Question

What is 12 8/15 − 7 + 7/15 + 15 ? Simplify your answer.(1 point)
Responses

A. 20 15/15

B. 41 15/15

C. 35

D. 21

Answer 1

To solve the expression \(12 \frac{8}{15} - 7 + \frac{7}{15} + 15\), follow these steps:

1. Convert all mixed numbers to improper fractions or a consistent format.

\(12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15}\)

2. Rewrite the whole numbers (7 and 15) with a common denominator of 15.

\(7 = \frac{7 \times 15}{15} = \frac{105}{15}\)

\(15 = \frac{15 \times 15}{15} = \frac{225}{15}\)

3. Now substitute these values back into the expression:

\[
\frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15}
\]

4. Combine all the fractions over a common denominator:

\[
= \frac{188 - 105 + 7 + 225}{15}
\]

5. Perform the calculations in the numerator:

\[
188 - 105 = 83
\]
\[
83 + 7 = 90
\]
\[
90 + 225 = 315
\]

So, we have:

\[
= \frac{315}{15}
\]

6. Simplify this fraction:

\[
= 21
\]

Thus, the simplified answer is:

**D. 21**