Solve 1/3+5/7-8/70

$$\frac { 1 } { 3 } + \frac { 5 } { 7 } - \frac { 8 } { 70 }$$

Evaluate

$$\frac{14}{15}\approx 0.933333333$$

Solution Steps

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{5}{7} to fractions with denominator 21.

$$\frac{7}{21}+\frac{15}{21}-\frac{8}{70}$$

Since \frac{7}{21} and \frac{15}{21} have the same denominator, add them by adding their numerators.

$$\frac{7+15}{21}-\frac{8}{70}$$

Add 7 and 15 to get 22.

$$\frac{22}{21}-\frac{8}{70}$$

Reduce the fraction \frac{8}{70} to lowest terms by extracting and canceling out 2.

$$\frac{22}{21}-\frac{4}{35}$$

Least common multiple of 21 and 35 is 105. Convert \frac{22}{21} and \frac{4}{35} to fractions with denominator 105.

$$\frac{110}{105}-\frac{12}{105}$$

Since \frac{110}{105} and \frac{12}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{110-12}{105}$$

Subtract 12 from 110 to get 98.

$$\frac{98}{105}$$

Reduce the fraction \frac{98}{105} to lowest terms by extracting and canceling out 7.

$$\frac{14}{15}$$

Factor

$$\frac{2 \cdot 7}{3 \cdot 5} = 0.9333333333333333$$