Solve 90/5/frac{5{6}}=100/n

$$\frac { \frac { 90 } { 5 } } { \frac { 5 } { 6 } } = \frac { 100 } { n }$$

Solve for n

$$n = \frac{125}{27} = 4\frac{17}{27} \approx 4.62962963$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$n\times \frac{\frac{90}{5}}{\frac{5}{6}}=100$$

Divide 90 by 5 to get 18.

$$n\times \frac{18}{\frac{5}{6}}=100$$

Divide 18 by \frac{5}{6} by multiplying 18 by the reciprocal of \frac{5}{6}.

$$n\times 18\times \frac{6}{5}=100$$

Express 18\times \frac{6}{5} as a single fraction.

$$n\times \frac{18\times 6}{5}=100$$

Multiply 18 and 6 to get 108.

$$n\times \frac{108}{5}=100$$

Multiply both sides by \frac{5}{108}, the reciprocal of \frac{108}{5}.

$$n=100\times \frac{5}{108}$$

Express 100\times \frac{5}{108} as a single fraction.

$$n=\frac{100\times 5}{108}$$

Multiply 100 and 5 to get 500.

$$n=\frac{500}{108}$$

Reduce the fraction \frac{500}{108} to lowest terms by extracting and canceling out 4.

$$n=\frac{125}{27}$$