(1) 10(e + 0.5)g
Using distributive property, a × (b + c) = a × b + a × c
10(e + 0.5)g = 10 eg + 10 × 0.5g
Therefore, 10(e + 0.5g) and 10e + 5g are not equivalent.
(2) 6(p + q)
Using distributive property,
6(p + q) = 6p + 6q
Therefore, 6(p + q) and 6p + q are not equivalent.
(3) 7y – 15 + 2y
Using commutative property, a + b = b + a
7y – 15 + 2y = 7y + 2y – 15
= 9y – 15
Therefore 7y – 15 + 2y and 9y – 15 are equivalent.
(4) 1 + (8r + 9)
Using associative property, a + (b + c) = (a + b) + c
1 + (8r + 9) = (1 + 9) + 8r
= 10 + 8r
= (2 + 8) + 8r
Therefore 1 + (8r + 9) and (2 + 8) + 8r are equivalent.
(5) 0 × 11 + 5n
Using multiplicative identity property: a × 0 = 0
0 × 11 + 5n = 0 + 5n
= 5n
Therefore, 0 × 11 + 5n and 5n are equivalent.
(6) 16s – 4 + s
Using associative property, a + (b + c) = (a + b) + c
16s – 4 + s = 16s + s – 4
= 17s – 4
Therefore, 16s – 4 + s and 12s not equivalent.
(7) 11d × 2 = 22d
Therefore, 11d × 2 and 22d are equivalent.
(8) 8m + (9m – 1)
Using associative property, a + (b + c) = (a + b) + c
8m + (9m – 1) = (8m + 9m) – 1
= 17m – 1
Therefore, 8m + (9m – 1) and 8m – 8 not equivalent.