Solve 4/7+1/3-2/5+1/6=

$$\frac { 4 } { 7 } + \frac { 1 } { 3 } - \frac { 2 } { 5 } + \frac { 1 } { 6 } =$$

Evaluate

$$\frac{47}{70}\approx 0.671428571$$

Solution Steps

Least common multiple of 7 and 3 is 21. Convert \frac{4}{7} and \frac{1}{3} to fractions with denominator 21.

$$\frac{12}{21}+\frac{7}{21}-\frac{2}{5}+\frac{1}{6}$$

Since \frac{12}{21} and \frac{7}{21} have the same denominator, add them by adding their numerators.

$$\frac{12+7}{21}-\frac{2}{5}+\frac{1}{6}$$

Add 12 and 7 to get 19.

$$\frac{19}{21}-\frac{2}{5}+\frac{1}{6}$$

Least common multiple of 21 and 5 is 105. Convert \frac{19}{21} and \frac{2}{5} to fractions with denominator 105.

$$\frac{95}{105}-\frac{42}{105}+\frac{1}{6}$$

Since \frac{95}{105} and \frac{42}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-42}{105}+\frac{1}{6}$$

Subtract 42 from 95 to get 53.

$$\frac{53}{105}+\frac{1}{6}$$

Least common multiple of 105 and 6 is 210. Convert \frac{53}{105} and \frac{1}{6} to fractions with denominator 210.

$$\frac{106}{210}+\frac{35}{210}$$

Since \frac{106}{210} and \frac{35}{210} have the same denominator, add them by adding their numerators.

$$\frac{106+35}{210}$$

Add 106 and 35 to get 141.

$$\frac{141}{210}$$

Reduce the fraction \frac{141}{210} to lowest terms by extracting and canceling out 3.

$$\frac{47}{70}$$

Factor

$$\frac{47}{2 \cdot 5 \cdot 7} = 0.6714285714285714$$