Solve 51/6+(31/2-31/2)

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

Evaluate

$$\frac{31}{6}\approx 5.166666667$$

Solution Steps

Multiply 5 and 6 to get 30.

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

Add 30 and 1 to get 31.

$$\frac{31}{6}+\frac{3\times 2+1}{2}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{31}{6}+\frac{6+1}{2}-\frac{3\times 2+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{31}{6}+\frac{7}{2}-\frac{3\times 2+1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{31}{6} and \frac{7}{2} to fractions with denominator 6.

$$\frac{31}{6}+\frac{21}{6}-\frac{3\times 2+1}{2}$$

Since \frac{31}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{31+21}{6}-\frac{3\times 2+1}{2}$$

Add 31 and 21 to get 52.

$$\frac{52}{6}-\frac{3\times 2+1}{2}$$

Reduce the fraction \frac{52}{6} to lowest terms by extracting and canceling out 2.

$$\frac{26}{3}-\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{26}{3}-\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{26}{3}-\frac{7}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{26}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{52}{6}-\frac{21}{6}$$

Since \frac{52}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{52-21}{6}$$

Subtract 21 from 52 to get 31.

$$\frac{31}{6}$$

Factor

$$\frac{31}{2 \cdot 3} = 5\frac{1}{6} = 5.166666666666667$$