Solve 3/10div12/5*(1/3+1/7)

$$\frac { 3 } { 10 } \div 1 \frac { 2 } { 5 } \times ( \frac { 1 } { 3 } + \frac { 1 } { 7 } )$$

Evaluate

$$\frac{5}{49}\approx 0.102040816$$

Solution Steps

Divide \frac{3}{10} by \frac{1\times 5+2}{5} by multiplying \frac{3}{10} by the reciprocal of \frac{1\times 5+2}{5}.

$$\frac{3\times 5}{10\left(1\times 5+2\right)}\left(\frac{1}{3}+\frac{1}{7}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{3}{2\left(2+5\right)}\left(\frac{1}{3}+\frac{1}{7}\right)$$

Add 2 and 5 to get 7.

$$\frac{3}{2\times 7}\left(\frac{1}{3}+\frac{1}{7}\right)$$

Multiply 2 and 7 to get 14.

$$\frac{3}{14}\left(\frac{1}{3}+\frac{1}{7}\right)$$

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{1}{7} to fractions with denominator 21.

$$\frac{3}{14}\left(\frac{7}{21}+\frac{3}{21}\right)$$

Since \frac{7}{21} and \frac{3}{21} have the same denominator, add them by adding their numerators.

$$\frac{3}{14}\times \frac{7+3}{21}$$

Add 7 and 3 to get 10.

$$\frac{3}{14}\times \frac{10}{21}$$

Multiply \frac{3}{14} times \frac{10}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 10}{14\times 21}$$

Do the multiplications in the fraction \frac{3\times 10}{14\times 21}.

$$\frac{30}{294}$$

Reduce the fraction \frac{30}{294} to lowest terms by extracting and canceling out 6.

$$\frac{5}{49}$$

Factor

$$\frac{5}{7 ^ {2}} = 0.10204081632653061$$