Solve 1/15+5/6+8/9+3/10=

$$\frac { 1 } { 15 } + \frac { 5 } { 6 } + \frac { 8 } { 9 } + \frac { 3 } { 10 } =$$

Evaluate

$$\frac{94}{45}\approx 2.088888889$$

Solution Steps

Least common multiple of 15 and 6 is 30. Convert \frac{1}{15} and \frac{5}{6} to fractions with denominator 30.

$$\frac{2}{30}+\frac{25}{30}+\frac{8}{9}+\frac{3}{10}$$

Since \frac{2}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$\frac{2+25}{30}+\frac{8}{9}+\frac{3}{10}$$

Add 2 and 25 to get 27.

$$\frac{27}{30}+\frac{8}{9}+\frac{3}{10}$$

Reduce the fraction \frac{27}{30} to lowest terms by extracting and canceling out 3.

$$\frac{9}{10}+\frac{8}{9}+\frac{3}{10}$$

Least common multiple of 10 and 9 is 90. Convert \frac{9}{10} and \frac{8}{9} to fractions with denominator 90.

$$\frac{81}{90}+\frac{80}{90}+\frac{3}{10}$$

Since \frac{81}{90} and \frac{80}{90} have the same denominator, add them by adding their numerators.

$$\frac{81+80}{90}+\frac{3}{10}$$

Add 81 and 80 to get 161.

$$\frac{161}{90}+\frac{3}{10}$$

Least common multiple of 90 and 10 is 90. Convert \frac{161}{90} and \frac{3}{10} to fractions with denominator 90.

$$\frac{161}{90}+\frac{27}{90}$$

Since \frac{161}{90} and \frac{27}{90} have the same denominator, add them by adding their numerators.

$$\frac{161+27}{90}$$

Add 161 and 27 to get 188.

$$\frac{188}{90}$$

Reduce the fraction \frac{188}{90} to lowest terms by extracting and canceling out 2.

$$\frac{94}{45}$$

Factor

$$\frac{2 \cdot 47}{3 ^ {2} \cdot 5} = 2\frac{4}{45} = 2.088888888888889$$