Solve 4-1/3+(1/4-1/5-1/6)=

$$4 - \frac { 1 } { 3 } + ( \frac { 1 } { 4 } - \frac { 1 } { 5 } - \frac { 1 } { 6 } ) =$$

Evaluate

$$\frac{71}{20}=3.55$$

Solution Steps

Convert 4 to fraction \frac{12}{3}.

$$\frac{12}{3}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}$$

Since \frac{12}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}$$

Subtract 1 from 12 to get 11.

$$\frac{11}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}$$

Least common multiple of 3 and 4 is 12. Convert \frac{11}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{44}{12}+\frac{3}{12}-\frac{1}{5}-\frac{1}{6}$$

Since \frac{44}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{44+3}{12}-\frac{1}{5}-\frac{1}{6}$$

Add 44 and 3 to get 47.

$$\frac{47}{12}-\frac{1}{5}-\frac{1}{6}$$

Least common multiple of 12 and 5 is 60. Convert \frac{47}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{235}{60}-\frac{12}{60}-\frac{1}{6}$$

Since \frac{235}{60} and \frac{12}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{235-12}{60}-\frac{1}{6}$$

Subtract 12 from 235 to get 223.

$$\frac{223}{60}-\frac{1}{6}$$

Least common multiple of 60 and 6 is 60. Convert \frac{223}{60} and \frac{1}{6} to fractions with denominator 60.

$$\frac{223}{60}-\frac{10}{60}$$

Since \frac{223}{60} and \frac{10}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{223-10}{60}$$

Subtract 10 from 223 to get 213.

$$\frac{213}{60}$$

Reduce the fraction \frac{213}{60} to lowest terms by extracting and canceling out 3.

$$\frac{71}{20}$$

Factor

$$\frac{71}{2 ^ {2} \cdot 5} = 3\frac{11}{20} = 3.55$$