Explanation:
Let’s go step by step through each part.
Part 1: Matching expressions to properties
We need to match each equation (1–9) with the correct property from (a–i).
1.
11 + 0 = 11
Adding 0 doesn’t change the number → this is the
additive identity.
✔ Match:
e
2.
x × (y × z) = (x × y) × z
Grouping changes but result stays same — for multiplication →
associative property of multiplication.
✔ Match:
d
3.
8 + (−8) = 0
A number plus its opposite gives 0 →
additive inverse.
✔ Match:
h
4.
14 + 20 = 20 + 14
Order changed, sum same — addition →
commutative property of addition.
✔ Match:
a
5.
2 × ½ = 1
A number times its reciprocal gives 1 →
multiplicative inverse.
✔ Match:
i
6.
22 × 1 = 22
Multiplying by 1 doesn’t change the number →
multiplicative identity.
✔ Match:
f
7.
(19 + 12) + 8 = 19 + (12 + 8)
Grouping changed, sum same — addition →
associative property of addition.
✔ Match:
c
8.
a × 9 = 9 × a
Order changed, product same — multiplication →
commutative property of multiplication.
✔ Match:
b
9.
7(4 + 11) = 7(4) + 7(11)
Multiplying across a sum →
distributive property.
✔ Match:
g
So matches are:
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
10.
(19 + 15) + 5
Use associative property: group 15 + 5 = 20, then 19 + 20 =
39
11.
−3 + (23 + 48)
First, 23 + 48 = 71; then −3 + 71 =
68
12.
$9.50 + $11.49 + $0.50
Rearrange: $9.50 + $0.50 = $10.00, then $10.00 + $11.49 =
$21.49
13.
(9 · 25) · 4
Use associative: 25 · 4 = 100, then 9 · 100 =
900
14.
(−0.50 + 9.89) + 0.50
Rearrange: −0.50 + 0.50 = 0, then 0 + 9.89 =
9.89
15.
6 × 8 × 5
Multiply 8 × 5 = 40, then 6 × 40 =
240
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Part 3: Mental Math Word Problem (Problem 16)
Sparky bought:
- Socks: $2.50
- Jeans: $14.95
- Shoes: $12.50
Add them:
First, $2.50 + $12.50 = $15.00
Then $15.00 + $14.95 =
$29.95
Double-check:
2.50 + 14.95 = 17.45
17.45 + 12.50 = 29.95
✔
Final Answer:
1. e
2. d
3. h
4. a
5. i
6. f
7. c
8. b
9. g
10. 39
11. 68
12. $21.49
13. 900
14. 9.89
15. 240
16. $29.95
Parent Tip: Review the logic above to help your child master the concept of properties practice worksheet.
