Solve 221/5=198/9+r

$$22 \frac { 1 } { 5 } = 19 \frac { 8 } { 9 } + r$$

Solve for r

$$r = \frac{104}{45} = 2\frac{14}{45} \approx 2.311111111$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 45, the least common multiple of 5,9.

$$9\left(22\times 5+1\right)=5\left(19\times 9+8\right)+45r$$

Multiply 22 and 5 to get 110.

$$9\left(110+1\right)=5\left(19\times 9+8\right)+45r$$

Add 110 and 1 to get 111.

$$9\times 111=5\left(19\times 9+8\right)+45r$$

Multiply 9 and 111 to get 999.

$$999=5\left(19\times 9+8\right)+45r$$

Multiply 19 and 9 to get 171.

$$999=5\left(171+8\right)+45r$$

Add 171 and 8 to get 179.

$$999=5\times 179+45r$$

Multiply 5 and 179 to get 895.

$$999=895+45r$$

Swap sides so that all variable terms are on the left hand side.

$$895+45r=999$$

Subtract 895 from both sides.

$$45r=999-895$$

Subtract 895 from 999 to get 104.

$$45r=104$$

Divide both sides by 45.

$$r=\frac{104}{45}$$