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

Question

Responses

(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

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

(d÷8)÷4
and d÷(8÷4)
left parenthesis d divided by 8 right parenthesis divided by 4 and d divided by left parenthesis 8 divided by 4 right parenthesis

(y−9)−8
and y−(9−8)

Answer 1

To determine which pairs of expressions are equivalent, let's analyze each pair one by one:

1. (k⋅18)⋅0.5 and k⋅(18⋅0.5)

   By the associative and commutative properties of multiplication, both expressions evaluate to the same value: \[ (k \cdot 18) \cdot 0.5 = k \cdot (18 \cdot 0.5) \] So, these expressions are equivalent.

2. x⋅(5+2) and (x⋅5)+2

   The first expression simplifies as: \[ x \cdot (5 + 2) = x \cdot 7 \] The second expression simplifies as: \[ (x \cdot 5) + 2 \] Since \(x \cdot 7\) is not equal to \((x \cdot 5) + 2\), these expressions are not equivalent.

3. (d÷8)÷4 and d÷(8÷4)

   The first expression becomes: \[ \frac{d}{8} \div 4 = \frac{d}{8} \cdot \frac{1}{4} = \frac{d}{32} \] The second expression simplifies to: \[ d \div (8 \div 4) = d \div 2 = \frac{d}{2} \] Since \(\frac{d}{32}\) is not equal to \(\frac{d}{2}\), these expressions are not equivalent.

4. (y−9)−8 and y−(9−8)

   The first expression simplifies as: \[ (y - 9) - 8 = y - 17 \] The second expression simplifies as: \[ y - (9 - 8) = y - 1 \] Since \(y - 17\) is not equal to \(y - 1\), these expressions are not equivalent.

Final results: The only pair of expressions that are equivalent is:

• (k⋅18)⋅0.5 and k⋅(18⋅0.5).