Solve (1/8+2/5)*(5/2div1/4)

$$( \frac{ 1 }{ 8 } + \frac{ 2 }{ 5 } ) \times ( \frac{ 5 }{ 2 } \div \frac{ 1 }{ 4 } )$$

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{2}{5} to fractions with denominator 40.

$$\left(\frac{5}{40}+\frac{16}{40}\right)\times \frac{\frac{5}{2}}{\frac{1}{4}}$$

Since \frac{5}{40} and \frac{16}{40} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{40}\times \frac{\frac{5}{2}}{\frac{1}{4}}$$

Add 5 and 16 to get 21.

$$\frac{21}{40}\times \frac{\frac{5}{2}}{\frac{1}{4}}$$

Divide \frac{5}{2} by \frac{1}{4} by multiplying \frac{5}{2} by the reciprocal of \frac{1}{4}.

$$\frac{21}{40}\times \frac{5}{2}\times 4$$

Express \frac{5}{2}\times 4 as a single fraction.

$$\frac{21}{40}\times \frac{5\times 4}{2}$$

Multiply 5 and 4 to get 20.

$$\frac{21}{40}\times \frac{20}{2}$$

Divide 20 by 2 to get 10.

$$\frac{21}{40}\times 10$$

Express \frac{21}{40}\times 10 as a single fraction.

$$\frac{21\times 10}{40}$$

Multiply 21 and 10 to get 210.

$$\frac{210}{40}$$

Reduce the fraction \frac{210}{40} to lowest terms by extracting and canceling out 10.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$