Solve (19/33-9/22+1735/132)-(83/4+4frac{7}{11})

$$( \frac { 19 } { 33 } - \frac { 9 } { 22 } + 17 \frac { 35 } { 132 } ) - ( 8 \frac { 3 } { 4 } + 4 \frac { 7 } { 11 } )$$

Evaluate

$$\frac{89}{22}\approx 4.045454545$$

Solution Steps

Least common multiple of 33 and 22 is 66. Convert \frac{19}{33} and \frac{9}{22} to fractions with denominator 66.

$$\frac{38}{66}-\frac{27}{66}+\frac{17\times 132+35}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Since \frac{38}{66} and \frac{27}{66} have the same denominator, subtract them by subtracting their numerators.

$$\frac{38-27}{66}+\frac{17\times 132+35}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Subtract 27 from 38 to get 11.

$$\frac{11}{66}+\frac{17\times 132+35}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Reduce the fraction \frac{11}{66} to lowest terms by extracting and canceling out 11.

$$\frac{1}{6}+\frac{17\times 132+35}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Multiply 17 and 132 to get 2244.

$$\frac{1}{6}+\frac{2244+35}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Add 2244 and 35 to get 2279.

$$\frac{1}{6}+\frac{2279}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Least common multiple of 6 and 132 is 132. Convert \frac{1}{6} and \frac{2279}{132} to fractions with denominator 132.

$$\frac{22}{132}+\frac{2279}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Since \frac{22}{132} and \frac{2279}{132} have the same denominator, add them by adding their numerators.

$$\frac{22+2279}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Add 22 and 2279 to get 2301.

$$\frac{2301}{132}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Reduce the fraction \frac{2301}{132} to lowest terms by extracting and canceling out 3.

$$\frac{767}{44}-\left(\frac{8\times 4+3}{4}+\frac{4\times 11+7}{11}\right)$$

Multiply 8 and 4 to get 32.

$$\frac{767}{44}-\left(\frac{32+3}{4}+\frac{4\times 11+7}{11}\right)$$

Add 32 and 3 to get 35.

$$\frac{767}{44}-\left(\frac{35}{4}+\frac{4\times 11+7}{11}\right)$$

Multiply 4 and 11 to get 44.

$$\frac{767}{44}-\left(\frac{35}{4}+\frac{44+7}{11}\right)$$

Add 44 and 7 to get 51.

$$\frac{767}{44}-\left(\frac{35}{4}+\frac{51}{11}\right)$$

Least common multiple of 4 and 11 is 44. Convert \frac{35}{4} and \frac{51}{11} to fractions with denominator 44.

$$\frac{767}{44}-\left(\frac{385}{44}+\frac{204}{44}\right)$$

Since \frac{385}{44} and \frac{204}{44} have the same denominator, add them by adding their numerators.

$$\frac{767}{44}-\frac{385+204}{44}$$

Add 385 and 204 to get 589.

$$\frac{767}{44}-\frac{589}{44}$$

Since \frac{767}{44} and \frac{589}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{767-589}{44}$$

Subtract 589 from 767 to get 178.

$$\frac{178}{44}$$

Reduce the fraction \frac{178}{44} to lowest terms by extracting and canceling out 2.

$$\frac{89}{22}$$

Factor

$$\frac{89}{2 \cdot 11} = 4\frac{1}{22} = 4.045454545454546$$