Solve 11/13*2/3+11/2div13/14

$$1 \frac { 1 } { 13 } \times \frac { 2 } { 3 } + 1 \frac { 1 } { 2 } \div \frac { 13 } { 14 }$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

Multiply 1 and 13 to get 13.

$$\frac{13+1}{13}\times \frac{2}{3}+\frac{\frac{1\times 2+1}{2}}{\frac{13}{14}}$$

Add 13 and 1 to get 14.

$$\frac{14}{13}\times \frac{2}{3}+\frac{\frac{1\times 2+1}{2}}{\frac{13}{14}}$$

Multiply \frac{14}{13} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 2}{13\times 3}+\frac{\frac{1\times 2+1}{2}}{\frac{13}{14}}$$

Do the multiplications in the fraction \frac{14\times 2}{13\times 3}.

$$\frac{28}{39}+\frac{\frac{1\times 2+1}{2}}{\frac{13}{14}}$$

Divide \frac{1\times 2+1}{2} by \frac{13}{14} by multiplying \frac{1\times 2+1}{2} by the reciprocal of \frac{13}{14}.

$$\frac{28}{39}+\frac{\left(1\times 2+1\right)\times 14}{2\times 13}$$

Cancel out 2 in both numerator and denominator.

$$\frac{28}{39}+\frac{7\left(1+2\right)}{13}$$

Add 1 and 2 to get 3.

$$\frac{28}{39}+\frac{7\times 3}{13}$$

Multiply 7 and 3 to get 21.

$$\frac{28}{39}+\frac{21}{13}$$

Least common multiple of 39 and 13 is 39. Convert \frac{28}{39} and \frac{21}{13} to fractions with denominator 39.

$$\frac{28}{39}+\frac{63}{39}$$

Since \frac{28}{39} and \frac{63}{39} have the same denominator, add them by adding their numerators.

$$\frac{28+63}{39}$$

Add 28 and 63 to get 91.

$$\frac{91}{39}$$

Reduce the fraction \frac{91}{39} to lowest terms by extracting and canceling out 13.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$