Solve 1/5+2/9div5/9=3/5

$$\frac { 1 } { 5 } + \frac { 2 } { 9 } \div \frac { 5 } { 9 } = \frac { 3 } { 5 }$$

Verify

Solution Steps

Divide \frac{2}{9} by \frac{5}{9} by multiplying \frac{2}{9} by the reciprocal of \frac{5}{9}.

$$\frac{1}{5}+\frac{2}{9}\times \frac{9}{5}=\frac{3}{5}$$

Multiply \frac{2}{9} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}+\frac{2\times 9}{9\times 5}=\frac{3}{5}$$

Cancel out 9 in both numerator and denominator.

$$\frac{1}{5}+\frac{2}{5}=\frac{3}{5}$$

Since \frac{1}{5} and \frac{2}{5} have the same denominator, add them by adding their numerators.

$$\frac{1+2}{5}=\frac{3}{5}$$

Add 1 and 2 to get 3.

$$\frac{3}{5}=\frac{3}{5}$$

Compare \frac{3}{5} and \frac{3}{5}.

$$\text{true}$$