Solve 7/4div(2/3+1/2)*2/5

$$\frac { 7 } { 4 } \div ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) \times \frac { 2 } { 5 }$$

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{7}{4}}{\frac{4}{6}+\frac{3}{6}}\times \frac{2}{5}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{4}}{\frac{4+3}{6}}\times \frac{2}{5}$$

Add 4 and 3 to get 7.

$$\frac{\frac{7}{4}}{\frac{7}{6}}\times \frac{2}{5}$$

Divide \frac{7}{4} by \frac{7}{6} by multiplying \frac{7}{4} by the reciprocal of \frac{7}{6}.

$$\frac{7}{4}\times \frac{6}{7}\times \frac{2}{5}$$

Multiply \frac{7}{4} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 6}{4\times 7}\times \frac{2}{5}$$

Cancel out 7 in both numerator and denominator.

$$\frac{6}{4}\times \frac{2}{5}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}\times \frac{2}{5}$$

Multiply \frac{3}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{2\times 5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$