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

Question

Responses

21
21

35
35

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

41 15/15

Answer 1

Let's simplify the expression step by step:

1. Start with the expression:
   \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \)

2. Convert the mixed number to an improper fraction:
   \( 12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15} \)

3. Combine the whole numbers (converting them to fractions):

   • Convert 7 to a fraction:
     \( 7 = \frac{7 \times 15}{15} = \frac{105}{15} \)
   • Convert 15 to a fraction:
     \( 15 = \frac{15 \times 15}{15} = \frac{225}{15} \)

4. Now the expression looks like this:
   \( \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \)

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

6. Calculate the numerator:
   \( 188 + 7 = 195 \)
   \( 195 - 105 = 90 \)
   \( 90 + 225 = 315 \)

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

7. Simplify the fraction:
   \( 315 \div 15 = 21 \)

Hence, the answer is:
21