Solve 6/7*1/3+[2*(31/3-2)]div5=

$$\frac { 6 } { 7 } \cdot \frac { 1 } { 3 } + [ 2 \cdot ( 3 \frac { 1 } { 3 } - 2 ) ] \div 5 =$$

Evaluate

$$\frac{86}{105}\approx 0.819047619$$

Solution Steps

Multiply \frac{6}{7} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 1}{7\times 3}+\frac{2\left(\frac{3\times 3+1}{3}-2\right)}{5}$$

Do the multiplications in the fraction \frac{6\times 1}{7\times 3}.

$$\frac{6}{21}+\frac{2\left(\frac{3\times 3+1}{3}-2\right)}{5}$$

Reduce the fraction \frac{6}{21} to lowest terms by extracting and canceling out 3.

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

Multiply 3 and 3 to get 9.

$$\frac{2}{7}+\frac{2\left(\frac{9+1}{3}-2\right)}{5}$$

Add 9 and 1 to get 10.

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

Convert 2 to fraction \frac{6}{3}.

$$\frac{2}{7}+\frac{2\left(\frac{10}{3}-\frac{6}{3}\right)}{5}$$

Since \frac{10}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{7}+\frac{2\times \frac{10-6}{3}}{5}$$

Subtract 6 from 10 to get 4.

$$\frac{2}{7}+\frac{2\times \frac{4}{3}}{5}$$

Express 2\times \frac{4}{3} as a single fraction.

$$\frac{2}{7}+\frac{\frac{2\times 4}{3}}{5}$$

Multiply 2 and 4 to get 8.

$$\frac{2}{7}+\frac{\frac{8}{3}}{5}$$

Express \frac{\frac{8}{3}}{5} as a single fraction.

$$\frac{2}{7}+\frac{8}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{2}{7}+\frac{8}{15}$$

Least common multiple of 7 and 15 is 105. Convert \frac{2}{7} and \frac{8}{15} to fractions with denominator 105.

$$\frac{30}{105}+\frac{56}{105}$$

Since \frac{30}{105} and \frac{56}{105} have the same denominator, add them by adding their numerators.

$$\frac{30+56}{105}$$

Add 30 and 56 to get 86.

$$\frac{86}{105}$$

Factor

$$\frac{2 \cdot 43}{3 \cdot 5 \cdot 7} = 0.819047619047619$$