Solve 25/8-(2/7+5/8)

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

Evaluate

$$\frac{12}{7}\approx 1.714285714$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{16+5}{8}-\left(\frac{2}{7}+\frac{5}{8}\right)$$

Add 16 and 5 to get 21.

$$\frac{21}{8}-\left(\frac{2}{7}+\frac{5}{8}\right)$$

Least common multiple of 7 and 8 is 56. Convert \frac{2}{7} and \frac{5}{8} to fractions with denominator 56.

$$\frac{21}{8}-\left(\frac{16}{56}+\frac{35}{56}\right)$$

Since \frac{16}{56} and \frac{35}{56} have the same denominator, add them by adding their numerators.

$$\frac{21}{8}-\frac{16+35}{56}$$

Add 16 and 35 to get 51.

$$\frac{21}{8}-\frac{51}{56}$$

Least common multiple of 8 and 56 is 56. Convert \frac{21}{8} and \frac{51}{56} to fractions with denominator 56.

$$\frac{147}{56}-\frac{51}{56}$$

Since \frac{147}{56} and \frac{51}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{147-51}{56}$$

Subtract 51 from 147 to get 96.

$$\frac{96}{56}$$

Reduce the fraction \frac{96}{56} to lowest terms by extracting and canceling out 8.

$$\frac{12}{7}$$

Factor

$$\frac{2 ^ {2} \cdot 3}{7} = 1\frac{5}{7} = 1.7142857142857142$$