What is the result of this calculation?

Question

1/2 x 4/3 + 5/6 divided by 7/8 =

Answer 1

To solve the calculation $\frac{1}{2}\times \frac{4}{3}+\frac{5}{6}÷\frac{7}{8}$, we will break it down into two parts.

1. Calculate $\frac{1}{2}\times \frac{4}{3}$: $$\frac{1}{2}\times \frac{4}{3}=\frac{1\times 4}{2\times 3}=\frac{4}{6}=\frac{2}{3}(\text{by simplifying }\frac{4}{6}\text{ to }\frac{2}{3})$$

2. Calculate $\frac{5}{6}÷\frac{7}{8}$: Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{5}{6}÷\frac{7}{8}=\frac{5}{6}\times \frac{8}{7}=\frac{5\times 8}{6\times 7}=\frac{40}{42}=\frac{20}{21}(\text{by simplifying }\frac{40}{42}\text{ to }\frac{20}{21})$$

3. Now we add $\frac{2}{3}+\frac{20}{21}$: First, we need a common denominator for $\frac{2}{3}$ and $\frac{20}{21}$. The least common multiple of 3 and 21 is 21.

   Convert $\frac{2}{3}$ to have the denominator of 21: $$\frac{2}{3}=\frac{2\times 7}{3\times 7}=\frac{14}{21}$$

   Now add $\frac{14}{21}+\frac{20}{21}$: $$\frac{14+20}{21}=\frac{34}{21}$$

Thus, the result of the calculation is: $$\frac{34}{21}$$

This can also be expressed as a mixed number: $$1\frac{13}{21}$$

So the final answer is: $$\frac{34}{21}\text{ or }1\frac{13}{21}$$