Solve (3/8+1/7)-(1/6+5/2)

$$( \frac{ 3 }{ 8 } + \frac{ 1 }{ 7 } )-( \frac{ 1 }{ 6 } + \frac{ 5 }{ 2 } )$$

Evaluate

$$-\frac{361}{168}\approx -2.148809524$$

Solution Steps

Least common multiple of 8 and 7 is 56. Convert \frac{3}{8} and \frac{1}{7} to fractions with denominator 56.

$$\frac{21}{56}+\frac{8}{56}-\left(\frac{1}{6}+\frac{5}{2}\right)$$

Since \frac{21}{56} and \frac{8}{56} have the same denominator, add them by adding their numerators.

$$\frac{21+8}{56}-\left(\frac{1}{6}+\frac{5}{2}\right)$$

Add 21 and 8 to get 29.

$$\frac{29}{56}-\left(\frac{1}{6}+\frac{5}{2}\right)$$

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{5}{2} to fractions with denominator 6.

$$\frac{29}{56}-\left(\frac{1}{6}+\frac{15}{6}\right)$$

Since \frac{1}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{29}{56}-\frac{1+15}{6}$$

Add 1 and 15 to get 16.

$$\frac{29}{56}-\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{29}{56}-\frac{8}{3}$$

Least common multiple of 56 and 3 is 168. Convert \frac{29}{56} and \frac{8}{3} to fractions with denominator 168.

$$\frac{87}{168}-\frac{448}{168}$$

Since \frac{87}{168} and \frac{448}{168} have the same denominator, subtract them by subtracting their numerators.

$$\frac{87-448}{168}$$

Subtract 448 from 87 to get -361.

$$-\frac{361}{168}$$

Factor

$$-\frac{361}{168} = -2\frac{25}{168} = -2.1488095238095237$$