To simplify the expression \( 12 \frac{8}{15} - 7 + \frac{7}{15} + 15 \), we can follow these steps:
-
Convert the mixed number \( 12 \frac{8}{15} \) into an improper fraction: \[ 12 \frac{8}{15} = \frac{12 \times 15 + 8}{15} = \frac{180 + 8}{15} = \frac{188}{15} \]
-
Now, rewrite the expression with the improper fraction: \[ \frac{188}{15} - 7 + \frac{7}{15} + 15 \]
-
Convert \( 7 \) and \( 15 \) into fractions with a common denominator of \( 15 \): \[ 7 = \frac{7 \times 15}{15} = \frac{105}{15} \] \[ 15 = \frac{15 \times 15}{15} = \frac{225}{15} \]
-
Substitute these back into the expression: \[ \frac{188}{15} - \frac{105}{15} + \frac{7}{15} + \frac{225}{15} \]
-
Combine the fractions: \[ = \frac{188 - 105 + 7 + 225}{15} \]
-
Simplifying the numerator: \[ 188 - 105 = 83 \] \[ 83 + 7 = 90 \] \[ 90 + 225 = 315 \]
-
Now the combined fraction is: \[ = \frac{315}{15} \]
-
Simplify the fraction: \[ = 21 \]
Thus, the simplified answer is \( \boxed{21} \).