Solve 7/6+4/13(2/3-1/8)

$$\frac { 7 } { 6 } + \frac { 4 } { 13 } ( \frac { 2 } { 3 } - \frac { 1 } { 8 } )$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{1}{8} to fractions with denominator 24.

$$\frac{7}{6}+\frac{4}{13}\left(\frac{16}{24}-\frac{3}{24}\right)$$

Since \frac{16}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{6}+\frac{4}{13}\times \frac{16-3}{24}$$

Subtract 3 from 16 to get 13.

$$\frac{7}{6}+\frac{4}{13}\times \frac{13}{24}$$

Multiply \frac{4}{13} times \frac{13}{24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{6}+\frac{4\times 13}{13\times 24}$$

Cancel out 13 in both numerator and denominator.

$$\frac{7}{6}+\frac{4}{24}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

$$\frac{7}{6}+\frac{1}{6}$$

Since \frac{7}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{7+1}{6}$$

Add 7 and 1 to get 8.

$$\frac{8}{6}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$