Read the following prompt and type your response in the space provided.
Explain how the associative property can be used to solve this problem.
8/9 divided by 7/5x3/16
The associative property states that the grouping of numbers does not affect the result of multiplication or division. In this problem, we can use the associative property to simplify the expression.
To do so, we can rearrange the multiplication of 7/5 and 3/16 before dividing by 8/9. By multiplying the numerators and denominators together, we get (7*3)/(5*16), which equals 21/80.
Next, we divide the result by 8/9. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, (21/80) divided by (8/9) can be rewritten as (21/80) multiplied by (9/8).
Applying the associative property, we can group the multiplication of (21/80) and (9/8) to get (21*9)/(80*8), which simplifies to 189/640.
Therefore, using the associative property, we were able to simplify the expression 8/9 divided by 7/5x3/16 to 189/640.