Solve 22/4-31/3+61/2

$$2 \frac { 2 } { 4 } - 3 \frac { 1 } { 3 } + 6 \frac { 1 } { 2 }$$

Evaluate

$$\frac{17}{3}\approx 5.666666667$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+2}{4}-\frac{3\times 3+1}{3}+\frac{6\times 2+1}{2}$$

Add 8 and 2 to get 10.

$$\frac{10}{4}-\frac{3\times 3+1}{3}+\frac{6\times 2+1}{2}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

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

Multiply 3 and 3 to get 9.

$$\frac{5}{2}-\frac{9+1}{3}+\frac{6\times 2+1}{2}$$

Add 9 and 1 to get 10.

$$\frac{5}{2}-\frac{10}{3}+\frac{6\times 2+1}{2}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{10}{3} to fractions with denominator 6.

$$\frac{15}{6}-\frac{20}{6}+\frac{6\times 2+1}{2}$$

Since \frac{15}{6} and \frac{20}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-20}{6}+\frac{6\times 2+1}{2}$$

Subtract 20 from 15 to get -5.

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

Multiply 6 and 2 to get 12.

$$-\frac{5}{6}+\frac{12+1}{2}$$

Add 12 and 1 to get 13.

$$-\frac{5}{6}+\frac{13}{2}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{5}{6} and \frac{13}{2} to fractions with denominator 6.

$$-\frac{5}{6}+\frac{39}{6}$$

Since -\frac{5}{6} and \frac{39}{6} have the same denominator, add them by adding their numerators.

$$\frac{-5+39}{6}$$

Add -5 and 39 to get 34.

$$\frac{34}{6}$$

Reduce the fraction \frac{34}{6} to lowest terms by extracting and canceling out 2.

$$\frac{17}{3}$$

Factor

$$\frac{17}{3} = 5\frac{2}{3} = 5.666666666666667$$