What is 17 4/9 + 5/6 - 8 - 10?

Answer 1

To solve the expression $17\frac{4}{9}+\frac{5}{6}-8-10$, we can first convert the mixed number $17\frac{4}{9}$ to an improper fraction.

1. Convert $17\frac{4}{9}$ to an improper fraction: $$17\frac{4}{9}=17+\frac{4}{9}=\frac{17\times 9}{9}+\frac{4}{9}=\frac{153}{9}+\frac{4}{9}=\frac{157}{9}$$

2. Now we can rewrite the expression: $$\frac{157}{9}+\frac{5}{6}-8-10$$

   We can express $8$ and $10$ as fractions: $$8=\frac{72}{9},10=\frac{90}{9}$$

3. Substitute these values into the expression: $$\frac{157}{9}+\frac{5}{6}-\frac{72}{9}-\frac{90}{9}$$

4. Combine the fractions: $$=\frac{157}{9}-\frac{72}{9}-\frac{90}{9}+\frac{5}{6}$$ $$=\frac{157-72-90}{9}+\frac{5}{6}$$ $$=\frac{157-162}{9}+\frac{5}{6}$$ $$=\frac{-5}{9}+\frac{5}{6}$$

5. Now we need a common denominator to add $\frac{-5}{9}$ and $\frac{5}{6}$:

   • The least common multiple of 9 and 6 is 18.

6. Convert both fractions to have the same denominator: $$\frac{-5}{9}=\frac{-5\times 2}{9\times 2}=\frac{-10}{18}$$ $$\frac{5}{6}=\frac{5\times 3}{6\times 3}=\frac{15}{18}$$

7. Now combine the two fractions: $$\frac{-10}{18}+\frac{15}{18}=\frac{-10+15}{18}=\frac{5}{18}$$

Thus, the result of the expression $17\frac{4}{9}+\frac{5}{6}-8-10$ is $\frac{5}{18}$.