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Question

Give an example of a problem involving multiplication of fractions that can be made easier using the associative property. Explain how it makes the problem easier.

Answer 1

An example of a problem involving multiplication of fractions that can be made easier using the associative property is as follows:

Suppose we need to simplify the expression (2/3) * (4/5) * (6/7).

By using the associative property of multiplication, we can rearrange the order of the factors without changing the result. Therefore, we can rewrite the expression as (2/3 * 4/5) * 6/7.

This rearrangement allows us to simplify the problem by breaking it down into smaller, more manageable parts. In this case, we can first multiply (2/3) and (4/5) to get 8/15.

Now, we have (8/15) * (6/7), which can be further simplified by multiplying the numerators (8 * 6) to get 48 and multiplying the denominators (15 * 7) to get 105.

Thus, the final answer is 48/105, which can be reduced to 16/35.

Using the associative property in this problem made it easier by allowing us to break down the multiplication of fractions into smaller calculations, making it simpler to compute the result.