Solve 4/7*4/3div(2/5-4/15)

$$\frac { 4 } { 7 } \times \frac { 4 } { 3 } \div ( \frac { 2 } { 5 } - \frac { 4 } { 15 } )$$

Evaluate

$$\frac{40}{7}\approx 5.714285714$$

Solution Steps

Multiply \frac{4}{7} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 4}{7\times 3}}{\frac{2}{5}-\frac{4}{15}}$$

Do the multiplications in the fraction \frac{4\times 4}{7\times 3}.

$$\frac{\frac{16}{21}}{\frac{2}{5}-\frac{4}{15}}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{4}{15} to fractions with denominator 15.

$$\frac{\frac{16}{21}}{\frac{6}{15}-\frac{4}{15}}$$

Since \frac{6}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16}{21}}{\frac{6-4}{15}}$$

Subtract 4 from 6 to get 2.

$$\frac{\frac{16}{21}}{\frac{2}{15}}$$

Divide \frac{16}{21} by \frac{2}{15} by multiplying \frac{16}{21} by the reciprocal of \frac{2}{15}.

$$\frac{16}{21}\times \frac{15}{2}$$

Multiply \frac{16}{21} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 15}{21\times 2}$$

Do the multiplications in the fraction \frac{16\times 15}{21\times 2}.

$$\frac{240}{42}$$

Reduce the fraction \frac{240}{42} to lowest terms by extracting and canceling out 6.

$$\frac{40}{7}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{7} = 5\frac{5}{7} = 5.714285714285714$$