Solve {l}{87/15-7/9}{-22/9}

$$\left. \begin{array} { l } { 8 \frac { 7 } { 15 } - \frac { 7 } { 9 } } \\ { - 2 \frac { 2 } { 9 } } \end{array} \right.$$

Evaluate

$$\frac{82}{15}\approx 5.466666667$$

Solution Steps

Multiply 8 and 15 to get 120.

$$\frac{120+7}{15}-\frac{7}{9}-\frac{2\times 9+2}{9}$$

Add 120 and 7 to get 127.

$$\frac{127}{15}-\frac{7}{9}-\frac{2\times 9+2}{9}$$

Least common multiple of 15 and 9 is 45. Convert \frac{127}{15} and \frac{7}{9} to fractions with denominator 45.

$$\frac{381}{45}-\frac{35}{45}-\frac{2\times 9+2}{9}$$

Since \frac{381}{45} and \frac{35}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{381-35}{45}-\frac{2\times 9+2}{9}$$

Subtract 35 from 381 to get 346.

$$\frac{346}{45}-\frac{2\times 9+2}{9}$$

Multiply 2 and 9 to get 18.

$$\frac{346}{45}-\frac{18+2}{9}$$

Add 18 and 2 to get 20.

$$\frac{346}{45}-\frac{20}{9}$$

Least common multiple of 45 and 9 is 45. Convert \frac{346}{45} and \frac{20}{9} to fractions with denominator 45.

$$\frac{346}{45}-\frac{100}{45}$$

Since \frac{346}{45} and \frac{100}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{346-100}{45}$$

Subtract 100 from 346 to get 246.

$$\frac{246}{45}$$

Reduce the fraction \frac{246}{45} to lowest terms by extracting and canceling out 3.

$$\frac{82}{15}$$

Factor

$$\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5.466666666666667$$