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Answer Key
Page 1
1. 9
3. 1
2. 7
4. 6
Page 2
5. 7 8 15
8 7 15
15 7 8
15 8 7
6. 9 2 11
2 9 11
11 9 2
11 2 9
7. 6 8 14
8 6 14
14 6 8
14 8 6
8. 40 50 90
50 40 90
90 40 50
90 50 40
9. 60 50 110
50 60 110
110 60 50
110 50 60
10. 79 21 100
21 79 100
100 79 21
100 21 79
11. 9
12.
13. 5
14.
15. 9
16.
17. 25
18.
19. 37
15. k 70 35;
16. m 85 60;
Page 5
1. 8
3. 11
5. 40
7. 180
Page 6
8. 28
10. 40
12. 11
14. 14
16. 8
18. 22
20. 148
22. 60
24. a b
26. b a
6
17
22
18
Page 3
1. a 25 3;
2. b 49 39;
3. c 70 57;
4. x 75 25;
5. n 100 11;
a 22
b 10
c 13
x 50
n 89
Page 4
6. a 30 7;
7. b 87 67;
8. c 90 50;
9. d 100 75;
10. e 100 47;
11. f 125 25;
12. g 35 15;
13. h 100 45;
14. j 80 62;
a 23
b 20
c 40
d 25
e 53
f 100
g 20
h 55
j 18
© CSL Associates, Inc. (877) 790-7915
k 35
m 25
2. 9
4. 18
6. 40
9.
11.
13.
15.
17.
19.
21.
23.
25.
35
280
19
27
23
65
125
155
ab
Page 7
1. The sum of 3 plus 8 is the same
as the sum of 5 plus 6.
2. The product of 2 times 9 is the
same as the product of 3 times 6.
3. The difference of 15 minus 5 is
the same as the difference of
20 minus 10.
4. The quotient of 20 divided by
5 is the same as the quotient of
12 divided by 3.
Page 8
5. The product of 3 times 8 is the
same as the product of 4 times 6.
6. The sum of 2 plus 9 is the same
as the sum of 5 plus 6.
7. The quotient of 15 divided by
5 is the same as the quotient of
21 divided by 7.
8. The difference of 20 minus 5 is
the same as the difference of
32 minus 17.
9. a, c
10.
b, d
11. a, b
12.
a, d
13. a, b, d
14.
a, d
Page 9
1. true;
2. false;
3. true;
4. false;
28
24
24
61
≠
≠
28
23
24
60
Page 10
5. false;
18 ≠ 16
6. true;
60 60
7. false;
24 ≠ 28
8. true;
130 130
9. false;
71 ≠ 69
10. true;
40 40
11. true;
192 192
12. true;
17 17
13. 58 103
14. 87 61
15. 2 37
16. 3 3 3
17. 120 34
18. 5 13
Page 11
1. 3. Page 12
5. ;
6. ;
7. ;
8. ;
9. ;
10. ;
11. ;
12. ;
13. ;
14. ;
15. ;
16. ;
17. true
19. false
21. true
2. 4. 60 64
30 = 30
32 = 32
13 17
35 42
25 24
72 80
16 14
216 288
69 73
48 48
82 81
18. false
20. false
22. false
Page 13
1. 22 15 7
22 7 15
2. 15 20 35
20 15 35
3. 72 ÷ 12 6
72 ÷ 6 12
4. 7 20 140
20 7 140
Page 14
5. 42 24 18
42 18 24
6. 153 ÷ 17 9
153 ÷ 9 17
ARITHMETIC TO ALGEBRA
IL Workbook R
59
Answer Key
7. 26 32 58
32 26 58
8. 65 38 27
65 27 38
9. 4 39 156
39 4 156
10. 19 54 73
54 19 73
11. 184 ÷ 23 8
184 ÷ 8 23
12. 5 35 175
35 5 175
13. Checks
14. Wrong 706 349 357
15. Checks
16. Wrong 582 769 1,351
17. Checks
18. Wrong 245 164 81
19. c a b or c b a
20. t ÷ r s or t ÷ s r
Page 15
1. 1, 12,
2, 6
2. 1, 28
2, 14,
3. 2 2 2 = 8
4. 5 5 = 25
3, 4
4, 7
Page 16
5. Check students’ arrays:
1 dot by 16 dots; 2 dots by 8
dots; 4 dots by 4 dots
6. Check students’ arrays:
1 dot by 18 dots; 2 dots by 9
dots; 3 dots by 6 dots
7. Check students’ arrays:
1 dot by 23 dots
8. Check students’ arrays:
1 dot by 36 dots; 2 dots by
18 dots; 3 dots by 12 dots;
4 dots by 9 dots; 6 dots by 6
dots
9. 1, 2, 5, 10
10. 1, 3, 5, 15
11. 1, 17
12. 1, 2, 4, 5, 10, 20
13. 1, 5, 25
14. 1, 2, 4, 8, 16, 32
15. 1, 2, 3, 4, 6, 8, 12, 16,
24, 48
16. 1, 2, 4, 8, 16, 32, 64
17. 2 2 2 2 16
60
IL Workbook R
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
5 5 5 125
3 3 3 27
4 4 16
6 6 6 216
3 3 3 3 81
10 10 100
10 10 10 10 10,000
34
62
93
105
Page 17
1. 1, 7;
prime
2. 1, 2, 5, 10;
composite
3. 1, 17;
prime
4. 1, 3, 7, 21;
composite
5. 1, 23;
prime
6. 1, 3, 9, 27;
composite
7. 2 2 2 or 23
8. 2 2 5 or 22 5
Page 18
9. 1, 5; prime
10. 1, 2, 3, 6; composite
11. 1, 3, 9; composite
12. 1, 11; prime
13. 1, 2, 7, 14; composite
14. 1, 19; prime
15. 1, 5, 25; composite
16. 1, 31; prime
17. 1, 3, 11, 33; composite
18. 2 2 3 or 22 3
19. 2 3 3 or 2 32
20. 2 2 7 or 22 7
21. 2 2 2 5 or 23 5
22. 1 41
23. 2 2 2 7 or 23 7
24. 3 3 3 3 or 34
25. 2 2 5 5 or 22 52
Page 19
1.
3
7
2.
3
5
ARITHMETIC TO ALGEBRA
Page 20
3.
3
8
4.
9
10
5.
223
2225
3
25
3
10
6.
235
2233
5
23
5
6
7.
227
7
2235
35
8.
335
357
3
7
9.
333
2233
3
22
10.
235
2355
1
5
11.
237
77
23
7
12.
2233
337
13.
6
7
22
7
2223
2235
2
5
14.
255
557
2
7
15.
77
257
7
25
7
10
16.
333
355
33
55
9
25
17.
22223
35
2222
5
18.
337
235
7
15
3
4
4
7
16
5
37
25
Page 21
1. factors of 4: 1, 2, 4
factors of 10: 1, 2, 5,
GCF 2
2. factors of 9: 1, 3, 9
factors of 12: 1, 2, 3,
GCF 3
3. factors of 15: 1, 3, 5,
factors of 21: 1, 3, 7,
CGF 3
21
10
10
4, 6, 12
15
21
Page 22
4. factors of 9: 1, 3, 9
factors of 15: 1, 3, 5, 15
GCF 3
5. factors of 6: 1, 2, 3, 6
factors of 18: 1, 2, 3, 6, 9, 18
GCF 6
© CSL Associates, Inc. (877) 790-7915
Answer Key
6. factors of 5: 1, 5
factors of 18: 1, 2, 3, 6, 9, 18
GCF 1
7. factors of 16: 1, 2, 4, 8, 16
factors of 20: 1, 2, 4, 5, 10,
20
GCF 4
8. 36 2 2 3 3
48 2 2 2 2 3
GCF 12
9. 40 2 2 2 5
80 2 2 2 2 5
GCF 40
10. factors of 18: 1, 2, 3, 6, 9, 18
factors of 36: 1, 2, 3, 4, 6, 9,
12, 18, 36
factors of 72: 1, 2, 3, 4, 6,
9, 12, 18, 24, 36, 72
GCF 18
11. factors of 20: 1, 2, 4, 5, 10,
20
factors of 30: 1, 2, 3, 5, 6,
10, 15, 30
factors of 50: 1, 2, 5, 10, 25,
50
GCF 10
Page 23
1. yes
3. no
2. yes
Page 24
4. yes
6. yes
8. yes
10. 36
12. 18
14. 144
16. 36
18. 30
5.
7.
9.
11.
13.
15.
17.
19.
Page 25
1. n 3
Page 26
3. n 5. n 7. n 9. n 11. n 13. n 15. n 5
4
5
9
6
9
8
yes
yes
no
90
80
80
75
24
2. n 4
4.
6.
8.
10.
12.
14.
n
n
n
n
n
n
3
4
8
3
4
10
© CSL Associates, Inc. (877) 790-7915
Page 27
1. 9n = 54;
2. 12n = 36;
3. n = 2 x 12;
4. n = 27 x 3;
5. 25n = 75;
6. n = 2 x 8;
n
n
n
n
n
n
6
3
24
81
3
16
Page 28
7. 54 = 2n;
8. n = 4 x 20;
9. 112 = 8n;
10. n = 3 x 12;
11. 125 = 25n;
12. n = 2 x 18;
13. n = 6 x 15;
14. 5n = 45;
15. 25n = 150;
16. n = 73 - 45;
17. n = 84/14;
18. n = 16 + 82;
19. n = 23 - 18;
20. n = 7 x 32;
21. n = 91/13;
n
n
n
n
n
n
n
n
n
n
n
n
n
n
n
27
80
14
36
5
36
90
9
6
28
6
98
5
224
7
Page 30
1. Commutative Property of
Addition
2. Identity Property of Addition
3. Associative Property of Addition
4. Additive Inverse Property
5. Commutative Property of
Addition
6. Commutative Property of
Addition
7. –3
8. 5
9. 10
10. 0
11. –45
12. 52
13. –18
14. 0
15. 39
16. –30
17. 80
Page 32
1. Commutative Property of
Multiplication
2. Associative Property of
Multiplication
3. Zero Property of Multiplication
4. Commutative Property of
Multiplication
5. Commutative Property of
Multiplication
6. Identity Property of
Multiplication
7. –3
8. 5
9. 0
10. 1
11. –45
12. 52
13. 1
14. –64
15. 540
16. 0
17. 700
Page 33
1. Identity Property of Division
2. Division Property of 0
3. Identity Property of Division
4. Identity Property of Division
5. Identity Property of Division
6. Identity Property of Division
Page 34
7. 1
8. 1
9. 0
10. 1
11. 1
12. 0
13. 0
14. 76
15. 1
16. 67
17. Identity Property of Addition
18. Associative Property of
Multiplication
19. Identity Property of Division
20. Commutative Property of
Addition
21. Identity Property of
Multiplication
22. Division Property of 0
23. Associative Property of
Addition
24. Multiplication Property of 0
Page 35
1. 10
3. 12
5. 2
Page 36
7. 9
9. 15
11. 17
13. –10
15. –23
17. 77
19. 16
21. 60
23. 5
25. 6
ARITHMETIC TO ALGEBRA
2. 2
4. 7
6. 8
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
2
7
30
12
61
50
24
3
72
180
IL Workbook R
61
Answer Key
27.
29.
31.
33.
35.
37.
39.
41.
43.
45.
47.
49.
51.
53.
29
94
6
17
2
26
0
5
14
64
13
4
40
21
28.
30.
32.
34.
36.
38.
40.
42.
44.
46.
48.
50.
52.
54.
26
120
14
120
200
20
18
6
4
128
32
2
80
1
Page 37
1. 3. 5. 7. 9. 2.
4.
6.
8.
Page 38
10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 11.
13.
15.
17.
19.
21.
23.
25.
27.
29.
31.
33.
35.
Page 39
1. 7 9
3. 17 3
Page 40
5. 15 7
7. 5 9
9. 17 9
11. 15
13. 16
15. 42
17. 5
19. 1
21. 1
62
IL Workbook R
2. 52
4. 9 7
6.
8.
10.
12.
14.
16.
18.
20.
22.
65
23
96
13
39
7
3
2
2
23.
24.
25.
26.
16 (7 5) 4
(16 7) 5 14
(54 ÷ 3) 6 108
54 ÷ (-3 6) 3
Page 41
1. 12 d
2. 12 ÷ 10
3. 12 10
Page 44
5. 4
7. 12
9. 8
11. 7
13. yes
15. no
17. n 19. n 21. n 23. n 2
23
17
8
Page 45
1. divide
3. multiply
Page 46
5. 6
7. 12
9. 2
11. 7
Page 48
7. yes
9. yes
11. n 13. n 15. n 17. n 19. n 2. add
4. subtract
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
8
7
6
12
no
yes
n
n
n
n
20
12
2
61
2. multiply
4. divide
6.
8.
10.
12.
8
5
6
12
ARITHMETIC TO ALGEBRA
no
yes
yes;
no
n
n
n
n
80
5
60
25
18.
20.
22.
24.
n
n
n
n
8.
10.
12.
14.
16.
18.
20.
no
no
n
n
n
n
n
4
3
360
240
Page 47
1. Add 5.
2. Subtract 9.
3. Add 1.
4. Subtract 6.
5. Subtract 7.
6. Add 10.
Page 42
4. 5 12
5. 20 4
6. 15 20
7. 4 8
8. 8 ÷ 4
9. 300 20
10. 5 n
11. 5n
12. 16 n or n 16
13. 3t
14. 2(n 3)
15. 2n 3
16. (n 5)/2 or n + 5/2
17. 5n 6
18. m d
19. np
Page 43
1. subtract
3. add
13.
14.
15.
16.
17.
19.
21.
23.
3
4
9
9
24
16
2
20
4
4
Page 49
1. 3(17) 24 27
51 51
2. 5(6) 20 10
30 30
3. 2(13) 12 14
26 26
4. 6(13) 54 24
78 78
Page 50
5. 5(7) 25 10
35 35
6. 8(9) 72 0
72 72
7. 2(10) 8 12
20 20
8. 6(13) 30 48
78 78
9. y 8
10.
11. y 8
12.
13. y 7
14.
15. y 2
16.
17. y 4
18.
19. y 4
20.
21. y 3
22.
y
y
y
y
y
y
y
4
3
5
3
8
5
6
© CSL Associates, Inc. (877) 790-7915
Answer Key
Page 52
1. 5 d 22
2. 3n 6
3. m/2 9
4. t 2 5
5. 5s 80; 16 stamps
6. c 8 22; 14 candles
7. m 2.2 4.5; 2.3 miles
8. t/3 2; 6 hours
9. 2c 80; $40
10. 85 m 140; $55
Page 54
1.
2.
3.
4.
5.
6.
x
y
0
1
2
3
5
6
7
8
x
y
0
1
2
3
1
0
1
2
x
y
0
1
2
3
0
3
6
9
x
y
0
1
2
3
1
3
5
7
x
y
0
1
2
3
0
1
112
x
y
0
1
2
3
3
0
3
6
1
2
© CSL Associates, Inc. (877) 790-7915
7. (0, 7), (2, 9), (4, 11), (6, 13)
8. (0, 2), (2, 0), (4, 2), (6, 4)
9. (0, 0), (2, 10), (4, 20),
(6, 30)
10. (0, 0), (2, 2/3), (4, 1 1/3), (6,
2)
11. (0, 1), (2, 3), (4, 7), (6, 11)
12. (0, 2), (2, 6), (4, 10), (6, 14)
13. yes
14. yes
15. no
16. no
17. yes
18. yes
19. no
20. yes
Page 55
1.
8
7
6
5
4
3
2
1
–4 –3 –2 –1 0 1 2 3 4 5 6
–1
–2
–3
y
8
7
6
5
4
3
2
1
–4 –3 –2 –1 0 1 2 3 4 5 6
–1
–2
–3
x
2. no
3. yes
Page 56
4.
8
5. yes
6. no
7.
x
11. no
12. yes
Page 57
1. 150 miles
2. 35 square inches
y
7
6
5
4
3
2
1
–4 –3 –2 –1 0 1 2 3 4 5 6
–1
–2
–3
x
8. no
9. yes
10.
y
6
5
4
3
2
1
–4 –3 –2 –1 0 1 2 3 4 5
–1
–2
y
x
Page 58
3. 600 miles per hour
4. 220 miles
5. 5 hours
6. 24 square feet
7. 32 inches
8. 4.25 square centimeters
9. 13.95 square meters
10. 2 inches
11. 12 inches
12. 6 feet
13. 10 inches
14. 2
ARITHMETIC TO ALGEBRA
3
16
square inches
IL Workbook R
63