Solve (10/3-1/3):(2/5+1/2)

$$( \frac { 10 } { 3 } - \frac { 1 } { 3 } ) : ( \frac { 2 } { 5 } + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{10}{3}\approx 3.333333333$$

Solution Steps

Since \frac{10}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-1}{3}}{\frac{2}{5}+\frac{1}{2}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{9}{3}}{\frac{2}{5}+\frac{1}{2}}$$

Divide 9 by 3 to get 3.

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

Least common multiple of 5 and 2 is 10. Convert \frac{2}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{3}{\frac{4}{10}+\frac{5}{10}}$$

Since \frac{4}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{3}{\frac{4+5}{10}}$$

Add 4 and 5 to get 9.

$$\frac{3}{\frac{9}{10}}$$

Divide 3 by \frac{9}{10} by multiplying 3 by the reciprocal of \frac{9}{10}.

$$3\times \frac{10}{9}$$

Express 3\times \frac{10}{9} as a single fraction.

$$\frac{3\times 10}{9}$$

Multiply 3 and 10 to get 30.

$$\frac{30}{9}$$

Reduce the fraction \frac{30}{9} to lowest terms by extracting and canceling out 3.

$$\frac{10}{3}$$

Factor

$$\frac{2 \cdot 5}{3} = 3\frac{1}{3} = 3.3333333333333335$$