Answer Key
Chapter 5 – Number Patterns and Fractions 5.1 Factor Pairs Answers 1. 1, 12, 2, 6, 3, 4
2. 1, 10, 2, 5
3. 1, 15, 3, 5
4. 1, 16, 2, 8, 2, 28, 4, 14
5. 1, 56, 7, 8, 2, 28, 4, 14
6. 1, 18, 2, 9, 3, 6
7. 1, 20, 2, 10, 4, 5
8. 1, 22, 2, 11
9. 1, 23
10. 1, 25, 5
11. 1, 27, 3, 9
12. 1, 31
13. 1, 81, 9, 3, 27
14. 1, 48, 2, 24, 3, 16, 4, 12, 6, 8
15. 1, 24, 2, 12, 3, 8, 4, 6
16. 1, 30, 2, 15, 3, 10, 5, 6
5.2 Divisibility Rules to Find Factors Answers 1. Yes, sum of digits is divisible by 3 2. yes, even number 3. no, not divisible by 2 and 3 4. no – sum of digits is not divisible by 3 5. yes, multiple of 9 x 3 6. no, sum of digits is not divisible by 9 7. yes, last digit is even, sum of the digits is divisible by 3 8. yes, last two digits are divisible by 4 9. yes, ends in zero 10. no, doesn’t work with the rule 11. not 6, last number is not divisible by 3 12. yes 13. yes 14. yes, last digit is even 15.yes, sum of digits is divisible by 3 16. yes, ends in zero
Middle School Math Concepts - Grade 6
1
Answer Key
Chapter 5 – Number Patterns and Fractions 5.3 Prime and Composite Numbers Answers 1. composite
2. Composite
3. Composite
4. Composite
5. Composite
6. composite
7. Composite
8. Composite
9. Prime
10. Composite
11. composite
12. Prime
13. Composite
14. Composite
15. Composite
16. composite
5.4 Prime Factorization Answers 1. 23 x 7
2. 7 x 2
3. 112
4. 3 x 22 x 7
5. 52 x 2
6. 26
7. 22 x 23
8. 24
9. 23 x 3
10. 52 x 22 x 3
11. 27
12. 23 x 3 x 13
13. 52 x 7 x 3
14. 132
15. 3 x 71
5.5 Greatest Common Factor using Lists Answers 1. 3
2. 4
3. 2
4. 2
5. 6
6. None
7. 5
8. 11
9. 12
10. 15
11. None
12. 7
13. 9
14. 10
15. 11
16. None
17. 15
18. 7
19. None
20. 18
5.6 Greatest Common Factor using Factor trees Answers 1. 14
2. 2
3. 4
4. 12
5. 12
6. 9
7. 40
8. 33
9. 3
10. 63
11. None
12. 30
13. 8
14. 21
15. 8
Middle School Math Concepts - Grade 6
2
Answer Key
Chapter 5 – Number Patterns and Fractions
5.7 Equivalent Fractions Answers Many possible answers – here is one option 1. 3/6
2. 3/9
3. 25/100
4. 2/10
5. 4/6
6. 4/10
7. 75/100
8. 6/20
9. 4/18
10. 4/14
11. YES
12. NO
13. NO
14. YES
15. YES
5.8 Fractions in Simplest form Answers 1. 4/5
2. 2/5
3. 1/5
4. 1/6
5. 1/4
6. 4/9
7. 1/4
8. 1/2
9. 1/3
10. 1/4
11. 4/9
12. 9/10
13. 2/5
14. 11/20
15. 5/9
5.9 Common Multiples Answers 1. 3, 6, 9, 12, 15
2. 5, 10, 15, 20, 25
3. 6, 12, 18, 24, 30
4. 7, 14, 21, 28, 35
5. 8, 16, 24, 32, 40
6. 15, 30
7. 6, 12
8. 12, 24
9. 6, 12
10. 9, 18
11. 35, 70
12. 12, 24
13. 30, 60
14. 60, 120
15. 40, 80
5.10
Least Common Multiple
Answers 1. 15 6. 35
2. 6
3. 12
4. 6
5. 9
7. 12
8. 30
9. 60
10. 40
Middle School Math Concepts - Grade 6
3
Answer Key
Chapter 5 – Number Patterns and Fractions
5.11
Fraction Comparison with Lowest Common Denominator
Answers 1. 2/10
2. 6/10
3. 5/10
4. 8/10
5. 3/9
6. 12/18
7. 15/18
8. 4/14
9. 16/36
10. 36/48
11. 6
12. 20
13. 15
14. 14
15. 8
16. 12
17. 40
18. 60
19. 18
20. 42
21. >
22. >
23. =
24. <
25. =
5.12
Fraction Ordering with Lowest Common Denominator
Answers 1. 1/3, 4/9, 5/6
2. 1/4, 2/3, 6/7
3. 2/3, 4/5, 6/6
4. ½, 3/5 2/3
5. ¼, 2/7, 3/6
6. 1/6, 2/9, 2/5
7. 4/16, 3/7, 4/5
8. ¾, 4/5, 9/10
9. ½, 2/3, 4/5
10. 2/3, ¾, 9/11
11. 1/5, 3/8, 4/7
12. 1/3, 2/5, 6/7
13. 1/3, 4/5, 7/8
14. 1/6, 2/4, 4/5
15. 1/9, 2/9, 4/7, 7/8
5.13
Length Measurements to a Fraction of an Inch
Answers 1-5 Answers will vary
5.14
Mixed Numbers as Improper Fractions
Answers 1. 5/2
2. 13/4
3. 16/3
4. 14/3
5. 25/4
6. 32/5
8. 42/5
9. 39/5
10. 58/7
11. 35/4
12. 59/6
13. 53/8
14. 29/3
15. 11/2
16. 65/4
Middle School Math Concepts - Grade 6
7. 22/3
4
Answer Key
Chapter 5 – Number Patterns and Fractions
5.15
Improper Fractions as Mixed Numbers
Answers 1. 7 1/3
2. 8 4/5
3. 4 2/3
4. 3 ½
5. 3 1/3
6. 5 2/9
7. 7 1/7
8. 7 ½
9. 5 3/8
10. 3 4/5
11. 5 4/7
12. 7 ½
13. 1 4/7
14. 5 1/5
15. 11 1/8
16. 5
5.16
Fraction and Mixed Number Comparison
Answers 1. >
2. <
3. <
4. <
5. =
6. =
7. >
8. <
9. >
10. >
12. =
13. >
14. >
15. >
11. =
5.17
Decimals as Fractions
Answers 1. 67/100
2. 33/100
3. 45/100
4. 27/100
5. 56/100
6. 7/10
7. 98/100
8. 32/100
9. 4/100
10. 7/100
11. 56/1000
12. 897/1000
5.18
13. 372/1000
14. 652/1000
15. 32/1000
Decimals as Mixed Numbers
Answers 1. 3/12
2. 2 2/5
3. 13 1/5
4. 3/5
5. 3 9/20
6. 7 17/100
7. 18 9/50
8. 9 1/5
9. 7 13/20
10. 13 11/100
11. 7 ¼
12. 9 ¾
13. 10 1/10
14. 4 33/100
15. 8 11/50
Middle School Math Concepts - Grade 6
5
Answer Key
Chapter 5 – Number Patterns and Fractions
5.19
Fractions as Decimals
Answers 1. .3
2. .23
3. .09
4. .8
5. .182
6. .25
7. .6
8. .125
9. .1
10. .02
11. .5
12. .25
13. .75
14. .5
5.20
15. .6
Mixed Numbers as Decimals
Answers 1. 4.1
2. 6.8
3. 14.06
4. 7.18
5. 12.9
6. 24.11
7. 8.19
8. 5.5
9. 4.5
10. 7.33
11. 5.2
12. 9.125
13. 10.02
14. 46.25
15. 65.8
5.21
Repeating Decimals
Answers 1. Repeating
2. Repeating
3. Repeating
4. Terminating
5. Repeating
6. Terminating
7. Repeating
8. Terminating
9. Repeating
10. Terminating
11. Terminating
12. Repeating
13. Terminating
14. Terminating
15. Terminating
Middle School Math Concepts - Grade 6
6