12 8/15 − 7 + 7/15 + 15

Answer 1

To solve the expression $12\frac{8}{15}-7+\frac{7}{15}+15$, we first convert the mixed number $12\frac{8}{15}$ into an improper fraction.

1. Convert $12\frac{8}{15}$: $$12\frac{8}{15}=\frac{12\times 15+8}{15}=\frac{180+8}{15}=\frac{188}{15}$$

2. Rewrite the entire expression: $$\frac{188}{15}-7+\frac{7}{15}+15$$

3. Convert the whole numbers 7 and 15 into fractions with a denominator of 15: $$7=\frac{7\times 15}{15}=\frac{105}{15}$$ $$15=\frac{15\times 15}{15}=\frac{225}{15}$$

4. Now, substitute these back into the expression: $$\frac{188}{15}-\frac{105}{15}+\frac{7}{15}+\frac{225}{15}$$

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

6. Calculate the numerator: $$188-105=83$$ $$83+7=90$$ $$90+225=315$$ So the numerator is 315.

7. This gives: $$\frac{315}{15}$$

8. Simplify the fraction: $$\frac{315}{15}=21$$

Thus, the final answer is: $$\boxed{{\displaystyle 21}}$$