Solve 3-frac{1/4/frac{1{2}}-2-1/5/frac{1{3}}}{3-frac{1}{2}}*(frac{3}{4}+frac{1}{25})

$$\frac { \frac { 3 - \frac { 1 } { 4 } } { \frac { 1 } { 2 } } - \frac { 2 - \frac { 1 } { 5 } } { \frac { 1 } { 3 } } } { 3 - \frac { 1 } { 2 } } \times ( \frac { 3 } { 4 } + \frac { 1 } { 25 } )$$

Evaluate

$$\frac{79}{2500}=0.0316$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$\frac{\frac{\frac{12}{4}-\frac{1}{4}}{\frac{1}{2}}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Since \frac{12}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{12-1}{4}}{\frac{1}{2}}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Subtract 1 from 12 to get 11.

$$\frac{\frac{\frac{11}{4}}{\frac{1}{2}}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Divide \frac{11}{4} by \frac{1}{2} by multiplying \frac{11}{4} by the reciprocal of \frac{1}{2}.

$$\frac{\frac{11}{4}\times 2-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Express \frac{11}{4}\times 2 as a single fraction.

$$\frac{\frac{11\times 2}{4}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Multiply 11 and 2 to get 22.

$$\frac{\frac{22}{4}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Reduce the fraction \frac{22}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{2}-\frac{2-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{11}{2}-\frac{\frac{10}{5}-\frac{1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{2}-\frac{\frac{10-1}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{11}{2}-\frac{\frac{9}{5}}{\frac{1}{3}}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Divide \frac{9}{5} by \frac{1}{3} by multiplying \frac{9}{5} by the reciprocal of \frac{1}{3}.

$$\frac{\frac{11}{2}-\frac{9}{5}\times 3}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Express \frac{9}{5}\times 3 as a single fraction.

$$\frac{\frac{11}{2}-\frac{9\times 3}{5}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Multiply 9 and 3 to get 27.

$$\frac{\frac{11}{2}-\frac{27}{5}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{11}{2} and \frac{27}{5} to fractions with denominator 10.

$$\frac{\frac{55}{10}-\frac{54}{10}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Since \frac{55}{10} and \frac{54}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{55-54}{10}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Subtract 54 from 55 to get 1.

$$\frac{\frac{1}{10}}{3-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{1}{10}}{\frac{6}{2}-\frac{1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{10}}{\frac{6-1}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{1}{10}}{\frac{5}{2}}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Divide \frac{1}{10} by \frac{5}{2} by multiplying \frac{1}{10} by the reciprocal of \frac{5}{2}.

$$\frac{1}{10}\times \frac{2}{5}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Multiply \frac{1}{10} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{10\times 5}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Do the multiplications in the fraction \frac{1\times 2}{10\times 5}.

$$\frac{2}{50}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Reduce the fraction \frac{2}{50} to lowest terms by extracting and canceling out 2.

$$\frac{1}{25}\left(\frac{3}{4}+\frac{1}{25}\right)$$

Least common multiple of 4 and 25 is 100. Convert \frac{3}{4} and \frac{1}{25} to fractions with denominator 100.

$$\frac{1}{25}\left(\frac{75}{100}+\frac{4}{100}\right)$$

Since \frac{75}{100} and \frac{4}{100} have the same denominator, add them by adding their numerators.

$$\frac{1}{25}\times \frac{75+4}{100}$$

Add 75 and 4 to get 79.

$$\frac{1}{25}\times \frac{79}{100}$$

Multiply \frac{1}{25} times \frac{79}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 79}{25\times 100}$$

Do the multiplications in the fraction \frac{1\times 79}{25\times 100}.

$$\frac{79}{2500}$$

Factor

$$\frac{79}{2 ^ {2} \cdot 5 ^ {4}} = 0.0316$$