Question

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

41.1515
41 Start Fraction 15 over 15 End Fraction

20 15/15
20 Start Fraction 15 over 15 End Fraction

35
35

21

Answer 1

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

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

2. Convert \(7\) and \(15\) to 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. Rewrite the expression using the fractions:
\[
\frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15}
\]

4. Combine the fractions:
\[
\frac{188 - 105 + 7 + 225}{15} = \frac{188 - 105 + 7 + 225}{15} = \frac{188 + 225 - 105 + 7}{15} = \frac{188 + 225 - 105 + 7}{15}
\]
Calculate this step by step:
- First, \(188 - 105 = 83\)
- Then, \(83 + 7 = 90\)
- Lastly, \(90 + 225 = 315\)

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

6. Simplifying \( \frac{315}{15} \):
\[
315 \div 15 = 21
\]

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