Solve 8-12/3+21/6quad10-27/30-11/60quad1frac{2}{3}+2frac{1}{2}-3frac{5}{6}

$$8 - 1 \frac { 2 } { 3 } + 2 \frac { 1 } { 6 } \quad 10 - 2 \frac { 7 } { 30 } - 1 \frac { 1 } { 60 } \quad 1 \frac { 2 } { 3 } + 2 \frac { 1 } { 2 } - 3 \frac { 5 } { 6 }$$

Evaluate

$$\frac{4093}{180}\approx 22.738888889$$

Solution Steps

Multiply 1 and 3 to get 3.

$$8-\frac{3+2}{3}+\frac{2\times 6+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 3 and 2 to get 5.

$$8-\frac{5}{3}+\frac{2\times 6+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Convert 8 to fraction \frac{24}{3}.

$$\frac{24}{3}-\frac{5}{3}+\frac{2\times 6+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Since \frac{24}{3} and \frac{5}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-5}{3}+\frac{2\times 6+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Subtract 5 from 24 to get 19.

$$\frac{19}{3}+\frac{2\times 6+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{19}{3}+\frac{12+1}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 12 and 1 to get 13.

$$\frac{19}{3}+\frac{13}{6}\times 10-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Express \frac{13}{6}\times 10 as a single fraction.

$$\frac{19}{3}+\frac{13\times 10}{6}-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 13 and 10 to get 130.

$$\frac{19}{3}+\frac{130}{6}-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Reduce the fraction \frac{130}{6} to lowest terms by extracting and canceling out 2.

$$\frac{19}{3}+\frac{65}{3}-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Since \frac{19}{3} and \frac{65}{3} have the same denominator, add them by adding their numerators.

$$\frac{19+65}{3}-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 19 and 65 to get 84.

$$\frac{84}{3}-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Divide 84 by 3 to get 28.

$$28-\frac{2\times 30+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 2 and 30 to get 60.

$$28-\frac{60+7}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 60 and 7 to get 67.

$$28-\frac{67}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Convert 28 to fraction \frac{840}{30}.

$$\frac{840}{30}-\frac{67}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Since \frac{840}{30} and \frac{67}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{840-67}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Subtract 67 from 840 to get 773.

$$\frac{773}{30}-\frac{1\times 60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 1 and 60 to get 60.

$$\frac{773}{30}-\frac{60+1}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 60 and 1 to get 61.

$$\frac{773}{30}-\frac{61}{60}\times \frac{1\times 3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 1 and 3 to get 3.

$$\frac{773}{30}-\frac{61}{60}\times \frac{3+2}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Add 3 and 2 to get 5.

$$\frac{773}{30}-\frac{61}{60}\times \frac{5}{3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply \frac{61}{60} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{773}{30}-\frac{61\times 5}{60\times 3}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Do the multiplications in the fraction \frac{61\times 5}{60\times 3}.

$$\frac{773}{30}-\frac{305}{180}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Reduce the fraction \frac{305}{180} to lowest terms by extracting and canceling out 5.

$$\frac{773}{30}-\frac{61}{36}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Least common multiple of 30 and 36 is 180. Convert \frac{773}{30} and \frac{61}{36} to fractions with denominator 180.

$$\frac{4638}{180}-\frac{305}{180}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Since \frac{4638}{180} and \frac{305}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4638-305}{180}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Subtract 305 from 4638 to get 4333.

$$\frac{4333}{180}+\frac{2\times 2+1}{2}-\frac{3\times 6+5}{6}$$

Multiply 2 and 2 to get 4.

$$\frac{4333}{180}+\frac{4+1}{2}-\frac{3\times 6+5}{6}$$

Add 4 and 1 to get 5.

$$\frac{4333}{180}+\frac{5}{2}-\frac{3\times 6+5}{6}$$

Least common multiple of 180 and 2 is 180. Convert \frac{4333}{180} and \frac{5}{2} to fractions with denominator 180.

$$\frac{4333}{180}+\frac{450}{180}-\frac{3\times 6+5}{6}$$

Since \frac{4333}{180} and \frac{450}{180} have the same denominator, add them by adding their numerators.

$$\frac{4333+450}{180}-\frac{3\times 6+5}{6}$$

Add 4333 and 450 to get 4783.

$$\frac{4783}{180}-\frac{3\times 6+5}{6}$$

Multiply 3 and 6 to get 18.

$$\frac{4783}{180}-\frac{18+5}{6}$$

Add 18 and 5 to get 23.

$$\frac{4783}{180}-\frac{23}{6}$$

Least common multiple of 180 and 6 is 180. Convert \frac{4783}{180} and \frac{23}{6} to fractions with denominator 180.

$$\frac{4783}{180}-\frac{690}{180}$$

Since \frac{4783}{180} and \frac{690}{180} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4783-690}{180}$$

Subtract 690 from 4783 to get 4093.

$$\frac{4093}{180}$$

Factor

$$\frac{4093}{2 ^ {2} \cdot 3 ^ {2} \cdot 5} = 22\frac{133}{180} = 22.738888888888887$$