in opposite
directions without end.

AB
line AB or line BA

Glossary 681

line graph A graph that connects points to show how
information changes over time.

Carl’s Weight

Weight (pounds) 40 line graph
30
20
10

12 34
Age (years)

line of symmetry A line that divides a figure into two halves
that are mirror images of each other.

lines of symmetry not lines of symmetry

line plot A method of plotting a set of numbers by placing a
mark above a number on a number line each time it occurs in
the set.

X This is a line plot of the
X numbers 5, 8, 8, 10, 10,
X X XX X 11, 12, 12, 12, 12, 13, 13,
X X XXXXX XXXX 14, 16, 17, 17, 18, and 19.

0 5 10 15 20

line segment A part of a line with two distinct endpoints.

A B AB is a line segment.

lowest terms A fraction is in lowest terms if it cannot be
reduced.

In lowest terms, the fraction 8 is 2 .
20 5

mean See average.

measure of central tendency A value that describes a
property of a list of data, such as the middle number of the
list or the number that appears in the list most often. See also
mean, median, and mode.

1, 3, 5, 6, 8, 9, 13 The median of this set is 6.
The median of a set is one
measure of central tendency.

682 Saxon Math 6/5

median The middle number (or the average of the two
central numbers) of a list of data when the numbers are
arranged in order from the least to the greatest.

1, 1, 2, 4, 5, 7, 9, 15, 24, 36, 44

In this list of data 7 is the median.

metric system An international system of measurement in
which units are related by a power of ten. Also called
International System.

Centimeters and kilograms are units in the metric system.

millennium A period of one thousand years.

The years 2001–3000 make up one millennium.

mixed number A whole number and a fraction together.

The mixed number 2C means “two and one third.”

mode The number or numbers that appear most often in a
list of data.

5, 12, 32, 5, 16, 5, 7, 12

In this list of data the number 5 is the mode.

multiple A product of a counting number and another number.

The multiples of 3 include 3, 6, 9, and 12.

mutually exclusive Categories are mutually exclusive if
each data point can be placed in one and only one of the
categories.

When flipping one coin, the categories are “landing heads-up”
and “landing tails-up.” One coin cannot land both heads-up
and tails-up on the same toss. Thus, the categories “landing
heads-up” and “landing tails-up” are mutually exclusive.

negative numbers Numbers less than zero.

–15 and –2.86 are negative numbers.
19 and 0.74 are not negative numbers.

number line A line for representing and graphing numbers.
Each point on the line corresponds to a number.

number line

–2 –1 0 1 2 3 4 5

Glossary 683

numeral A symbol or group of symbols that represents a
number.

4, 72, and A are examples of numerals.
“Four,” “seventy-two,” and “one half” are words that name
numbers but are not numerals.

numerator The top number of a fraction; the number that
tells how many parts of a whole are counted.

1 The numerator of the fraction is 1. One
4 part of the whole circle is shaded.

oblique (1) Slanted or sloping; not horizontal or vertical.

horizontal line vertical line

oblique line not oblique lines

(2) Lines in the same plane that are neither parallel nor
perpendicular.

perpendicular

lines parallel lines

oblique lines not oblique lines

obtuse angle An angle whose measure is more than 90° and
less than 180°.

right angle acute angle

obtuse angle not obtuse angles

An obtuse angle is larger than both a right angle and an
acute angle.

obtuse triangle A triangle whose largest angle measures
more than 90° and less than 180°.

acute right
triangle triangle

obtuse triangle not obtuse triangles

684 Saxon Math 6/5

odd numbers Numbers that have a remainder of 1 when
divided by 2; the numbers in this sequence: 1, 3, 5, 7, 9, 11, ....

Odd numbers have 1, 3, 5, 7, or 9 in the ones place.

operations of arithmetic The four basic mathematical
operations: addition, subtraction, multiplication, and division.

1 + 9 21 – 8 6 ¥ 22 3 ÷ 1

the operations of arithmetic

ordinal numbers Numbers that describe position or order.

“First,” “second,” and “third” are ordinal numbers.

origin (1) The location of the number 0 on a number line.

–3 –2 –1 0 1 2 3
origin on a number line

(2) The point (0,0) on a coordinate plane.

y

2 origin on a
1 coordinate plane

– 2 ––11 x
–2
12

outcome Any possible result of an experiment.

When rolling a number cube, the possible outcomes are 1, 2, 3,
4, 5, and 6.

outlier A number that is distant from most of the other
numbers in a list of data.

In the data at right the number 28 1, 5, 4, 3, 6, 28, 7, 2
is an outlier, because it is distant
from the other numbers in the list.

parallel lines Lines that stay the same distance apart; lines
that do not cross.

parallel lines

Glossary 685

parallelogram A quadrilateral that has two pairs of parallel
sides.

parallelograms not a
parallelogram

parentheses A pair of symbols used to set apart parts of an
expression so that those parts may be evaluated first: ( ).

15 – (12 – 4)

In the expression 15 – (12 – 4), the parentheses indicate
that 12 – 4 should be calculated before subtracting the result
from 15.

partial product When multiplying using pencil and paper,
a product resulting from multiplying one factor by one digit
of the other factor. The final product is the sum of the shifted
partial products.

53 partial products
¥ 26

318
106
1378

percent A fraction whose denominator of 100 is expressed
as a percent sign (%).

99 = 99% = 99 percent
100

perfect square The product when a whole number is
multiplied by itself.

The number 9 is a perfect square because 3 ¥ 3 = 9.

perimeter The distance around a closed, flat shape.

10 in. A

6 in. 6 in. The perimeter of this rectangle
(from point A around to point A)
is 32 inches.

10 in.

period The number of terms in a repeating unit of a sequence.

4, 1, 3, 5, 4, 1, 3, 5, 4, ...

The repeating unit of this sequence is “4, 1, 3, 5.” There are four
terms in the repeating unit. The period of this sequence is four.

686 Saxon Math 6/5

permutation One possible arrangement of a set of objects.

2431
The arrangement above is one possible permutation of the
numbers 1, 2, 3, and 4.

perpendicular lines Two lines that intersect at right angles.

perpendicular lines not perpendicular lines

pictograph A graph that uses symbols to represent data.

Stars We Saw

Tom

Bob This is a pictograph.
Sue It shows how many stars
Ming each person saw.

Juan

pie graph See circle graph.

place value The value of a digit based on its position within
a number.

341 Place value tells us that 4 in 341 is worth “4 tens.”
23 In addition problems, we align digits with the same
place value.
+7
371

plane A flat surface that has no boundaries.

The flat surface of a desk is part of a plane.

plane figure A flat shape.

plane figures not a plane figure

p.m. The period of time from noon to just before midnight.

I go to bed at 9 p.m., which is 9 o’clock at night.

point An exact position.

A This dot represents point A.

Glossary 687
polygon A closed, flat shape with straight sides.

polygons not polygons

positive numbers Numbers greater than zero.

0.25 and 157 are positive numbers.
–40 and 0 are not positive numbers.

power (1) The value of an exponential expression.

16 is the fourth power of 2 because 24 = 16.

(2) An exponent.

The expression 24 is read “two to the fourth power.”

prime number A counting number greater than 1 whose
only two factors are the number 1 and itself.

7 is a prime number. Its only factors are 1 and 7.
10 is not a prime number. Its factors are 1, 2, 5, and 10.

probability A way of describing the likelihood of an event;
the ratio of favorable outcomes to all possible outcomes.

The probability of rolling a 3 with a standard number cube is O.

product The result of multiplication.

5 ¥ 4 = 20 The product of 5 and 4 is 20.

proper fraction A fraction whose denominator is greater
than its numerator.

H is a proper fraction.

4 is an improper fraction.
3

property of zero for multiplication Zero times any number
is zero. In symbolic form, 0 ¥ a = 0.

The property of zero for multiplication tells us that
89 ¥ 0 = 0.

protractor A tool used to measure and draw angles.

60 70 80 90 100 110 120
50130 120 110 100 90 80 70

60 50130
14040 30
30 150 protractor
150 14040

20160 160
20

10 170
170 10

0 180
180 0

688 Saxon Math 6/5
pyramid A three-dimensional solid with a polygon as its
base and triangular faces that meet at a vertex.

pyramid

quadrilateral Any four-sided polygon.

Each of these polygons has 4 sides. They are all quadrilaterals.

quotient The result of division.

12 ÷ 3 = 4 4 12 = 4 The quotient is 4 in
3 12 3 each of these problems.

radius (Plural: radii) The distance from the center of a circle
to a point on the circle.

2 in. The radius of this circle is 2 inches.

range The difference between the largest number and the
smallest number in a list.

5, 17, 12, 34, 29, 13

To calculate the range of this list, we subtract the smallest
number from the largest number. The range of this list is 29.

ratio A comparison of two numbers by division.

There are 3 triangles and 5 stars.
The ratio of triangles to stars is
“three to five,” or 53.

ray A part of a line that begins at a point and continues
without end in one direction.

AB

ray AB

Glossary 689

reciprocals Two numbers whose product is 1.

3 4 12 Thus, the fractions 3 and 4 are
4 3 12 4 3
¥ = =1 reciprocals. The reciprocal of

3 is 34.
4

rectangle A quadrilateral that has four right angles.

rectangles not rectangles

rectangular solid A three-dimensional solid having six
rectangular faces. Adjacent faces are perpendicular and
opposite faces are parallel.

rectangular solid

reduce To rewrite a fraction in lowest terms.

If we reduce the fraction ë, we get H.

reflection Flipping a figure to produce a mirror image.

reflection

reflective symmetry A figure has reflective symmetry if it
can be divided into two halves that are mirror images of each

Dother. See also line of symmetry.
F

These figures have reflective symmetry. These figures do not
have reflective symmetry.

regular polygon A polygon in which all sides have equal
lengths and all angles have equal measures.

regular polygons not regular polygons

690 Saxon Math 6/5

relative frequency table A frequency table in which the
frequencies for all categories are displayed as the numerator
of a fraction with the total number of outcomes as the
denominator.

Outcome Tally Relative
1 Frequency
2 2
1 3 17
50
3
28
50

5
50

This relative frequency table shows data obtained by
spinning the spinner at left 50 times.

remainder An amount left after division.

7R1 When 15 is divided by 2,
there is a remainder of 1.
2 15
14

1

rhombus A parallelogram with all four sides of equal length.

rhombuses not rhombuses

right angle An angle that forms a square corner and
measures 90°. It is often marked with a small square.

obtuse angle acute angle

right angle not right angles

A right angle is larger than an acute angle and smaller than an
obtuse angle.

right triangle A triangle whose largest angle measures 90°.

acute obtuse
triangle triangle

right triangle not right triangles

Roman numerals Symbols used by the ancient Romans to
write numbers.

The Roman numeral for 3 is III.

The Roman numeral for 13 is XIII.

Glossary 691
rotation Turning a figure about a specified point called the
center of rotation.

rotation

rotational symmetry A figure has rotational symmetry if it
can be rotated less than a full turn and appear in its original
orientation.

SZ M

These figures have rotational symmetry. These figures do not
have rotational symmetry.

round To express a calculation or measure to a specific
degree of accuracy.

To find about how many hundred feet make a mile, we round
5280 feet to 5300 feet.

round number A whole number that ends with one or more
zeroes.

100, 20, 570, and 6380 are round numbers.

101, 30.2, 573, and 6384 are not round numbers.

scale (1) A type of number line used for measuring.

cm 1 2 3 4 5 6 7

The distance between each mark on this ruler’s scale is
1 centimeter.

(2) A ratio that shows the relationship between a scale model
and the actual object.

If a model airplane is 1 the size of the actual airplane, the
24

scale of the model is 1 to 24.

scale drawing A two-dimensional representation of a larger
or smaller object.

Blueprints and maps are examples of scale drawings.

scale model A three-dimensional rendering of a larger or
smaller object.

Globes and model airplanes are examples of scale models.