Solve (22/5+12/3)-27/30

$$( 2 \frac { 2 } { 5 } + 1 \frac { 2 } { 3 } ) - 2 \frac { 7 } { 30 }$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{10+2}{5}+\frac{1\times 3+2}{3}-\frac{2\times 30+7}{30}$$

Add 10 and 2 to get 12.

$$\frac{12}{5}+\frac{1\times 3+2}{3}-\frac{2\times 30+7}{30}$$

Multiply 1 and 3 to get 3.

$$\frac{12}{5}+\frac{3+2}{3}-\frac{2\times 30+7}{30}$$

Add 3 and 2 to get 5.

$$\frac{12}{5}+\frac{5}{3}-\frac{2\times 30+7}{30}$$

Least common multiple of 5 and 3 is 15. Convert \frac{12}{5} and \frac{5}{3} to fractions with denominator 15.

$$\frac{36}{15}+\frac{25}{15}-\frac{2\times 30+7}{30}$$

Since \frac{36}{15} and \frac{25}{15} have the same denominator, add them by adding their numerators.

$$\frac{36+25}{15}-\frac{2\times 30+7}{30}$$

Add 36 and 25 to get 61.

$$\frac{61}{15}-\frac{2\times 30+7}{30}$$

Multiply 2 and 30 to get 60.

$$\frac{61}{15}-\frac{60+7}{30}$$

Add 60 and 7 to get 67.

$$\frac{61}{15}-\frac{67}{30}$$

Least common multiple of 15 and 30 is 30. Convert \frac{61}{15} and \frac{67}{30} to fractions with denominator 30.

$$\frac{122}{30}-\frac{67}{30}$$

Since \frac{122}{30} and \frac{67}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{122-67}{30}$$

Subtract 67 from 122 to get 55.

$$\frac{55}{30}$$

Reduce the fraction \frac{55}{30} to lowest terms by extracting and canceling out 5.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$