Solve 2/3+(1/2+2/3)*2/7

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

Evaluate

$$1$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{2}{3}+\left(\frac{3}{6}+\frac{4}{6}\right)\times \frac{2}{7}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}+\frac{3+4}{6}\times \frac{2}{7}$$

Add 3 and 4 to get 7.

$$\frac{2}{3}+\frac{7}{6}\times \frac{2}{7}$$

Multiply \frac{7}{6} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{7\times 2}{6\times 7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{2}{3}+\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Since \frac{2}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 1 to get 3.

$$\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$1$$

Factor

$$1$$