Solve 3-1/2*frac{1{2}}+3+1/2*frac{1{3}}-3-1/3frac{1{4}}*2+2/2*frac{1{4}}divfrac{1+1}{2*frac{1}{2}}=

$$\frac { 3 - 1 } { 2 \cdot \frac { 1 } { 2 } } + \frac { 3 + 1 } { 2 \cdot \frac { 1 } { 3 } } - \frac { 3 - 1 } { 3 \frac { 1 } { 4 } } \cdot \frac { 2 + 2 } { 2 \cdot \frac { 1 } { 4 } } \div \frac { 1 + 1 } { 2 \cdot \frac { 1 } { 2 } } =$$

Evaluate

$$\frac{72}{13}\approx 5.538461538$$

Solution Steps

Subtract 1 from 3 to get 2.

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

Cancel out 2 and 2.

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

Anything divided by one gives itself.

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

Add 3 and 1 to get 4.

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

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

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

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

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

Express 4\times \frac{3}{2} as a single fraction.

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

Multiply 4 and 3 to get 12.

$$2+\frac{12}{2}-\frac{\frac{3-1}{\frac{3\times 4+1}{4}}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Divide 12 by 2 to get 6.

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

Add 2 and 6 to get 8.

$$8-\frac{\frac{3-1}{\frac{3\times 4+1}{4}}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Subtract 1 from 3 to get 2.

$$8-\frac{\frac{2}{\frac{3\times 4+1}{4}}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Multiply 3 and 4 to get 12.

$$8-\frac{\frac{2}{\frac{12+1}{4}}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Add 12 and 1 to get 13.

$$8-\frac{\frac{2}{\frac{13}{4}}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Divide 2 by \frac{13}{4} by multiplying 2 by the reciprocal of \frac{13}{4}.

$$8-\frac{2\times \frac{4}{13}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Express 2\times \frac{4}{13} as a single fraction.

$$8-\frac{\frac{2\times 4}{13}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Multiply 2 and 4 to get 8.

$$8-\frac{\frac{8}{13}\times \frac{2+2}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Add 2 and 2 to get 4.

$$8-\frac{\frac{8}{13}\times \frac{4}{2\times \frac{1}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$8-\frac{\frac{8}{13}\times \frac{4}{\frac{2}{4}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

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

$$8-\frac{\frac{8}{13}\times \frac{4}{\frac{1}{2}}}{\frac{1+1}{2\times \frac{1}{2}}}$$

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

$$8-\frac{\frac{8}{13}\times 4\times 2}{\frac{1+1}{2\times \frac{1}{2}}}$$

Multiply 4 and 2 to get 8.

$$8-\frac{\frac{8}{13}\times 8}{\frac{1+1}{2\times \frac{1}{2}}}$$

Express \frac{8}{13}\times 8 as a single fraction.

$$8-\frac{\frac{8\times 8}{13}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Multiply 8 and 8 to get 64.

$$8-\frac{\frac{64}{13}}{\frac{1+1}{2\times \frac{1}{2}}}$$

Add 1 and 1 to get 2.

$$8-\frac{\frac{64}{13}}{\frac{2}{2\times \frac{1}{2}}}$$

Cancel out 2 and 2.

$$8-\frac{\frac{64}{13}}{\frac{2}{1}}$$

Anything divided by one gives itself.

$$8-\frac{\frac{64}{13}}{2}$$

Express \frac{\frac{64}{13}}{2} as a single fraction.

$$8-\frac{64}{13\times 2}$$

Multiply 13 and 2 to get 26.

$$8-\frac{64}{26}$$

Reduce the fraction \frac{64}{26} to lowest terms by extracting and canceling out 2.

$$8-\frac{32}{13}$$

Convert 8 to fraction \frac{104}{13}.

$$\frac{104}{13}-\frac{32}{13}$$

Since \frac{104}{13} and \frac{32}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{104-32}{13}$$

Subtract 32 from 104 to get 72.

$$\frac{72}{13}$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {2}}{13} = 5\frac{7}{13} = 5.538461538461538$$