Solve 2-frac{3/5-1/frac{4{3}}}{1/3+9/4-frac{1}{2}}=

$$\frac { 2 - \frac { \frac { 3 } { 5 } - 1 } { \frac { 4 } { 3 } } } { \frac { 1 } { 3 } + \frac { 9 } { 4 } - \frac { 1 } { 2 } } =$$

Evaluate

$$\frac{138}{125}=1.104$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\frac{2-\frac{\frac{3}{5}-\frac{5}{5}}{\frac{4}{3}}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Since \frac{3}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\frac{\frac{3-5}{5}}{\frac{4}{3}}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Subtract 5 from 3 to get -2.

$$\frac{2-\frac{-\frac{2}{5}}{\frac{4}{3}}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Divide -\frac{2}{5} by \frac{4}{3} by multiplying -\frac{2}{5} by the reciprocal of \frac{4}{3}.

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

Multiply -\frac{2}{5} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2-\frac{-2\times 3}{5\times 4}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Do the multiplications in the fraction \frac{-2\times 3}{5\times 4}.

$$\frac{2-\frac{-6}{20}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

$$\frac{2-\left(-\frac{3}{10}\right)}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

The opposite of -\frac{3}{10} is \frac{3}{10}.

$$\frac{2+\frac{3}{10}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Convert 2 to fraction \frac{20}{10}.

$$\frac{\frac{20}{10}+\frac{3}{10}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Since \frac{20}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+3}{10}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Add 20 and 3 to get 23.

$$\frac{\frac{23}{10}}{\frac{1}{3}+\frac{9}{4}-\frac{1}{2}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{9}{4} to fractions with denominator 12.

$$\frac{\frac{23}{10}}{\frac{4}{12}+\frac{27}{12}-\frac{1}{2}}$$

Since \frac{4}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{23}{10}}{\frac{4+27}{12}-\frac{1}{2}}$$

Add 4 and 27 to get 31.

$$\frac{\frac{23}{10}}{\frac{31}{12}-\frac{1}{2}}$$

Least common multiple of 12 and 2 is 12. Convert \frac{31}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{\frac{23}{10}}{\frac{31}{12}-\frac{6}{12}}$$

Since \frac{31}{12} and \frac{6}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{10}}{\frac{31-6}{12}}$$

Subtract 6 from 31 to get 25.

$$\frac{\frac{23}{10}}{\frac{25}{12}}$$

Divide \frac{23}{10} by \frac{25}{12} by multiplying \frac{23}{10} by the reciprocal of \frac{25}{12}.

$$\frac{23}{10}\times \frac{12}{25}$$

Multiply \frac{23}{10} times \frac{12}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 12}{10\times 25}$$

Do the multiplications in the fraction \frac{23\times 12}{10\times 25}.

$$\frac{276}{250}$$

Reduce the fraction \frac{276}{250} to lowest terms by extracting and canceling out 2.

$$\frac{138}{125}$$

Factor

$$\frac{2 \cdot 3 \cdot 23}{5 ^ {3}} = 1\frac{13}{125} = 1.104$$