Solve ((1+3/4-1/2)*3/5)/(2frac{1{3}-frac{5}{4})*frac{4}{13}}

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

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

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

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

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

Add 4 and 3 to get 7.

$$\frac{\left(\frac{7}{4}-\frac{1}{2}\right)\times \frac{3}{5}}{\left(\frac{2\times 3+1}{3}-\frac{5}{4}\right)\times \frac{4}{13}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{7}{4} and \frac{1}{2} to fractions with denominator 4.

$$\frac{\left(\frac{7}{4}-\frac{2}{4}\right)\times \frac{3}{5}}{\left(\frac{2\times 3+1}{3}-\frac{5}{4}\right)\times \frac{4}{13}}$$

Since \frac{7}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-2}{4}\times \frac{3}{5}}{\left(\frac{2\times 3+1}{3}-\frac{5}{4}\right)\times \frac{4}{13}}$$

Subtract 2 from 7 to get 5.

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

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

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

Cancel out 5 in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{\frac{3}{4}}{\left(\frac{7}{3}-\frac{5}{4}\right)\times \frac{4}{13}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{7}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{3}{4}}{\left(\frac{28}{12}-\frac{15}{12}\right)\times \frac{4}{13}}$$

Since \frac{28}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{4}}{\frac{28-15}{12}\times \frac{4}{13}}$$

Subtract 15 from 28 to get 13.

$$\frac{\frac{3}{4}}{\frac{13}{12}\times \frac{4}{13}}$$

Multiply \frac{13}{12} times \frac{4}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3}{4}}{\frac{13\times 4}{12\times 13}}$$

Cancel out 13 in both numerator and denominator.

$$\frac{\frac{3}{4}}{\frac{4}{12}}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3}{4}}{\frac{1}{3}}$$

Divide \frac{3}{4} by \frac{1}{3} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{3}.

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

Express \frac{3}{4}\times 3 as a single fraction.

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

Multiply 3 and 3 to get 9.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$