Solve 24[3/8-7/24]-3/7[1/3+frac{5}{6}]

$$24 [ \frac { 3 } { 8 } - \frac { 7 } { 24 } ] - \frac { 3 } { 7 } [ \frac { 1 } { 3 } + \frac { 5 } { 6 } ]$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Least common multiple of 8 and 24 is 24. Convert \frac{3}{8} and \frac{7}{24} to fractions with denominator 24.

$$24\left(\frac{9}{24}-\frac{7}{24}\right)-\frac{3}{7}\left(\frac{1}{3}+\frac{5}{6}\right)$$

Since \frac{9}{24} and \frac{7}{24} have the same denominator, subtract them by subtracting their numerators.

$$24\times \frac{9-7}{24}-\frac{3}{7}\left(\frac{1}{3}+\frac{5}{6}\right)$$

Subtract 7 from 9 to get 2.

$$24\times \frac{2}{24}-\frac{3}{7}\left(\frac{1}{3}+\frac{5}{6}\right)$$

Reduce the fraction \frac{2}{24} to lowest terms by extracting and canceling out 2.

$$24\times \frac{1}{12}-\frac{3}{7}\left(\frac{1}{3}+\frac{5}{6}\right)$$

Multiply 24 and \frac{1}{12} to get \frac{24}{12}.

$$\frac{24}{12}-\frac{3}{7}\left(\frac{1}{3}+\frac{5}{6}\right)$$

Divide 24 by 12 to get 2.

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

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$2-\frac{3}{7}\left(\frac{2}{6}+\frac{5}{6}\right)$$

Since \frac{2}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$2-\frac{3}{7}\times \frac{2+5}{6}$$

Add 2 and 5 to get 7.

$$2-\frac{3}{7}\times \frac{7}{6}$$

Multiply \frac{3}{7} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$2-\frac{3\times 7}{7\times 6}$$

Cancel out 7 in both numerator and denominator.

$$2-\frac{3}{6}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Convert 2 to fraction \frac{4}{2}.

$$\frac{4}{2}-\frac{1}{2}$$

Since \frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{2}$$

Subtract 1 from 4 to get 3.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$