Solve (1-1/10)div(1/10+1/8)

$$( 1 - \frac { 1 } { 10 } ) \div ( \frac { 1 } { 10 } + \frac { 1 } { 8 } )$$

Evaluate

$$4$$

Solution Steps

Convert 1 to fraction \frac{10}{10}.

$$\frac{\frac{10}{10}-\frac{1}{10}}{\frac{1}{10}+\frac{1}{8}}$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-1}{10}}{\frac{1}{10}+\frac{1}{8}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{9}{10}}{\frac{1}{10}+\frac{1}{8}}$$

Least common multiple of 10 and 8 is 40. Convert \frac{1}{10} and \frac{1}{8} to fractions with denominator 40.

$$\frac{\frac{9}{10}}{\frac{4}{40}+\frac{5}{40}}$$

Since \frac{4}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{10}}{\frac{4+5}{40}}$$

Add 4 and 5 to get 9.

$$\frac{\frac{9}{10}}{\frac{9}{40}}$$

Divide \frac{9}{10} by \frac{9}{40} by multiplying \frac{9}{10} by the reciprocal of \frac{9}{40}.

$$\frac{9}{10}\times \frac{40}{9}$$

Multiply \frac{9}{10} times \frac{40}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 40}{10\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{40}{10}$$

Divide 40 by 10 to get 4.

$$4$$

Factor

$$2^{2}$$