Solve f[61/4div{21/4-1/2(21/2-frac{1}{4}-frac{1}{6})}]

$$f [ 6 \frac { 1 } { 4 } \div \{ 2 \frac { 1 } { 4 } - \frac { 1 } { 2 } ( 2 \frac { 1 } { 2 } - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \} ]$$

Evaluate

$$\frac{150f}{29}$$

Solution Steps

Multiply 6 and 4 to get 24.

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

Add 24 and 1 to get 25.

$$f\times \frac{\frac{25}{4}}{\frac{2\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Multiply 2 and 4 to get 8.

$$f\times \frac{\frac{25}{4}}{\frac{8+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Add 8 and 1 to get 9.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Multiply 2 and 2 to get 4.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{4+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Add 4 and 1 to get 5.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{10}{4}-\frac{1}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{10-1}{4}-\frac{1}{6}\right)}$$

Subtract 1 from 10 to get 9.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{9}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{27}{12}-\frac{2}{12}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\times \frac{27-2}{12}}$$

Subtract 2 from 27 to get 25.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\times \frac{25}{12}}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1\times 25}{2\times 12}}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{25}{24}}$$

Least common multiple of 4 and 24 is 24. Convert \frac{9}{4} and \frac{25}{24} to fractions with denominator 24.

$$f\times \frac{\frac{25}{4}}{\frac{54}{24}-\frac{25}{24}}$$

Since \frac{54}{24} and \frac{25}{24} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{\frac{25}{4}}{\frac{54-25}{24}}$$

Subtract 25 from 54 to get 29.

$$f\times \frac{\frac{25}{4}}{\frac{29}{24}}$$

Divide \frac{25}{4} by \frac{29}{24} by multiplying \frac{25}{4} by the reciprocal of \frac{29}{24}.

$$f\times \frac{25}{4}\times \frac{24}{29}$$

Multiply \frac{25}{4} times \frac{24}{29} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{25\times 24}{4\times 29}$$

Do the multiplications in the fraction \frac{25\times 24}{4\times 29}.

$$f\times \frac{600}{116}$$

Reduce the fraction \frac{600}{116} to lowest terms by extracting and canceling out 4.

$$f\times \frac{150}{29}$$

Expand

$$\frac{150f}{29}$$

Solution Steps

Multiply 6 and 4 to get 24.

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

Add 24 and 1 to get 25.

$$f\times \frac{\frac{25}{4}}{\frac{2\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Multiply 2 and 4 to get 8.

$$f\times \frac{\frac{25}{4}}{\frac{8+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Add 8 and 1 to get 9.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Multiply 2 and 2 to get 4.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{4+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

Add 4 and 1 to get 5.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{10}{4}-\frac{1}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{10-1}{4}-\frac{1}{6}\right)}$$

Subtract 1 from 10 to get 9.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{9}{4}-\frac{1}{6}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\left(\frac{27}{12}-\frac{2}{12}\right)}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\times \frac{27-2}{12}}$$

Subtract 2 from 27 to get 25.

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1}{2}\times \frac{25}{12}}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{1\times 25}{2\times 12}}$$

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

$$f\times \frac{\frac{25}{4}}{\frac{9}{4}-\frac{25}{24}}$$

Least common multiple of 4 and 24 is 24. Convert \frac{9}{4} and \frac{25}{24} to fractions with denominator 24.

$$f\times \frac{\frac{25}{4}}{\frac{54}{24}-\frac{25}{24}}$$

Since \frac{54}{24} and \frac{25}{24} have the same denominator, subtract them by subtracting their numerators.

$$f\times \frac{\frac{25}{4}}{\frac{54-25}{24}}$$

Subtract 25 from 54 to get 29.

$$f\times \frac{\frac{25}{4}}{\frac{29}{24}}$$

Divide \frac{25}{4} by \frac{29}{24} by multiplying \frac{25}{4} by the reciprocal of \frac{29}{24}.

$$f\times \frac{25}{4}\times \frac{24}{29}$$

Multiply \frac{25}{4} times \frac{24}{29} by multiplying numerator times numerator and denominator times denominator.

$$f\times \frac{25\times 24}{4\times 29}$$

Do the multiplications in the fraction \frac{25\times 24}{4\times 29}.

$$f\times \frac{600}{116}$$

Reduce the fraction \frac{600}{116} to lowest terms by extracting and canceling out 4.

$$f\times \frac{150}{29}$$