Solve 1/5(1/4-1/8)+27/8

$$\frac { 1 } { 5 } ( \frac { 1 } { 4 } - \frac { 1 } { 8 } ) + 2 \frac { 7 } { 8 }$$

Evaluate

$$\frac{29}{10}=2.9$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{1}{5}\left(\frac{2}{8}-\frac{1}{8}\right)+\frac{2\times 8+7}{8}$$

Since \frac{2}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}\times \frac{2-1}{8}+\frac{2\times 8+7}{8}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{5}\times \frac{1}{8}+\frac{2\times 8+7}{8}$$

Multiply \frac{1}{5} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{5\times 8}+\frac{2\times 8+7}{8}$$

Do the multiplications in the fraction \frac{1\times 1}{5\times 8}.

$$\frac{1}{40}+\frac{2\times 8+7}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{1}{40}+\frac{16+7}{8}$$

Add 16 and 7 to get 23.

$$\frac{1}{40}+\frac{23}{8}$$

Least common multiple of 40 and 8 is 40. Convert \frac{1}{40} and \frac{23}{8} to fractions with denominator 40.

$$\frac{1}{40}+\frac{115}{40}$$

Since \frac{1}{40} and \frac{115}{40} have the same denominator, add them by adding their numerators.

$$\frac{1+115}{40}$$

Add 1 and 115 to get 116.

$$\frac{116}{40}$$

Reduce the fraction \frac{116}{40} to lowest terms by extracting and canceling out 4.

$$\frac{29}{10}$$

Factor

$$\frac{29}{2 \cdot 5} = 2\frac{9}{10} = 2.9$$