Solve 23/9*(44/9-22/9

$$2 \frac { 3 } { 9 } \times ( 4 \frac { 4 } { 9 } - \frac { 22 } { 9 }$$

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

Solution Steps

Multiply 2 and 9 to get 18.

$$\frac{18+3}{9}\left(\frac{4\times 9+4}{9}-\frac{22}{9}\right)$$

Add 18 and 3 to get 21.

$$\frac{21}{9}\left(\frac{4\times 9+4}{9}-\frac{22}{9}\right)$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$\frac{7}{3}\left(\frac{4\times 9+4}{9}-\frac{22}{9}\right)$$

Multiply 4 and 9 to get 36.

$$\frac{7}{3}\left(\frac{36+4}{9}-\frac{22}{9}\right)$$

Add 36 and 4 to get 40.

$$\frac{7}{3}\left(\frac{40}{9}-\frac{22}{9}\right)$$

Since \frac{40}{9} and \frac{22}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{3}\times \frac{40-22}{9}$$

Subtract 22 from 40 to get 18.

$$\frac{7}{3}\times \frac{18}{9}$$

Divide 18 by 9 to get 2.

$$\frac{7}{3}\times 2$$

Express \frac{7}{3}\times 2 as a single fraction.

$$\frac{7\times 2}{3}$$

Multiply 7 and 2 to get 14.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$