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 divide by 7/5 x 3/16
The associative property states that the grouping of numbers being multiplied or divided does not affect the result. In the given problem, we can rearrange the expression using the associative property as follows:
(8/9 ÷ 7/5) x 3/16
We can first solve the division part by multiplying the dividend (8/9) by the reciprocal of the divisor (7/5):
(8/9) x (5/7) x 3/16
Next, we can use the associative property of multiplication to rearrange the order of multiplication without changing the result:
8/9 x 5/7 x 3/16
By multiplying the numerators together and denominators together, we can simplify further:
(8 x 5 x 3) / (9 x 7 x 16)
Finally, evaluating the numerator and denominator:
120 / 1008
The expression is now simplified and we can divide 120 by 1008 to get the final answer, which is 0.119.
In summary, by using the associative property, we were able to rearrange the expression to simplify it further and solve the problem.