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

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

Evaluate

$$-\frac{23}{84}\approx -0.273809524$$

Solution Steps

Least common multiple of 7 and 4 is 28. Convert \frac{3}{7} and \frac{1}{4} to fractions with denominator 28.

$$\frac{12}{28}+\frac{7}{28}-\left(\frac{2}{7}+\frac{4}{6}\right)$$

Since \frac{12}{28} and \frac{7}{28} have the same denominator, add them by adding their numerators.

$$\frac{12+7}{28}-\left(\frac{2}{7}+\frac{4}{6}\right)$$

Add 12 and 7 to get 19.

$$\frac{19}{28}-\left(\frac{2}{7}+\frac{4}{6}\right)$$

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

$$\frac{19}{28}-\left(\frac{2}{7}+\frac{2}{3}\right)$$

Least common multiple of 7 and 3 is 21. Convert \frac{2}{7} and \frac{2}{3} to fractions with denominator 21.

$$\frac{19}{28}-\left(\frac{6}{21}+\frac{14}{21}\right)$$

Since \frac{6}{21} and \frac{14}{21} have the same denominator, add them by adding their numerators.

$$\frac{19}{28}-\frac{6+14}{21}$$

Add 6 and 14 to get 20.

$$\frac{19}{28}-\frac{20}{21}$$

Least common multiple of 28 and 21 is 84. Convert \frac{19}{28} and \frac{20}{21} to fractions with denominator 84.

$$\frac{57}{84}-\frac{80}{84}$$

Since \frac{57}{84} and \frac{80}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{57-80}{84}$$

Subtract 80 from 57 to get -23.

$$-\frac{23}{84}$$

Factor

$$-\frac{23}{84} = -0.27380952380952384$$