Solve (2-3/4*4/5)div(1/12+4/15)

$$( 2 - \frac { 3 } { 4 } \times \frac { 4 } { 5 } ) \div ( \frac { 1 } { 12 } + \frac { 4 } { 15 } )$$

Evaluate

$$4$$

Solution Steps

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

$$\frac{2-\frac{3\times 4}{4\times 5}}{\frac{1}{12}+\frac{4}{15}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2-\frac{3}{5}}{\frac{1}{12}+\frac{4}{15}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{10}{5}-\frac{3}{5}}{\frac{1}{12}+\frac{4}{15}}$$

Since \frac{10}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-3}{5}}{\frac{1}{12}+\frac{4}{15}}$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{7}{5}}{\frac{1}{12}+\frac{4}{15}}$$

Least common multiple of 12 and 15 is 60. Convert \frac{1}{12} and \frac{4}{15} to fractions with denominator 60.

$$\frac{\frac{7}{5}}{\frac{5}{60}+\frac{16}{60}}$$

Since \frac{5}{60} and \frac{16}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{5}}{\frac{5+16}{60}}$$

Add 5 and 16 to get 21.

$$\frac{\frac{7}{5}}{\frac{21}{60}}$$

Reduce the fraction \frac{21}{60} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{5}}{\frac{7}{20}}$$

Divide \frac{7}{5} by \frac{7}{20} by multiplying \frac{7}{5} by the reciprocal of \frac{7}{20}.

$$\frac{7}{5}\times \frac{20}{7}$$

Multiply \frac{7}{5} times \frac{20}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 20}{5\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$4$$

Factor

$$2^{2}$$