Question

Which of the pairs of expressions are equivalent?(1 point)
Responses

x⋅(5+2)
and (x⋅5)+2

x times left parenthesis 5 plus 2 right parenthesis and left parenthesis x times 5 right parenthesis plus 2

(k⋅18)⋅0.5
and k⋅(18⋅0.5)

left parenthesis k times 18 right parenthesis times 0.5 and k times left parenthesis 18 times 0.5 right parenthesis

(y−9)−8
and y−(9−8)

left parenthesis y minus 9 right parenthesis minus 8 and y minus left parenthesis 9 minus 8 right parenthesis

(d÷8)÷4
and d÷(8÷4)

Answer 1

Only the second pair is equivalent:

- x·(5+2) and (x·5)+2 — Not equivalent. x·(5+2)=7x, but (x·5)+2=5x+2.
- (k·18)·0.5 and k·(18·0.5) — Equivalent. Multiplication is associative, so (k·18)·0.5 = k·(18·0.5).
- (y−9)−8 and y−(9−8) — Not equivalent. (y−9)−8 = y−17, while y−(9−8) = y−1.
- (d÷8)÷4 and d÷(8÷4) — Not equivalent. (d÷8)÷4 = d÷32, while d÷(8÷4) = d÷2.