Solve (1/2-1/3)-(1/6-1/10)+(1+frac{3}{4})=

$$( \frac { 1 } { 2 } - \frac { 1 } { 3 } ) - ( \frac { 1 } { 6 } - \frac { 1 } { 10 } ) + ( 1 + \frac { 3 } { 4 } ) =$$

Evaluate

$$\frac{37}{20}=1.85$$

Solution Steps

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{3}{6}-\frac{2}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)+1+\frac{3}{4}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)+1+\frac{3}{4}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{6}-\left(\frac{1}{6}-\frac{1}{10}\right)+1+\frac{3}{4}$$

Least common multiple of 6 and 10 is 30. Convert \frac{1}{6} and \frac{1}{10} to fractions with denominator 30.

$$\frac{1}{6}-\left(\frac{5}{30}-\frac{3}{30}\right)+1+\frac{3}{4}$$

Since \frac{5}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}-\frac{5-3}{30}+1+\frac{3}{4}$$

Subtract 3 from 5 to get 2.

$$\frac{1}{6}-\frac{2}{30}+1+\frac{3}{4}$$

Reduce the fraction \frac{2}{30} to lowest terms by extracting and canceling out 2.

$$\frac{1}{6}-\frac{1}{15}+1+\frac{3}{4}$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{1}{15} to fractions with denominator 30.

$$\frac{5}{30}-\frac{2}{30}+1+\frac{3}{4}$$

Since \frac{5}{30} and \frac{2}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-2}{30}+1+\frac{3}{4}$$

Subtract 2 from 5 to get 3.

$$\frac{3}{30}+1+\frac{3}{4}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}+1+\frac{3}{4}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{1}{10}+\frac{10}{10}+\frac{3}{4}$$

Since \frac{1}{10} and \frac{10}{10} have the same denominator, add them by adding their numerators.

$$\frac{1+10}{10}+\frac{3}{4}$$

Add 1 and 10 to get 11.

$$\frac{11}{10}+\frac{3}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{11}{10} and \frac{3}{4} to fractions with denominator 20.

$$\frac{22}{20}+\frac{15}{20}$$

Since \frac{22}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{22+15}{20}$$

Add 22 and 15 to get 37.

$$\frac{37}{20}$$

Factor

$$\frac{37}{2 ^ {2} \cdot 5} = 1\frac{17}{20} = 1.85$$