Solve [31/4div{11/4-1/2(21/2-frac{1}{4}-frac{1}{6})}]div(frac{1}{2}text{of}4frac{1}{3})

$$[ 3 \frac { 1 } { 4 } \div \{ 1 \frac { 1 } { 4 } - \frac { 1 } { 2 } ( 2 \frac { 1 } { 2 } - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \} ] \div ( \frac { 1 } { 2 } \text { of } 4 \frac { 1 } { 3 } )$$

Evaluate

$$\frac{36}{5}=7.2$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{\frac{12+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{\frac{13}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{\frac{13}{4}}{\frac{4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{4+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{1}{4} to fractions with denominator 4.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{10}{4}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Since \frac{10}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{10-1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Least common multiple of 4 and 6 is 12. Convert \frac{9}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{27}{12}-\frac{2}{12}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Since \frac{27}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{27-2}{12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Subtract 2 from 27 to get 25.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{25}{12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Multiply \frac{1}{2} times \frac{25}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1\times 25}{2\times 12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Do the multiplications in the fraction \frac{1\times 25}{2\times 12}.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Least common multiple of 4 and 24 is 24. Convert \frac{5}{4} and \frac{25}{24} to fractions with denominator 24.

$$\frac{\frac{\frac{13}{4}}{\frac{30}{24}-\frac{25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Since \frac{30}{24} and \frac{25}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{13}{4}}{\frac{30-25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Subtract 25 from 30 to get 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Divide \frac{13}{4} by \frac{5}{24} by multiplying \frac{13}{4} by the reciprocal of \frac{5}{24}.

$$\frac{\frac{13}{4}\times \frac{24}{5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Multiply \frac{13}{4} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{13\times 24}{4\times 5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Do the multiplications in the fraction \frac{13\times 24}{4\times 5}.

$$\frac{\frac{312}{20}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Reduce the fraction \frac{312}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{12+1}{3}}$$

Add 12 and 1 to get 13.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{13}{3}}$$

Multiply \frac{1}{2} times \frac{13}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{78}{5}}{\frac{1\times 13}{2\times 3}}$$

Do the multiplications in the fraction \frac{1\times 13}{2\times 3}.

$$\frac{\frac{78}{5}}{\frac{13}{6}}$$

Divide \frac{78}{5} by \frac{13}{6} by multiplying \frac{78}{5} by the reciprocal of \frac{13}{6}.

$$\frac{78}{5}\times \frac{6}{13}$$

Multiply \frac{78}{5} times \frac{6}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{78\times 6}{5\times 13}$$

Do the multiplications in the fraction \frac{78\times 6}{5\times 13}.

$$\frac{468}{65}$$

Reduce the fraction \frac{468}{65} to lowest terms by extracting and canceling out 13.

$$\frac{36}{5}$$

Factor

$$\frac{2 ^ {2} \cdot 3 ^ {2}}{5} = 7\frac{1}{5} = 7.2$$