Question

What is 12 8/15 − 7 + 7/15 + 15 ? Simplify your answer. double check it too

Answer 1

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

1. 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. Now, rewrite the expression with the improper fraction:
\[
\frac{188}{15} - 7 + \frac{7}{15} + 15
\]

3. Convert \( 7 \) and \( 15 \) into fractions with a common denominator of \( 15 \):
\[
7 = \frac{7 \times 15}{15} = \frac{105}{15}
\]
\[
15 = \frac{15 \times 15}{15} = \frac{225}{15}
\]

4. 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. Simplifying the numerator:
\[
188 - 105 = 83
\]
\[
83 + 7 = 90
\]
\[
90 + 225 = 315
\]

7. Now the combined fraction is:
\[
= \frac{315}{15}
\]

8. Simplify the fraction:
\[
= 21
\]

Thus, the simplified answer is \( \boxed{21} \).