Solve 121/3-23/8+22/3-85/8

$$12 \frac { 1 } { 3 } - 2 \frac { 3 } { 8 } + 2 \frac { 2 } { 3 } - 8 \frac { 5 } { 8 }$$

Evaluate

$$4$$

Solution Steps

Multiply 12 and 3 to get 36.

$$\frac{36+1}{3}-\frac{2\times 8+3}{8}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Add 36 and 1 to get 37.

$$\frac{37}{3}-\frac{2\times 8+3}{8}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{37}{3}-\frac{16+3}{8}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Add 16 and 3 to get 19.

$$\frac{37}{3}-\frac{19}{8}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Least common multiple of 3 and 8 is 24. Convert \frac{37}{3} and \frac{19}{8} to fractions with denominator 24.

$$\frac{296}{24}-\frac{57}{24}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Since \frac{296}{24} and \frac{57}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{296-57}{24}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Subtract 57 from 296 to get 239.

$$\frac{239}{24}+\frac{2\times 3+2}{3}-\frac{8\times 8+5}{8}$$

Multiply 2 and 3 to get 6.

$$\frac{239}{24}+\frac{6+2}{3}-\frac{8\times 8+5}{8}$$

Add 6 and 2 to get 8.

$$\frac{239}{24}+\frac{8}{3}-\frac{8\times 8+5}{8}$$

Least common multiple of 24 and 3 is 24. Convert \frac{239}{24} and \frac{8}{3} to fractions with denominator 24.

$$\frac{239}{24}+\frac{64}{24}-\frac{8\times 8+5}{8}$$

Since \frac{239}{24} and \frac{64}{24} have the same denominator, add them by adding their numerators.

$$\frac{239+64}{24}-\frac{8\times 8+5}{8}$$

Add 239 and 64 to get 303.

$$\frac{303}{24}-\frac{8\times 8+5}{8}$$

Reduce the fraction \frac{303}{24} to lowest terms by extracting and canceling out 3.

$$\frac{101}{8}-\frac{8\times 8+5}{8}$$

Multiply 8 and 8 to get 64.

$$\frac{101}{8}-\frac{64+5}{8}$$

Add 64 and 5 to get 69.

$$\frac{101}{8}-\frac{69}{8}$$

Since \frac{101}{8} and \frac{69}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101-69}{8}$$

Subtract 69 from 101 to get 32.

$$\frac{32}{8}$$

Divide 32 by 8 to get 4.

$$4$$

Factor

$$2^{2}$$