Solve 21/3-11/2+33/4=

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

Evaluate

$$\frac{55}{12}\approx 4.583333333$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

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

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{7}{3}-\frac{3}{2}+\frac{3\times 4+3}{4}$$

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

$$\frac{14}{6}-\frac{9}{6}+\frac{3\times 4+3}{4}$$

Since \frac{14}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-9}{6}+\frac{3\times 4+3}{4}$$

Subtract 9 from 14 to get 5.

$$\frac{5}{6}+\frac{3\times 4+3}{4}$$

Multiply 3 and 4 to get 12.

$$\frac{5}{6}+\frac{12+3}{4}$$

Add 12 and 3 to get 15.

$$\frac{5}{6}+\frac{15}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{15}{4} to fractions with denominator 12.

$$\frac{10}{12}+\frac{45}{12}$$

Since \frac{10}{12} and \frac{45}{12} have the same denominator, add them by adding their numerators.

$$\frac{10+45}{12}$$

Add 10 and 45 to get 55.

$$\frac{55}{12}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {2} \cdot 3} = 4\frac{7}{12} = 4.583333333333333$$