Solve 1/6+8/15+3/28-2/35-frac{7}{44}

$$\frac { 1 } { 6 } + \frac { 8 } { 15 } + \frac { 3 } { 28 } - \frac { 2 } { 35 } - \frac { 7 } { 44 }$$

Evaluate

$$\frac{13}{22}\approx 0.590909091$$

Solution Steps

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{8}{15} to fractions with denominator 30.

$$\frac{5}{30}+\frac{16}{30}+\frac{3}{28}-\frac{2}{35}-\frac{7}{44}$$

Since \frac{5}{30} and \frac{16}{30} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{30}+\frac{3}{28}-\frac{2}{35}-\frac{7}{44}$$

Add 5 and 16 to get 21.

$$\frac{21}{30}+\frac{3}{28}-\frac{2}{35}-\frac{7}{44}$$

Reduce the fraction \frac{21}{30} to lowest terms by extracting and canceling out 3.

$$\frac{7}{10}+\frac{3}{28}-\frac{2}{35}-\frac{7}{44}$$

Least common multiple of 10 and 28 is 140. Convert \frac{7}{10} and \frac{3}{28} to fractions with denominator 140.

$$\frac{98}{140}+\frac{15}{140}-\frac{2}{35}-\frac{7}{44}$$

Since \frac{98}{140} and \frac{15}{140} have the same denominator, add them by adding their numerators.

$$\frac{98+15}{140}-\frac{2}{35}-\frac{7}{44}$$

Add 98 and 15 to get 113.

$$\frac{113}{140}-\frac{2}{35}-\frac{7}{44}$$

Least common multiple of 140 and 35 is 140. Convert \frac{113}{140} and \frac{2}{35} to fractions with denominator 140.

$$\frac{113}{140}-\frac{8}{140}-\frac{7}{44}$$

Since \frac{113}{140} and \frac{8}{140} have the same denominator, subtract them by subtracting their numerators.

$$\frac{113-8}{140}-\frac{7}{44}$$

Subtract 8 from 113 to get 105.

$$\frac{105}{140}-\frac{7}{44}$$

Reduce the fraction \frac{105}{140} to lowest terms by extracting and canceling out 35.

$$\frac{3}{4}-\frac{7}{44}$$

Least common multiple of 4 and 44 is 44. Convert \frac{3}{4} and \frac{7}{44} to fractions with denominator 44.

$$\frac{33}{44}-\frac{7}{44}$$

Since \frac{33}{44} and \frac{7}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-7}{44}$$

Subtract 7 from 33 to get 26.

$$\frac{26}{44}$$

Reduce the fraction \frac{26}{44} to lowest terms by extracting and canceling out 2.

$$\frac{13}{22}$$

Factor

$$\frac{13}{2 \cdot 11} = 0.5909090909090909$$