Solve 8/100m=1/17n+(m-n)*1/9

$$\frac { 8 } { 100 } m = \frac { 1 } { 17 } n + ( m - n ) \times \frac { 1 } { 9 }$$

Solve for m

$$m=\frac{200n}{119}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{2}{25}m=\frac{1}{17}n+\left(m-n\right)\times \frac{1}{9}$$

Use the distributive property to multiply m-n by \frac{1}{9}.

$$\frac{2}{25}m=\frac{1}{17}n+\frac{1}{9}m-\frac{1}{9}n$$

Combine \frac{1}{17}n and -\frac{1}{9}n to get -\frac{8}{153}n.

$$\frac{2}{25}m=-\frac{8}{153}n+\frac{1}{9}m$$

Subtract \frac{1}{9}m from both sides.

$$\frac{2}{25}m-\frac{1}{9}m=-\frac{8}{153}n$$

Combine \frac{2}{25}m and -\frac{1}{9}m to get -\frac{7}{225}m.

$$-\frac{7}{225}m=-\frac{8}{153}n$$

The equation is in standard form.

$$-\frac{7}{225}m=-\frac{8n}{153}$$

Divide both sides of the equation by -\frac{7}{225}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{7}{225}m}{-\frac{7}{225}}=-\frac{\frac{8n}{153}}{-\frac{7}{225}}$$

Dividing by -\frac{7}{225} undoes the multiplication by -\frac{7}{225}.

$$m=-\frac{\frac{8n}{153}}{-\frac{7}{225}}$$

Divide -\frac{8n}{153} by -\frac{7}{225} by multiplying -\frac{8n}{153} by the reciprocal of -\frac{7}{225}.

$$m=\frac{200n}{119}$$

Solve for n

$$n=\frac{119m}{200}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{2}{25}m=\frac{1}{17}n+\left(m-n\right)\times \frac{1}{9}$$

Use the distributive property to multiply m-n by \frac{1}{9}.

$$\frac{2}{25}m=\frac{1}{17}n+\frac{1}{9}m-\frac{1}{9}n$$

Combine \frac{1}{17}n and -\frac{1}{9}n to get -\frac{8}{153}n.

$$\frac{2}{25}m=-\frac{8}{153}n+\frac{1}{9}m$$

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

$$-\frac{8}{153}n+\frac{1}{9}m=\frac{2}{25}m$$

Subtract \frac{1}{9}m from both sides.

$$-\frac{8}{153}n=\frac{2}{25}m-\frac{1}{9}m$$

Combine \frac{2}{25}m and -\frac{1}{9}m to get -\frac{7}{225}m.

$$-\frac{8}{153}n=-\frac{7}{225}m$$

The equation is in standard form.

$$-\frac{8}{153}n=-\frac{7m}{225}$$

Divide both sides of the equation by -\frac{8}{153}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{8}{153}n}{-\frac{8}{153}}=-\frac{\frac{7m}{225}}{-\frac{8}{153}}$$

Dividing by -\frac{8}{153} undoes the multiplication by -\frac{8}{153}.

$$n=-\frac{\frac{7m}{225}}{-\frac{8}{153}}$$

Divide -\frac{7m}{225} by -\frac{8}{153} by multiplying -\frac{7m}{225} by the reciprocal of -\frac{8}{153}.

$$n=\frac{119m}{200}$$