Question

Which of the pairs of expressions are equivalent?(1 point) 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, we can analyze each pair:

1. (k⋅18)⋅0.5 and k⋅(18⋅0.5):

   • By the associative property of multiplication, both expressions evaluate to the same result: \( k \cdot 18 \cdot 0.5 = k \cdot (18 \cdot 0.5) \).
   • Equivalent.

2. (k times 18) times 0.5 and k times (18 times 0.5):

   • Same as the first pair; both evaluate to the same result.
   • Equivalent.

3. x⋅(5+2) and (x⋅5)+2:

   • \( x \cdot (5 + 2) \) equals \( x \cdot 7 \).
   • \( (x \cdot 5) + 2 \) does not equal \( x \cdot 7 \) unless \( x = 1 \).
   • Not Equivalent.

4. x times (5 plus 2) and (x times 5) plus 2:

   • Same reasoning as the previous pair; \( x \cdot (5 + 2) \) equals \( x \cdot 7 \) and \( (x \cdot 5) + 2 \) is not the same.
   • Not Equivalent.

5. (d÷8)÷4 and d÷(8÷4):

   • \( (d ÷ 8) ÷ 4 \) is \( d ÷ (8 \cdot 4) = d ÷ 32 \).
   • \( d ÷ (8 ÷ 4) \) is \( d ÷ 2 \).
   • Not Equivalent.

6. (y−9)−8 and y−(9−8):

   • \( (y - 9) - 8 \) simplifies to \( y - 17 \).
   • \( y - (9 - 8) \) simplifies to \( y - 1 \).
   • Not Equivalent.

In conclusion, the equivalent pairs are:

• (1) (k⋅18)⋅0.5 and k⋅(18⋅0.5)
• (2) (k times 18) times 0.5 and k times (18 times 0.5)

The remaining pairs (3, 4, 5, and 6) are not equivalent.