Solve 4/5-1/3/frac{1{5}+7/15}

$$\frac { \frac { 4 } { 5 } - \frac { 1 } { 3 } } { \frac { 1 } { 5 } + \frac { 7 } { 15 } }$$

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{1}{3} to fractions with denominator 15.

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

Since \frac{12}{15} and \frac{5}{15} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 5 from 12 to get 7.

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

Least common multiple of 5 and 15 is 15. Convert \frac{1}{5} and \frac{7}{15} to fractions with denominator 15.

$$\frac{\frac{7}{15}}{\frac{3}{15}+\frac{7}{15}}$$

Since \frac{3}{15} and \frac{7}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{15}}{\frac{3+7}{15}}$$

Add 3 and 7 to get 10.

$$\frac{\frac{7}{15}}{\frac{10}{15}}$$

Reduce the fraction \frac{10}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{15}}{\frac{2}{3}}$$

Divide \frac{7}{15} by \frac{2}{3} by multiplying \frac{7}{15} by the reciprocal of \frac{2}{3}.

$$\frac{7}{15}\times \frac{3}{2}$$

Multiply \frac{7}{15} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{15\times 2}$$

Do the multiplications in the fraction \frac{7\times 3}{15\times 2}.

$$\frac{21}{30}$$

Reduce the fraction \frac{21}{30} to lowest terms by extracting and canceling out 3.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$