Solve 8/15+7/18+2/15+7/9

$$\frac{ 8 }{ 15 } + \frac{ 7 }{ 18 } + \frac{ 2 }{ 15 } + \frac{ 7 }{ 9 }$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Least common multiple of 15 and 18 is 90. Convert \frac{8}{15} and \frac{7}{18} to fractions with denominator 90.

$$\frac{48}{90}+\frac{35}{90}+\frac{2}{15}+\frac{7}{9}$$

Since \frac{48}{90} and \frac{35}{90} have the same denominator, add them by adding their numerators.

$$\frac{48+35}{90}+\frac{2}{15}+\frac{7}{9}$$

Add 48 and 35 to get 83.

$$\frac{83}{90}+\frac{2}{15}+\frac{7}{9}$$

Least common multiple of 90 and 15 is 90. Convert \frac{83}{90} and \frac{2}{15} to fractions with denominator 90.

$$\frac{83}{90}+\frac{12}{90}+\frac{7}{9}$$

Since \frac{83}{90} and \frac{12}{90} have the same denominator, add them by adding their numerators.

$$\frac{83+12}{90}+\frac{7}{9}$$

Add 83 and 12 to get 95.

$$\frac{95}{90}+\frac{7}{9}$$

Reduce the fraction \frac{95}{90} to lowest terms by extracting and canceling out 5.

$$\frac{19}{18}+\frac{7}{9}$$

Least common multiple of 18 and 9 is 18. Convert \frac{19}{18} and \frac{7}{9} to fractions with denominator 18.

$$\frac{19}{18}+\frac{14}{18}$$

Since \frac{19}{18} and \frac{14}{18} have the same denominator, add them by adding their numerators.

$$\frac{19+14}{18}$$

Add 19 and 14 to get 33.

$$\frac{33}{18}$$

Reduce the fraction \frac{33}{18} to lowest terms by extracting and canceling out 3.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$