Worksheet on properties of real numbers with matching and simplification exercises.

Let's solve this step by step.

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Part 1: Match each expression with one of the properties shown

We are given expressions and a list of properties. We need to match each expression to the correct property.

#### List of Properties:
a. commutative property of addition
b. commutative property of multiplication
c. associative property of addition
d. associative property of multiplication
e. additive identity
f. multiplicative identity
g. distributive property
h. additive inverse
i. multiplicative inverse

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Now, let’s go through each expression:

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1. $ 11 + 0 = 11 $
→ Adding zero doesn’t change the number → Additive Identity
✔ Answer: e

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2. $ x \times (y \times z) = (x \times y) \times z $
→ Grouping in multiplication doesn’t matter → Associative Property of Multiplication
✔ Answer: d

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3. $ 8 + (-8) = 0 $
→ A number plus its opposite equals zero → Additive Inverse
✔ Answer: h

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4. $ 14 + 20 = 20 + 14 $
→ Order of addition doesn’t matter → Commutative Property of Addition
✔ Answer: a

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5. $ 2 \times \frac{1}{2} = 1 $
→ A number times its reciprocal equals 1 → Multiplicative Inverse
✔ Answer: i

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6. $ 22 \times 1 = 22 $
→ Multiplying by 1 doesn’t change the number → Multiplicative Identity
✔ Answer: f

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7. $ (19 + 12) + 8 = 19 + (12 + 8) $
→ Grouping in addition doesn’t matter → Associative Property of Addition
✔ Answer: c

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8. $ a \times 9 = 9 \times a $
→ Order of multiplication doesn’t matter → Commutative Property of Multiplication
✔ Answer: b

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9. $ 7(4 + 11) = 7(4) + 7(11) $
→ Distributing multiplication over addition → Distributive Property
✔ Answer: g

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✔ Part 1 Answers:

1. e
2. d
3. h
4. a
5. i
6. f
7. c
8. b
9. g

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Part 2: Use properties to simplify mentally

We’ll use the properties (like commutative, associative, etc.) to simplify these expressions.

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10. $ (19 + 15) + 5 $
→ First add: $ 19 + 15 = 34 $, then $ 34 + 5 = 39 $
Or use associative property: $ 19 + (15 + 5) = 19 + 20 = 39 $
✔ Answer: 39

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11. $ -3 + (23 + 48) $
→ First: $ 23 + 48 = 71 $, then $ -3 + 71 = 68 $
✔ Answer: 68

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12. $ \$9.50 + \$11.49 + \$0.50 $
→ Rearrange using commutative property:
$ (9.50 + 0.50) + 11.49 = 10.00 + 11.49 = 21.49 $
✔ Answer: \$21.49

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13. $ (9 \cdot 25) \cdot 4 $
→ Use associative property: $ 9 \cdot (25 \cdot 4) = 9 \cdot 100 = 900 $
✔ Answer: 900

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14. $ (-0.50 + 9.89) + 0.50 $
→ Rearranged: $ (-0.50 + 0.50) + 9.89 = 0 + 9.89 = 9.89 $
✔ Answer: 9.89

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15. $ 6 \times 8 \times 5 $
→ Use associative property: $ 6 \times (8 \times 5) = 6 \times 40 = 240 $
Or: $ (6 \times 5) \times 8 = 30 \times 8 = 240 $
✔ Answer: 240

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✔ Part 2 Answers:

10. 39
11. 68
12. \$21.49
13. 900
14. 9.89
15. 240

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Part 3: Word Problem

16. Mental Math:
Sparky bought:
- Socks: \$2.50
- Jeans: \$14.95
- Shoes: \$12.50

Total spent:
$ 2.50 + 14.95 + 12.50 $

Group: $ (2.50 + 12.50) + 14.95 = 15.00 + 14.95 = 29.95 $

✔ Answer: \$29.95

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✔ Final Answer Summary:

Matching (1–9):
1. e
2. d
3. h
4. a
5. i
6. f
7. c
8. b
9. g

Simplification (10–15):
10. 39
11. 68
12. \$21.49
13. 900
14. 9.89
15. 240

Word Problem (16):
16. \$29.95

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