Question

What is 12 8/15 − 7 + 7/15 + 15 ? Simplify your answer

Answer 1

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

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

2. Convert all numbers to fractions with a common denominator (15):
- Express \( 7 \) as \( \frac{7 \times 15}{15} = \frac{105}{15} \)
- Express \( 15 \) as \( \frac{15 \times 15}{15} = \frac{225}{15} \)

3. Substitute in the original expression:
\[
\frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15}
\]

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

5. Calculate the numerator:
- \( 188 - 105 = 83 \)
- \( 83 + 7 = 90 \)
- \( 90 + 225 = 315 \)

So, we have:
\[
\frac{315}{15}
\]

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

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