Solve 121/5-(35/6+21/2)+(43/10-1frac{2}{8})=

$$12 \frac { 1 } { 5 } - ( 3 \frac { 5 } { 6 } + 2 \frac { 1 } { 2 } ) + ( 4 \frac { 3 } { 10 } - 1 \frac { 2 } { 8 } ) =$$

Evaluate

$$\frac{107}{12}\approx 8.916666667$$

Solution Steps

Multiply 12 and 5 to get 60.

$$\frac{60+1}{5}-\left(\frac{3\times 6+5}{6}+\frac{2\times 2+1}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Add 60 and 1 to get 61.

$$\frac{61}{5}-\left(\frac{3\times 6+5}{6}+\frac{2\times 2+1}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Multiply 3 and 6 to get 18.

$$\frac{61}{5}-\left(\frac{18+5}{6}+\frac{2\times 2+1}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Add 18 and 5 to get 23.

$$\frac{61}{5}-\left(\frac{23}{6}+\frac{2\times 2+1}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Multiply 2 and 2 to get 4.

$$\frac{61}{5}-\left(\frac{23}{6}+\frac{4+1}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Add 4 and 1 to get 5.

$$\frac{61}{5}-\left(\frac{23}{6}+\frac{5}{2}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Least common multiple of 6 and 2 is 6. Convert \frac{23}{6} and \frac{5}{2} to fractions with denominator 6.

$$\frac{61}{5}-\left(\frac{23}{6}+\frac{15}{6}\right)+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Since \frac{23}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{61}{5}-\frac{23+15}{6}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Add 23 and 15 to get 38.

$$\frac{61}{5}-\frac{38}{6}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Reduce the fraction \frac{38}{6} to lowest terms by extracting and canceling out 2.

$$\frac{61}{5}-\frac{19}{3}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Least common multiple of 5 and 3 is 15. Convert \frac{61}{5} and \frac{19}{3} to fractions with denominator 15.

$$\frac{183}{15}-\frac{95}{15}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Since \frac{183}{15} and \frac{95}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{183-95}{15}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Subtract 95 from 183 to get 88.

$$\frac{88}{15}+\frac{4\times 10+3}{10}-\frac{1\times 8+2}{8}$$

Multiply 4 and 10 to get 40.

$$\frac{88}{15}+\frac{40+3}{10}-\frac{1\times 8+2}{8}$$

Add 40 and 3 to get 43.

$$\frac{88}{15}+\frac{43}{10}-\frac{1\times 8+2}{8}$$

Least common multiple of 15 and 10 is 30. Convert \frac{88}{15} and \frac{43}{10} to fractions with denominator 30.

$$\frac{176}{30}+\frac{129}{30}-\frac{1\times 8+2}{8}$$

Since \frac{176}{30} and \frac{129}{30} have the same denominator, add them by adding their numerators.

$$\frac{176+129}{30}-\frac{1\times 8+2}{8}$$

Add 176 and 129 to get 305.

$$\frac{305}{30}-\frac{1\times 8+2}{8}$$

Reduce the fraction \frac{305}{30} to lowest terms by extracting and canceling out 5.

$$\frac{61}{6}-\frac{1\times 8+2}{8}$$

Multiply 1 and 8 to get 8.

$$\frac{61}{6}-\frac{8+2}{8}$$

Add 8 and 2 to get 10.

$$\frac{61}{6}-\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{61}{6}-\frac{5}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{61}{6} and \frac{5}{4} to fractions with denominator 12.

$$\frac{122}{12}-\frac{15}{12}$$

Since \frac{122}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{122-15}{12}$$

Subtract 15 from 122 to get 107.

$$\frac{107}{12}$$

Factor

$$\frac{107}{2 ^ {2} \cdot 3} = 8\frac{11}{12} = 8.916666666666666$$