Solve 2/3/frac{1{6}}+1/4/frac{3{2}}-frac{frac{4}{5}}{frac{3}{10}}

$$\frac { \frac { 2 } { 3 } } { \frac { 1 } { 6 } } + \frac { \frac { 1 } { 4 } } { \frac { 3 } { 2 } } - \frac { \frac { 4 } { 5 } } { \frac { 3 } { 10 } }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Divide \frac{2}{3} by \frac{1}{6} by multiplying \frac{2}{3} by the reciprocal of \frac{1}{6}.

$$\frac{2}{3}\times 6+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{2\times 6}{3}+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Multiply 2 and 6 to get 12.

$$\frac{12}{3}+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Divide 12 by 3 to get 4.

$$4+\frac{\frac{1}{4}}{\frac{3}{2}}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Divide \frac{1}{4} by \frac{3}{2} by multiplying \frac{1}{4} by the reciprocal of \frac{3}{2}.

$$4+\frac{1}{4}\times \frac{2}{3}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$4+\frac{1\times 2}{4\times 3}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

$$4+\frac{2}{12}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$4+\frac{1}{6}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Convert 4 to fraction \frac{24}{6}.

$$\frac{24}{6}+\frac{1}{6}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Since \frac{24}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{24+1}{6}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Add 24 and 1 to get 25.

$$\frac{25}{6}-\frac{\frac{4}{5}}{\frac{3}{10}}$$

Divide \frac{4}{5} by \frac{3}{10} by multiplying \frac{4}{5} by the reciprocal of \frac{3}{10}.

$$\frac{25}{6}-\frac{4}{5}\times \frac{10}{3}$$

Multiply \frac{4}{5} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25}{6}-\frac{4\times 10}{5\times 3}$$

Do the multiplications in the fraction \frac{4\times 10}{5\times 3}.

$$\frac{25}{6}-\frac{40}{15}$$

Reduce the fraction \frac{40}{15} to lowest terms by extracting and canceling out 5.

$$\frac{25}{6}-\frac{8}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{25}{6} and \frac{8}{3} to fractions with denominator 6.

$$\frac{25}{6}-\frac{16}{6}$$

Since \frac{25}{6} and \frac{16}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25-16}{6}$$

Subtract 16 from 25 to get 9.

$$\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$