Solve 2-[1/5+(3/4-7/12)]

$$2 - [ \frac { 1 } { 5 } + ( \frac { 3 } { 4 } - \frac { 7 } { 12 } ) ]$$

Evaluate

$$\frac{49}{30}\approx 1.633333333$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{1}{5} and \frac{3}{4} to fractions with denominator 20.

$$2-\left(\frac{4}{20}+\frac{15}{20}-\frac{7}{12}\right)$$

Since \frac{4}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$2-\left(\frac{4+15}{20}-\frac{7}{12}\right)$$

Add 4 and 15 to get 19.

$$2-\left(\frac{19}{20}-\frac{7}{12}\right)$$

Least common multiple of 20 and 12 is 60. Convert \frac{19}{20} and \frac{7}{12} to fractions with denominator 60.

$$2-\left(\frac{57}{60}-\frac{35}{60}\right)$$

Since \frac{57}{60} and \frac{35}{60} have the same denominator, subtract them by subtracting their numerators.

$$2-\frac{57-35}{60}$$

Subtract 35 from 57 to get 22.

$$2-\frac{22}{60}$$

Reduce the fraction \frac{22}{60} to lowest terms by extracting and canceling out 2.

$$2-\frac{11}{30}$$

Convert 2 to fraction \frac{60}{30}.

$$\frac{60}{30}-\frac{11}{30}$$

Since \frac{60}{30} and \frac{11}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60-11}{30}$$

Subtract 11 from 60 to get 49.

$$\frac{49}{30}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 3 \cdot 5} = 1\frac{19}{30} = 1.6333333333333333$$