Read the following prompt and type your response in the space provided.
Rewrite the following multiplication problem using the associative property and then show that both results will be the same.
1/2x2/3x4/5
To rewrite the given multiplication problem using the associative property, we can group the numbers differently. Instead of multiplying 1/2 and 2/3 together first, we can multiply 2/3 and 4/5 first.
(1/2 x 2/3) x 4/5
Now, let's simplify each multiplication separately:
(1/2 x 2/3) = 2/6
2/6 x 4/5
To multiply fractions, we multiply the numerators together and the denominators together:
(2 x 4)/(6 x 5) = 8/30
Now let's express the original multiplication problem in a new way by grouping the numbers differently:
1/2 x (2/3 x 4/5)
Again, let's simplify each multiplication separately:
2/3 x 4/5 = 8/15
Therefore, we have:
(1/2 x 2/3) x 4/5 = 2/6 x 4/5 = 8/30
1/2 x (2/3 x 4/5) = 1/2 x 8/15 = 8/30
As we can see, both results are equal to 8/30, proving that the two multiplication calculations yield the same outcome.