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

1 answer

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

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

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