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

Question

Responses

35

20 15/15

21

41 15/15

Answer 1

To simplify the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we will first convert the mixed number and combine all the terms.

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 \( 7 \) to a fraction with a denominator of 15: \[ 7 = \frac{7 \times 15}{15} = \frac{105}{15} \]

3. Convert \( 15 \) to a fraction with a denominator of 15: \[ 15 = \frac{15 \times 15}{15} = \frac{225}{15} \]

Now rewrite the entire expression: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]

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

Calculating the numerator step by step: \[ 188 - 105 = 83 \] \[ 83 + 7 = 90 \] \[ 90 + 225 = 315 \]

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

5. Simplifying that fraction: \[ \frac{315}{15} = 21 \]

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