Solve (4/5*20/16)div(1/2+1/3)

$$( \frac { 4 } { 5 } \cdot \frac { 20 } { 16 } ) \div ( \frac { 1 } { 2 } + \frac { 1 } { 3 } )$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Reduce the fraction \frac{20}{16} to lowest terms by extracting and canceling out 4.

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

Cancel out \frac{4}{5} and its reciprocal \frac{5}{4}.

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

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

$$\frac{1}{\frac{3}{6}+\frac{2}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{\frac{3+2}{6}}$$

Add 3 and 2 to get 5.

$$\frac{1}{\frac{5}{6}}$$

Divide 1 by \frac{5}{6} by multiplying 1 by the reciprocal of \frac{5}{6}.

$$1\times \frac{6}{5}$$

Multiply 1 and \frac{6}{5} to get \frac{6}{5}.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$