Solve (2/5+5/9)+7/9

$$( \frac { 2 } { 5 } + \frac { 5 } { 9 } ) + \frac { 7 } { 9 }$$

Evaluate

$$\frac{26}{15}\approx 1.733333333$$

Solution Steps

Least common multiple of 5 and 9 is 45. Convert \frac{2}{5} and \frac{5}{9} to fractions with denominator 45.

$$\frac{18}{45}+\frac{25}{45}+\frac{7}{9}$$

Since \frac{18}{45} and \frac{25}{45} have the same denominator, add them by adding their numerators.

$$\frac{18+25}{45}+\frac{7}{9}$$

Add 18 and 25 to get 43.

$$\frac{43}{45}+\frac{7}{9}$$

Least common multiple of 45 and 9 is 45. Convert \frac{43}{45} and \frac{7}{9} to fractions with denominator 45.

$$\frac{43}{45}+\frac{35}{45}$$

Since \frac{43}{45} and \frac{35}{45} have the same denominator, add them by adding their numerators.

$$\frac{43+35}{45}$$

Add 43 and 35 to get 78.

$$\frac{78}{45}$$

Reduce the fraction \frac{78}{45} to lowest terms by extracting and canceling out 3.

$$\frac{26}{15}$$

Factor

$$\frac{2 \cdot 13}{3 \cdot 5} = 1\frac{11}{15} = 1.7333333333333334$$