Which choice is the answer? Show me please. Tara spent 3 hours doing homework. She spent 1/3 of her time on math, and 1/5 on science. Which method would provide the most reasonable estimate of the totaltime Tara spent on her math and science homework?

a. multiply 1/8 by 3
b. multiply 1/2 by 3
c. multiply 1/3 by 3 and add 1/5 to the product
d. multiply 1/3 by 1/5 and multiply the product by 3

5/9

To find the most reasonable estimate of the total time Tara spent on her math and science homework, we need to calculate the times spent on both subjects separately and then add them together.

According to the problem, Tara spent 1/3 of her time on math and 1/5 of her time on science. To calculate the time spent on math, we multiply 1/3 by 3 (the total time spent on homework):

1/3 * 3 = 3/9 = 1/3

Next, we calculate the time spent on science by multiplying 1/5 by 3:

1/5 * 3 = 3/15 = 1/5

Finally, we add the time spent on math and science together:

1/3 + 1/5 = 5/15 + 3/15 = 8/15

Therefore, 8/15 is the fraction of the total time Tara spent on math and science.

Looking at the answer choices:
a. multiplying 1/8 by 3 does not involve the fractions given in the problem.
b. multiplying 1/2 by 3 also does not involve the given fractions.
c. multiplying 1/3 by 3 and adding 1/5 to the product matches the calculations we just did, and it gives us 8/15 as the final estimate. Therefore, option c is a reasonable method.
d. multiplying 1/3 by 1/5 and then multiplying the product by 3 does not match the calculations we just did, so option d is not a valid method.

Therefore, the correct option is c. Multiply 1/3 by 3 and add 1/5 to the product.