Solve 1/8+(9/5-3/20)div1/4

$$\frac { 1 } { 8 } + ( \frac { 9 } { 5 } - \frac { 3 } { 20 } ) \div \frac { 1 } { 4 }$$

Evaluate

$$\frac{269}{40}=6.725$$

Solution Steps

Least common multiple of 5 and 20 is 20. Convert \frac{9}{5} and \frac{3}{20} to fractions with denominator 20.

$$\frac{1}{8}+\frac{\frac{36}{20}-\frac{3}{20}}{\frac{1}{4}}$$

Since \frac{36}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{8}+\frac{\frac{36-3}{20}}{\frac{1}{4}}$$

Subtract 3 from 36 to get 33.

$$\frac{1}{8}+\frac{\frac{33}{20}}{\frac{1}{4}}$$

Divide \frac{33}{20} by \frac{1}{4} by multiplying \frac{33}{20} by the reciprocal of \frac{1}{4}.

$$\frac{1}{8}+\frac{33}{20}\times 4$$

Express \frac{33}{20}\times 4 as a single fraction.

$$\frac{1}{8}+\frac{33\times 4}{20}$$

Multiply 33 and 4 to get 132.

$$\frac{1}{8}+\frac{132}{20}$$

Reduce the fraction \frac{132}{20} to lowest terms by extracting and canceling out 4.

$$\frac{1}{8}+\frac{33}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{33}{5} to fractions with denominator 40.

$$\frac{5}{40}+\frac{264}{40}$$

Since \frac{5}{40} and \frac{264}{40} have the same denominator, add them by adding their numerators.

$$\frac{5+264}{40}$$

Add 5 and 264 to get 269.

$$\frac{269}{40}$$

Factor

$$\frac{269}{2 ^ {3} \cdot 5} = 6\frac{29}{40} = 6.725$$