Solve 83/4+(71/2-15/6)

$$8 \frac { 3 } { 4 } + ( 7 \frac { 1 } { 2 } - 1 \frac { 5 } { 6 } )$$

Evaluate

$$\frac{173}{12}\approx 14.416666667$$

Solution Steps

Multiply 8 and 4 to get 32.

$$\frac{32+3}{4}+\frac{7\times 2+1}{2}-\frac{1\times 6+5}{6}$$

Add 32 and 3 to get 35.

$$\frac{35}{4}+\frac{7\times 2+1}{2}-\frac{1\times 6+5}{6}$$

Multiply 7 and 2 to get 14.

$$\frac{35}{4}+\frac{14+1}{2}-\frac{1\times 6+5}{6}$$

Add 14 and 1 to get 15.

$$\frac{35}{4}+\frac{15}{2}-\frac{1\times 6+5}{6}$$

Least common multiple of 4 and 2 is 4. Convert \frac{35}{4} and \frac{15}{2} to fractions with denominator 4.

$$\frac{35}{4}+\frac{30}{4}-\frac{1\times 6+5}{6}$$

Since \frac{35}{4} and \frac{30}{4} have the same denominator, add them by adding their numerators.

$$\frac{35+30}{4}-\frac{1\times 6+5}{6}$$

Add 35 and 30 to get 65.

$$\frac{65}{4}-\frac{1\times 6+5}{6}$$

Multiply 1 and 6 to get 6.

$$\frac{65}{4}-\frac{6+5}{6}$$

Add 6 and 5 to get 11.

$$\frac{65}{4}-\frac{11}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{65}{4} and \frac{11}{6} to fractions with denominator 12.

$$\frac{195}{12}-\frac{22}{12}$$

Since \frac{195}{12} and \frac{22}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{195-22}{12}$$

Subtract 22 from 195 to get 173.

$$\frac{173}{12}$$

Factor

$$\frac{173}{2 ^ {2} \cdot 3} = 14\frac{5}{12} = 14.416666666666666$$