Solve 3/14*7div(1/2+1/5)

$$\frac { 3 } { 14 } \times 7 \div ( \frac { 1 } { 2 } + \frac { 1 } { 5 } )$$

Evaluate

$$\frac{15}{7}\approx 2.142857143$$

Solution Steps

Express \frac{3}{14}\times 7 as a single fraction.

$$\frac{\frac{3\times 7}{14}}{\frac{1}{2}+\frac{1}{5}}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{21}{14}}{\frac{1}{2}+\frac{1}{5}}$$

Reduce the fraction \frac{21}{14} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{3}{2}}{\frac{1}{2}+\frac{1}{5}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{\frac{3}{2}}{\frac{5}{10}+\frac{2}{10}}$$

Since \frac{5}{10} and \frac{2}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}}{\frac{5+2}{10}}$$

Add 5 and 2 to get 7.

$$\frac{\frac{3}{2}}{\frac{7}{10}}$$

Divide \frac{3}{2} by \frac{7}{10} by multiplying \frac{3}{2} by the reciprocal of \frac{7}{10}.

$$\frac{3}{2}\times \frac{10}{7}$$

Multiply \frac{3}{2} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{2\times 7}$$

Do the multiplications in the fraction \frac{3\times 10}{2\times 7}.

$$\frac{30}{14}$$

Reduce the fraction \frac{30}{14} to lowest terms by extracting and canceling out 2.

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

Factor

$$\frac{3 \cdot 5}{7} = 2\frac{1}{7} = 2.142857142857143$$