Question

What is 12 8/15 − 7 + 7/15 + 15? Simplify your answer.
A. 21
B. 20 15/15
C. 41 15/15
D. 35

Answer 1

To simplify the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we'll follow the steps below:

1. First, convert the mixed number \( 12 \frac{8}{15} \) into an improper fraction:
\[
12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15}
\]

2. Convert the whole numbers \( -7 \) and \( +15 \) into fractions with a 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 the fractions:
\[
\frac{188 - 105 + 7 + 225}{15} = \frac{188 + 7 - 105 + 225}{15}
\]
Calculate the numerator:
\[
188 + 7 = 195
\]
\[
195 - 105 = 90
\]
\[
90 + 225 = 315
\]
Thus, the combined fraction becomes:
\[
\frac{315}{15}
\]

5. Finally, simplify \( \frac{315}{15} \):
\[
315 \div 15 = 21
\]

So the final answer is \( 21 \), which corresponds to option:
**A. 21**