Solve 23/4-15/8+31/3

$$2 \frac { 3 } { 4 } - 1 \frac { 5 } { 8 } + 3 \frac { 1 } { 3 }$$

Evaluate

$$\frac{107}{24}\approx 4.458333333$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+3}{4}-\frac{1\times 8+5}{8}+\frac{3\times 3+1}{3}$$

Add 8 and 3 to get 11.

$$\frac{11}{4}-\frac{1\times 8+5}{8}+\frac{3\times 3+1}{3}$$

Multiply 1 and 8 to get 8.

$$\frac{11}{4}-\frac{8+5}{8}+\frac{3\times 3+1}{3}$$

Add 8 and 5 to get 13.

$$\frac{11}{4}-\frac{13}{8}+\frac{3\times 3+1}{3}$$

Least common multiple of 4 and 8 is 8. Convert \frac{11}{4} and \frac{13}{8} to fractions with denominator 8.

$$\frac{22}{8}-\frac{13}{8}+\frac{3\times 3+1}{3}$$

Since \frac{22}{8} and \frac{13}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22-13}{8}+\frac{3\times 3+1}{3}$$

Subtract 13 from 22 to get 9.

$$\frac{9}{8}+\frac{3\times 3+1}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{8}+\frac{9+1}{3}$$

Add 9 and 1 to get 10.

$$\frac{9}{8}+\frac{10}{3}$$

Least common multiple of 8 and 3 is 24. Convert \frac{9}{8} and \frac{10}{3} to fractions with denominator 24.

$$\frac{27}{24}+\frac{80}{24}$$

Since \frac{27}{24} and \frac{80}{24} have the same denominator, add them by adding their numerators.

$$\frac{27+80}{24}$$

Add 27 and 80 to get 107.

$$\frac{107}{24}$$

Factor

$$\frac{107}{2 ^ {3} \cdot 3} = 4\frac{11}{24} = 4.458333333333333$$