Solve 3/4(1/2+2/3)-frac{1/8}{frac{1}{4}(frac{1}{2}+frac{3}{4}-frac{1}{3})-frac{1}{24}}

$$\frac { \frac { 3 } { 4 } ( \frac { 1 } { 2 } + \frac { 2 } { 3 } ) - \frac { 1 } { 8 } } { \frac { 1 } { 4 } ( \frac { 1 } { 2 } + \frac { 3 } { 4 } - \frac { 1 } { 3 } ) - \frac { 1 } { 24 } }$$

Evaluate

$$4$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{3}{4}\left(\frac{3}{6}+\frac{4}{6}\right)-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{4}\times \frac{3+4}{6}-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Add 3 and 4 to get 7.

$$\frac{\frac{3}{4}\times \frac{7}{6}-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Multiply \frac{3}{4} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 7}{4\times 6}-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Do the multiplications in the fraction \frac{3\times 7}{4\times 6}.

$$\frac{\frac{21}{24}-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{8}-\frac{1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Since \frac{7}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-1}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Subtract 1 from 7 to get 6.

$$\frac{\frac{6}{8}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{3}{4}}{\frac{1}{4}\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{\frac{3}{4}}{\frac{1}{4}\left(\frac{2}{4}+\frac{3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{4}}{\frac{1}{4}\left(\frac{2+3}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Add 2 and 3 to get 5.

$$\frac{\frac{3}{4}}{\frac{1}{4}\left(\frac{5}{4}-\frac{1}{3}\right)-\frac{1}{24}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{1}{3} to fractions with denominator 12.

$$\frac{\frac{3}{4}}{\frac{1}{4}\left(\frac{15}{12}-\frac{4}{12}\right)-\frac{1}{24}}$$

Since \frac{15}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{1}{4}\times \frac{15-4}{12}-\frac{1}{24}}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{3}{4}}{\frac{1}{4}\times \frac{11}{12}-\frac{1}{24}}$$

Multiply \frac{1}{4} times \frac{11}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{4}}{\frac{1\times 11}{4\times 12}-\frac{1}{24}}$$

Do the multiplications in the fraction \frac{1\times 11}{4\times 12}.

$$\frac{\frac{3}{4}}{\frac{11}{48}-\frac{1}{24}}$$

Least common multiple of 48 and 24 is 48. Convert \frac{11}{48} and \frac{1}{24} to fractions with denominator 48.

$$\frac{\frac{3}{4}}{\frac{11}{48}-\frac{2}{48}}$$

Since \frac{11}{48} and \frac{2}{48} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{11-2}{48}}$$

Subtract 2 from 11 to get 9.

$$\frac{\frac{3}{4}}{\frac{9}{48}}$$

Reduce the fraction \frac{9}{48} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{4}}{\frac{3}{16}}$$

Divide \frac{3}{4} by \frac{3}{16} by multiplying \frac{3}{4} by the reciprocal of \frac{3}{16}.

$$\frac{3}{4}\times \frac{16}{3}$$

Multiply \frac{3}{4} times \frac{16}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 16}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$4$$

Factor

$$2^{2}$$