Solve 5/frac{2{5}}=n/frac{1{10}}

$$\frac { 5 } { \frac { 2 } { 5 } } = \frac { n } { \frac { 1 } { 10 } }$$

Solve for n

$$n = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

Divide 5 by \frac{2}{5} by multiplying 5 by the reciprocal of \frac{2}{5}.

$$5\times \frac{5}{2}=\frac{n}{\frac{1}{10}}$$

Express 5\times \frac{5}{2} as a single fraction.

$$\frac{5\times 5}{2}=\frac{n}{\frac{1}{10}}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{2}=\frac{n}{\frac{1}{10}}$$

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

$$\frac{n}{\frac{1}{10}}=\frac{25}{2}$$

Multiply both sides by \frac{1}{10}.

$$n=\frac{25}{2}\times \frac{1}{10}$$

Multiply \frac{25}{2} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$n=\frac{25\times 1}{2\times 10}$$

Do the multiplications in the fraction \frac{25\times 1}{2\times 10}.

$$n=\frac{25}{20}$$

Reduce the fraction \frac{25}{20} to lowest terms by extracting and canceling out 5.

$$n=\frac{5}{4}$$