Solve (1/4-1/5)div2/5+3/4

$$( \frac { 1 } { 4 } - \frac { 1 } { 5 } ) \div \frac { 2 } { 5 } + \frac { 3 } { 4 }$$

Evaluate

$$\frac{7}{8}=0.875$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}-\frac{4}{20}}{\frac{2}{5}}+\frac{3}{4}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-4}{20}}{\frac{2}{5}}+\frac{3}{4}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{1}{20}}{\frac{2}{5}}+\frac{3}{4}$$

Divide \frac{1}{20} by \frac{2}{5} by multiplying \frac{1}{20} by the reciprocal of \frac{2}{5}.

$$\frac{1}{20}\times \frac{5}{2}+\frac{3}{4}$$

Multiply \frac{1}{20} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 5}{20\times 2}+\frac{3}{4}$$

Do the multiplications in the fraction \frac{1\times 5}{20\times 2}.

$$\frac{5}{40}+\frac{3}{4}$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$\frac{1}{8}+\frac{3}{4}$$

Least common multiple of 8 and 4 is 8. Convert \frac{1}{8} and \frac{3}{4} to fractions with denominator 8.

$$\frac{1}{8}+\frac{6}{8}$$

Since \frac{1}{8} and \frac{6}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{8}$$

Add 1 and 6 to get 7.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$