Solve 4/5<1/5+2/10<5/5

$$\frac { 4 } { 5 } < \frac { 1 } { 5 } + \frac { 2 } { 10 } < \frac { 5 } { 5 }$$

Verify

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{4}{5}<\frac{1}{5}+\frac{2}{10}\text{ and }\frac{1}{5}+\frac{2}{10}<1$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}<\frac{1}{5}+\frac{1}{5}\text{ and }\frac{1}{5}+\frac{2}{10}<1$$

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

$$\frac{4}{5}<\frac{1+1}{5}\text{ and }\frac{1}{5}+\frac{2}{10}<1$$

Add 1 and 1 to get 2.

$$\frac{4}{5}<\frac{2}{5}\text{ and }\frac{1}{5}+\frac{2}{10}<1$$

Compare \frac{4}{5} and \frac{2}{5}.

$$\text{false}\text{ and }\frac{1}{5}+\frac{2}{10}<1$$

Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\text{false}\text{ and }\frac{1}{5}+\frac{1}{5}<1$$

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

$$\text{false}\text{ and }\frac{1+1}{5}<1$$

Add 1 and 1 to get 2.

$$\text{false}\text{ and }\frac{2}{5}<1$$

Convert 1 to fraction \frac{5}{5}.

$$\text{false}\text{ and }\frac{2}{5}<\frac{5}{5}$$

Compare \frac{2}{5} and \frac{5}{5}.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$