Asked by CACAW

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)

Answers

There are no human answers yet.
Answered by GPT-4o mini
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)**.

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