Answer:
b) Associative property of multiplication
c) Associative property of addition
d) Associative property of multiplication
Step-by-step explanation:
The Associative Property states that the grouping of numbers by parentheses in a different way does not affect their sum or product. This property applies to addition and multiplication only:
Question b
v × (y × b) = (v × y) × b
The property used to find the equivalent expression of v × (y × b) is the associative property of multiplication.
If we evaluate the given equation, we can see that both sides are equivalent, thus proving the property:
[tex]\begin{aligned}\sf v \times(y \times b)&=\sf (v \times y)\times b\\\sf v \times(yb)&=\sf (vy)\times b\\\sf vyb&=\sf vyb\end{aligned}[/tex]
(8 + 1) + 6 = 8 + (1 + 6)
The property used to find the equivalent expression of (8 + 1) + 6 is the associative property of addition.
If we evaluate the given equation, we can see that both sides are equivalent, thus proving the property:
[tex]\begin{aligned}(8 + 1) + 6 &= 8 + (1 + 6)\\(9) + 6 &= 8 + (7)\\15&=15\end{aligned}[/tex]
(9 × 13) × 14 = (13 × 9) × 14
The property used to find the equivalent expression of (9 × 13) × 14 is the associative property of multiplication.
If we evaluate the given equation, we can see that both sides are equivalent, thus proving the property:
[tex]\begin{aligned}(9 \times 13)\times 14&=(13 \times 9)\times 14\\(117)\times 14&=(117)\times 14\\1638&=1638 \end{aligned}[/tex]
