Solve 7/3-2/5+4/9-3/2=

$$\frac { 7 } { 3 } - \frac { 2 } { 5 } + \frac { 4 } { 9 } - \frac { 3 } { 2 } =$$

Evaluate

$$\frac{79}{90}\approx 0.877777778$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{35}{15}-\frac{6}{15}+\frac{4}{9}-\frac{3}{2}$$

Since \frac{35}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-6}{15}+\frac{4}{9}-\frac{3}{2}$$

Subtract 6 from 35 to get 29.

$$\frac{29}{15}+\frac{4}{9}-\frac{3}{2}$$

Least common multiple of 15 and 9 is 45. Convert \frac{29}{15} and \frac{4}{9} to fractions with denominator 45.

$$\frac{87}{45}+\frac{20}{45}-\frac{3}{2}$$

Since \frac{87}{45} and \frac{20}{45} have the same denominator, add them by adding their numerators.

$$\frac{87+20}{45}-\frac{3}{2}$$

Add 87 and 20 to get 107.

$$\frac{107}{45}-\frac{3}{2}$$

Least common multiple of 45 and 2 is 90. Convert \frac{107}{45} and \frac{3}{2} to fractions with denominator 90.

$$\frac{214}{90}-\frac{135}{90}$$

Since \frac{214}{90} and \frac{135}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{214-135}{90}$$

Subtract 135 from 214 to get 79.

$$\frac{79}{90}$$

Factor

$$\frac{79}{2 \cdot 3 ^ {2} \cdot 5} = 0.8777777777777778$$