1i) a.

1g) Answers will vary: ones', tens', or hundreds' place.

1f) Answers will vary.

2i) a.

2g) Answers will vary.

2f) Answers will vary.

3i)

	0	1	2	3	4	5	6	7	8	9	10	11	12
0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9	10	11	12
2	0	2	4	6	8	10	12	14	16	18	20	22	24
3	0	3	6	9	12	15	18	21	24	27	30	33	36
4	0	4	8	12	16	20	24	28	32	36	40	44	48
5	0	5	10	15	20	25	30	35	40	45	50	55	60
6	0	6	12	18	24	30	36	42	48	54	60	66	72
7	0	7	14	21	28	35	42	49	56	63	70	77	84
8	0	8	16	24	32	40	48	56	64	72	80	88	96
9	0	9	18	27	36	45	54	63	72	81	90	99	108
10	0	10	30	30	40	50	60	70	80	90	100	110	120
11	0	11	22	33	44	55	66	77	88	99	110	121	132
12	0	12	24	36	48	60	72	84	96	108	120	132	144

3g)

1. b.
2. c.
3. a.

3f) Some patterns are:

• 0 times any number, or any number times 0, is 0.
• 1 times any number, or any number times 1, is that number.
• Diagonals between two identical factors are palindromes.

4i) b.

4g) a.

4f)

128 ounces ÷ 4 = 32 ounces in a quart

32 ounces ÷ 2 = 16 ounces in a pint

16 ounces ÷ 2 = 8 ounces in a cup

5i)

1. a.
2. c.
3. b.

5g)

1. 24 x 800 = 24 x 20 x 40 = 480 x 40 = 19,200
2. 32 x 1200 = 32 x 30 x 40 = 960 x 40 = 38,400
3. 15 x 1500 = 15 x 30 x 50 = 450 x 50 = 22,500

5f)

1. 30 days x 20 miles per day = 600 miles
2. 80 days x 20 miles per day = 3600 miles
3. 365 days x 20 miles per day = 7300 miles

6i)

1. b.
2. a.
3. c.
4. b.
5. a.
6. c.
7. b.

6g) Answers will vary. Students may not be able to do all of them.

6f)

1. ¹/₂ + ²/₅ = 50% + 40% = 90%
2. ¹/₄ + ¹/₂ = 25% + 50% = 75%
3. ³/₅ + ¹/₂ = 60% + 50% = 110%

7i)

1. b.
2. a.

7g)

1. c.
2. a.
3. b.

7f) Answers will vary.

8i) a.

8g) Answers will vary depending on the number of students in the class.

8f) Answers will vary depending on the number and ages of people in your family.

9i)

1. b.
2. a.

9g)

1. ten thousands' and tens'
2. one hundred millions' and one hundred thousands'
3. millions' and tens'

9f)

Number	Number in Words
10	ten
100	one hundred
1,000	one thousand
10,000	ten thousand
100,000	one hundred thousand
1,000,000	one million
10,000,000	ten million
100,000,000	one hundred million

10i)

1. b.
2. a.

10g)

Estimate: 1) 20 X 40 = 800; 2) 10 X 50 = 500; 3) 40 X 30 = 1200

Actual: 1) 24 X 36 = 864; 2) 12 X 48 = 576; 3) 42 X 29 = 1218

10f) Answers will vary. The estimates should be within about 100.

11i)

1. c.
2. a.
3. a.

11g) Answers will vary.

11f) Answers will vary. If your child has difficulty or incorrect answers, have him or her refer to the textbook and review the process with your child.

12i)

1. a.
2. c.

12g)

1. a.
2. c.
3. a.

12f) Answers will vary.

1. c.
2. a.
3. b.

13g)

1. 72 ÷ 3 = 24; so multiply by ²⁴/₂₄
2. 80 ÷ 5 = 16, and ¹⁶/₁₆ = 1; so ¹⁶/₈₀ = ¹/₅
3. 72 ÷ 5 = 12; so multiply by ¹²/₁₂
   (1) + (3) = ⁴⁸/₇₂ + ¹²/₇₂ = ⁶⁰/₇₂ or ⁵/₆

13f) ¹/₂, ²/₄, ³/₆; ⁴/₅, ⁸/₁₀, ¹²/₁₅; ²/₃, ⁴/₆, ⁶/₉

To write an equivalent fraction, multiply both parts by the same number. For example, ¹/₂ X ²/₂ = ²/₄.

14i)

1. b.
2. a.

14g)

1024 ÷ 2 = 512

512 ÷ 2 = 256

256 ÷ 2 = 128

128 ÷ 2 = 64

64 ÷ 2 = 32

32 ÷ 2 = 16

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

Ten people got to answer a question.

729 ÷ 3 = 243

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9 9 ( 3 = 3

3 ÷ 3 = 1

Six people got to answer a question.

1024 ÷ 4 = 256

256 ÷ 4 = 64

64 ÷ 4 = 16

16 ÷ 4 = 4

4 ÷ 4 = 1

Five people got to answer a question.

14f)

1. 3/4 ( 12/1 = 36/4 = 9 months
2. 5/6 ( 24/1 = 120/6 = 20 months
3. 3/7 ( 21/1 = 63/7 = 9 days

15i) b.

15g) Answers will vary.

15f) Answers will vary, depending on mileage.

16i)

1. c.
2. b.

16g) Answers will vary.

16f) Answers will vary.

17i) a.

17g) Answers will vary.

17f) Answers will vary.

18i) b.

18g) The combinations are:
1 foot by 24 feet 2 feet by 12 feet 3 feet by 8 feet 4 feet by 6 feet

18f) Answers will vary, depending on the size of your home.

19i)

1. a.
2. b.
3. b.
4. c.

19g)

1. 12 ⁵/₈ + 53 ¹/₄ = 12 ⁵/₈ + 53 ²/₈ = 65 ⁷/₈
2. 2 ¹/₃ + 5 ¹/₆ = 2 ²/₆ + 5 ¹/₆ = 7 ³/₆, or 7 ¹/₂
3. 7 ³/₄ - 2 ¹/₂ = 7 ³/₄ - 2 ²/₄ = 5 ¹/₄
4. 84 ¹³/₁₆ - 36 ³/₈ = 84 ¹³/₁₆ - 36 ⁶/₁₆ = 48 ⁷/₁₆

19f)

1 ¹/₃ cups + 1 ¹/₄ cups +²/₃ cup + ¹/₂ cup + ¹/₄ cup

= 1 ⁴/₁₂ cups + 1 ³/₁₂ cups + ⁸/₁₂ cup + ⁶/₁₂ cup + ³/₁₂ cup

= 2 ²⁴/₁₂ cups = 4 cups

4 cups = 2 pints

2 pints = 1 quart

20i)

1. a.
2. c.

20g)

¹/₂ X 2 ¹/₂ groups = ¹/₂ X ⁵/₂ groups = ⁵/₄ group = 1 ¹/₄ group = 5 students

¹/₃ X 1 ¹/₂ groups = ¹/₃ X ³/₂ groups = ³/₆ group = ¹/₂ group = 2 students

20f) Answers will vary. The actual area and the rounded area should be fairly close.