Question: Each equation is either (1) true because of the commutative property, (2) true because of the associative property, or (3) false. Mark the correct choice, then write the corresponding letter in the box containing the exercise number.
1 $n + 5 = 5 + n$
E - TRUE (commutative property)
V - TRUE (associative property)
P - FALSE
2 $n \cdot 5 = 5 \cdot n$
T - TRUE (commutative property)
U - TRUE (associative property)
Q - FALSE
3 $n - 5 = 5 - n$
A - TRUE (commutative property)
K - TRUE (associative property)
O - FALSE
4 $n \div 5 = 5 \div n$
C - TRUE (commutative property)
W - TRUE (associative property)
H - FALSE
5 $3 + (8 + x) = (3 + 8) + x$
G - TRUE (commutative property)
F - TRUE (associative property)
B - FALSE
6 $3 \cdot (8x) = (3 \cdot 8)x$
N - TRUE (commutative property)
T - TRUE (associative property)
Y - FALSE
7 $3 - (8 - x) = (3 - 8) - x$
R - TRUE (commutative property)
U - TRUE (associative property)
H - FALSE
8 $3 \div (8 \div x) = (3 \div 8) \div x$
H - TRUE (commutative property)
U - TRUE (associative property)
A - FALSE
9 $3 + (8x) = (3 + 8)x$
E - TRUE (commutative property)
P - TRUE (associative property)
U - FALSE
10 $4 + (a + b) = (a + b) + 4$
T - TRUE (commutative property)
G - TRUE (associative property)
S - FALSE
11 $4 + (a + b) = (4 + a) + b$
A - TRUE (commutative property)
I - TRUE (associative property)
O - FALSE
12 $4 + (a + b) = 4 + (b + a)$
O - TRUE (commutative property)
R - TRUE (associative property)
L - FALSE
13 $7(2w) = (2w)7$
E - TRUE (commutative property)
A - TRUE (associative property)
R - FALSE
14 $7(2w) = (7 \cdot 2)w$
C - TRUE (commutative property)
J - TRUE (associative property)
B - FALSE
15 $7(2w) = 7(w \cdot 2)$
T - TRUE (commutative property)
I - TRUE (associative property)
M - FALSE
16 $15 + (6y) = 15 + (y \cdot 6)$
P - TRUE (commutative property)
N - TRUE (associative property)
D - FALSE
17 $15 + (5y) = (5y) + 15$
S - TRUE (commutative property)
L - TRUE (associative property)
T - FALSE
18 $15 + (6y) = (15 \div 6)y$
M - TRUE (commutative property)
P - TRUE (associative property)
T - FALSE
19 $p(9q) = (p \cdot 9)q$
A - TRUE (commutative property)
F - TRUE (associative property)
I - FALSE
20 $p + (9 + q) = (p + 9) + q$
E - TRUE (commutative property)
L - TRUE (associative property)
R - FALSE
21 $p - (9 + q) = (p - 9) + q$
N - TRUE (commutative property)
T - TRUE (associative property)
W - FALSE
1. **Problem:** Determine if each equation is true by the commutative property, associative property, or false.
2. **Recall properties:**
- Commutative property: $a + b = b + a$ or $a \cdot b = b \cdot a$
- Associative property: $(a + b) + c = a + (b + c)$ or $(a \cdot b) \cdot c = a \cdot (b \cdot c)$
3. **Evaluate each equation:**
- 1. $n + 5 = 5 + n$ is commutative addition, so TRUE (E).
- 2. $n \cdot 5 = 5 \cdot n$ is commutative multiplication, so TRUE (T).
- 3. $n - 5 = 5 - n$ is NOT commutative subtraction, so FALSE (O).
- 4. $n \div 5 = 5 \div n$ is NOT commutative division, so FALSE (H).
- 5. $3 + (8 + x) = (3 + 8) + x$ is associative addition, so TRUE (F).
- 6. $3 \cdot (8x) = (3 \cdot 8)x$ is associative multiplication, so TRUE (T).
- 7. $3 - (8 - x) = (3 - 8) - x$ is NOT associative subtraction, so FALSE (H).
- 8. $3 \div (8 \div x) = (3 \div 8) \div x$ is NOT associative division, so FALSE (A).
- 9. $3 + (8x) = (3 + 8)x$ is FALSE (U) because addition and multiplication are not interchangeable.
- 10. $4 + (a + b) = (a + b) + 4$ is commutative addition, so TRUE (T).
- 11. $4 + (a + b) = (4 + a) + b$ is associative addition, so TRUE (I).
- 12. $4 + (a + b) = 4 + (b + a)$ is commutative addition inside parentheses, so TRUE (O).
- 13. $7(2w) = (2w)7$ is commutative multiplication, so TRUE (E).
- 14. $7(2w) = (7 \cdot 2)w$ is associative multiplication, so TRUE (J).
- 15. $7(2w) = 7(w \cdot 2)$ is commutative multiplication inside parentheses, so TRUE (T).
- 16. $15 + (6y) = 15 + (y \cdot 6)$ is commutative multiplication inside parentheses, so TRUE (N).
- 17. $15 + (5y) = (5y) + 15$ is commutative addition, so TRUE (S).
- 18. $15 + (6y) = (15 \div 6)y$ is FALSE (T) because addition and division are not interchangeable.
- 19. $p(9q) = (p \cdot 9)q$ is associative multiplication, so TRUE (F).
- 20. $p + (9 + q) = (p + 9) + q$ is associative addition, so TRUE (L).
- 21. $p - (9 + q) = (p - 9) + q$ is FALSE (W) because subtraction is not associative.
4. **Final answers:**
1:E
2:T
3:O
4:H
5:F
6:T
7:H
8:A
9:U
10:T
11:I
12:O
13:E
14:J
15:T
16:N
17:S
18:T
19:F
20:L
21:W