Question
Which property would be used first to make the following problem easier to work?
²/³ · (³/² · 5)
multiplicative property
distributive property
associative property of multiplication
commutative property of multiplication
²/³ · (³/² · 5)
multiplicative property
distributive property
associative property of multiplication
commutative property of multiplication
Answers
GPT-4o mini
In the expression \( \frac{2}{3} \cdot \left( \frac{3}{2} \cdot 5 \right) \), the most useful property to use first to simplify the calculation is the **associative property of multiplication**.
The associative property states that the way in which factors are grouped in multiplication does not affect the product. Therefore, you can regroup the factors in a way that makes the calculation easier.
In this case, you could regroup it as:
\[
\left( \frac{2}{3} \cdot \frac{3}{2} \right) \cdot 5
\]
This allows you to multiply \( \frac{2}{3} \) and \( \frac{3}{2} \) first, which simplifies to 1:
\[
\frac{2}{3} \cdot \frac{3}{2} = 1
\]
Then, you multiply by 5:
\[
1 \cdot 5 = 5
\]
Thus, using the associative property of multiplication first makes the problem simpler and easier to solve.
The associative property states that the way in which factors are grouped in multiplication does not affect the product. Therefore, you can regroup the factors in a way that makes the calculation easier.
In this case, you could regroup it as:
\[
\left( \frac{2}{3} \cdot \frac{3}{2} \right) \cdot 5
\]
This allows you to multiply \( \frac{2}{3} \) and \( \frac{3}{2} \) first, which simplifies to 1:
\[
\frac{2}{3} \cdot \frac{3}{2} = 1
\]
Then, you multiply by 5:
\[
1 \cdot 5 = 5
\]
Thus, using the associative property of multiplication first makes the problem simpler and easier to solve.