Solve 8/15div[(3/5+1/6)*4/23]=

$$\frac { 8 } { 15 } \div [ ( \frac { 3 } { 5 } + \frac { 1 } { 6 } ) \times \frac { 4 } { 23 } ] =$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 5 and 6 is 30. Convert \frac{3}{5} and \frac{1}{6} to fractions with denominator 30.

$$\frac{\frac{8}{15}}{\left(\frac{18}{30}+\frac{5}{30}\right)\times \frac{4}{23}}$$

Since \frac{18}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{8}{15}}{\frac{18+5}{30}\times \frac{4}{23}}$$

Add 18 and 5 to get 23.

$$\frac{\frac{8}{15}}{\frac{23}{30}\times \frac{4}{23}}$$

Multiply \frac{23}{30} times \frac{4}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{8}{15}}{\frac{23\times 4}{30\times 23}}$$

Cancel out 23 in both numerator and denominator.

$$\frac{\frac{8}{15}}{\frac{4}{30}}$$

Reduce the fraction \frac{4}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{8}{15}}{\frac{2}{15}}$$

Divide \frac{8}{15} by \frac{2}{15} by multiplying \frac{8}{15} by the reciprocal of \frac{2}{15}.

$$\frac{8}{15}\times \frac{15}{2}$$

Multiply \frac{8}{15} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 15}{15\times 2}$$

Cancel out 15 in both numerator and denominator.

$$\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$4$$

Factor

$$2^{2}$$