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

Responses

21
21

35
35

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

41 15/15

1 answer

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:
\[ \frac{315}{15} \]

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

Hence, the answer is:
21