Question

12 8/15 − 7 + 7/15 + 15

Answer 1

To solve the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we first convert the mixed number \( 12 \frac{8}{15} \) into an improper fraction.

1. Convert \( 12 \frac{8}{15} \):
\[
12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15}
\]

2. Rewrite the entire expression:
\[
\frac{188}{15} - 7 + \frac{7}{15} + 15
\]

3. Convert the whole numbers 7 and 15 into fractions with a denominator of 15:
\[
7 = \frac{7 \times 15}{15} = \frac{105}{15}
\]
\[
15 = \frac{15 \times 15}{15} = \frac{225}{15}
\]

4. Now, substitute these back into the expression:
\[
\frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15}
\]

5. Combine the fractions:
\[
\frac{188 - 105 + 7 + 225}{15}
\]

6. Calculate the numerator:
\[
188 - 105 = 83
\]
\[
83 + 7 = 90
\]
\[
90 + 225 = 315
\]
So the numerator is 315.

7. This gives:
\[
\frac{315}{15}
\]

8. Simplify the fraction:
\[
\frac{315}{15} = 21
\]

Thus, the final answer is:
\[
\boxed{21}
\]