Solve 2-frac{1/3/frac{3{4}}+1+2/3/frac{1{4}}}{1-frac{1}{2}}*frac{9}{40}

$$\frac { \frac { 2 - \frac { 1 } { 3 } } { \frac { 3 } { 4 } } + \frac { 1 + \frac { 2 } { 3 } } { \frac { 1 } { 4 } } } { 1 - \frac { 1 } { 2 } } \times \frac { 9 } { 40 }$$

Evaluate

$$4$$

Solution Steps

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

$$\frac{\frac{\frac{6}{3}-\frac{1}{3}}{\frac{3}{4}}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\frac{6-1}{3}}{\frac{3}{4}}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{\frac{5}{3}}{\frac{3}{4}}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

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

$$\frac{\frac{5}{3}\times \frac{4}{3}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

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

$$\frac{\frac{5\times 4}{3\times 3}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

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

$$\frac{\frac{20}{9}+\frac{1+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{20}{9}+\frac{\frac{3}{3}+\frac{2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20}{9}+\frac{\frac{3+2}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Add 3 and 2 to get 5.

$$\frac{\frac{20}{9}+\frac{\frac{5}{3}}{\frac{1}{4}}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Divide \frac{5}{3} by \frac{1}{4} by multiplying \frac{5}{3} by the reciprocal of \frac{1}{4}.

$$\frac{\frac{20}{9}+\frac{5}{3}\times 4}{1-\frac{1}{2}}\times \frac{9}{40}$$

Express \frac{5}{3}\times 4 as a single fraction.

$$\frac{\frac{20}{9}+\frac{5\times 4}{3}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{20}{9}+\frac{20}{3}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Least common multiple of 9 and 3 is 9. Convert \frac{20}{9} and \frac{20}{3} to fractions with denominator 9.

$$\frac{\frac{20}{9}+\frac{60}{9}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Since \frac{20}{9} and \frac{60}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20+60}{9}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Add 20 and 60 to get 80.

$$\frac{\frac{80}{9}}{1-\frac{1}{2}}\times \frac{9}{40}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{80}{9}}{\frac{2}{2}-\frac{1}{2}}\times \frac{9}{40}$$

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

$$\frac{\frac{80}{9}}{\frac{2-1}{2}}\times \frac{9}{40}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{80}{9}}{\frac{1}{2}}\times \frac{9}{40}$$

Divide \frac{80}{9} by \frac{1}{2} by multiplying \frac{80}{9} by the reciprocal of \frac{1}{2}.

$$\frac{80}{9}\times 2\times \frac{9}{40}$$

Express \frac{80}{9}\times 2 as a single fraction.

$$\frac{80\times 2}{9}\times \frac{9}{40}$$

Multiply 80 and 2 to get 160.

$$\frac{160}{9}\times \frac{9}{40}$$

Multiply \frac{160}{9} times \frac{9}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{160\times 9}{9\times 40}$$

Cancel out 9 in both numerator and denominator.

$$\frac{160}{40}$$

Divide 160 by 40 to get 4.

$$4$$

Factor

$$2^{2}$$