Solve 9*(7/30-7/90+1/3)

$$9 \times ( \frac{ 7 }{ 30 } - \frac{ 7 }{ 90 } + \frac{ 1 }{ 3 } )$$

Evaluate

$$\frac{22}{5}=4.4$$

Solution Steps

Least common multiple of 30 and 90 is 90. Convert \frac{7}{30} and \frac{7}{90} to fractions with denominator 90.

$$9\left(\frac{21}{90}-\frac{7}{90}+\frac{1}{3}\right)$$

Since \frac{21}{90} and \frac{7}{90} have the same denominator, subtract them by subtracting their numerators.

$$9\left(\frac{21-7}{90}+\frac{1}{3}\right)$$

Subtract 7 from 21 to get 14.

$$9\left(\frac{14}{90}+\frac{1}{3}\right)$$

Reduce the fraction \frac{14}{90} to lowest terms by extracting and canceling out 2.

$$9\left(\frac{7}{45}+\frac{1}{3}\right)$$

Least common multiple of 45 and 3 is 45. Convert \frac{7}{45} and \frac{1}{3} to fractions with denominator 45.

$$9\left(\frac{7}{45}+\frac{15}{45}\right)$$

Since \frac{7}{45} and \frac{15}{45} have the same denominator, add them by adding their numerators.

$$9\times \frac{7+15}{45}$$

Add 7 and 15 to get 22.

$$9\times \frac{22}{45}$$

Express 9\times \frac{22}{45} as a single fraction.

$$\frac{9\times 22}{45}$$

Multiply 9 and 22 to get 198.

$$\frac{198}{45}$$

Reduce the fraction \frac{198}{45} to lowest terms by extracting and canceling out 9.

$$\frac{22}{5}$$

Factor

$$\frac{2 \cdot 11}{5} = 4\frac{2}{5} = 4.4$$