Solve (1/2+1/3)*4/5-1/8

$$( \frac { 1 } { 2 } + \frac { 1 } { 3 } ) \cdot \frac { 4 } { 5 } - \frac { 1 } { 8 }$$

Evaluate

$$\frac{13}{24}\approx 0.541666667$$

Solution Steps

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

$$\left(\frac{3}{6}+\frac{2}{6}\right)\times \frac{4}{5}-\frac{1}{8}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+2}{6}\times \frac{4}{5}-\frac{1}{8}$$

Add 3 and 2 to get 5.

$$\frac{5}{6}\times \frac{4}{5}-\frac{1}{8}$$

Multiply \frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{6\times 5}-\frac{1}{8}$$

Cancel out 5 in both numerator and denominator.

$$\frac{4}{6}-\frac{1}{8}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}-\frac{1}{8}$$

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

$$\frac{16}{24}-\frac{3}{24}$$

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

$$\frac{16-3}{24}$$

Subtract 3 from 16 to get 13.

$$\frac{13}{24}$$

Factor

$$\frac{13}{2 ^ {3} \cdot 3} = 0.5416666666666666$$