Solve 4/5<1/5+9/10<5/5

$$\frac { 4 } { 5 } < \frac { 1 } { 5 } + \frac { 9 } { 10 } < \frac { 5 } { 5 }$$

Verify

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{4}{5}<\frac{1}{5}+\frac{9}{10}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{9}{10} to fractions with denominator 10.

$$\frac{4}{5}<\frac{2}{10}+\frac{9}{10}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Since \frac{2}{10} and \frac{9}{10} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}<\frac{2+9}{10}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Add 2 and 9 to get 11.

$$\frac{4}{5}<\frac{11}{10}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Least common multiple of 5 and 10 is 10. Convert \frac{4}{5} and \frac{11}{10} to fractions with denominator 10.

$$\frac{8}{10}<\frac{11}{10}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Compare \frac{8}{10} and \frac{11}{10}.

$$\text{true}\text{ and }\frac{1}{5}+\frac{9}{10}<1$$

Least common multiple of 5 and 10 is 10. Convert \frac{1}{5} and \frac{9}{10} to fractions with denominator 10.

$$\text{true}\text{ and }\frac{2}{10}+\frac{9}{10}<1$$

Since \frac{2}{10} and \frac{9}{10} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{2+9}{10}<1$$

Add 2 and 9 to get 11.

$$\text{true}\text{ and }\frac{11}{10}<1$$

Convert 1 to fraction \frac{10}{10}.

$$\text{true}\text{ and }\frac{11}{10}<\frac{10}{10}$$

Compare \frac{11}{10} and \frac{10}{10}.

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

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

$$\text{false}$$