Solve 2/5<1/5+6/25<3/5

$$\frac{ 2 }{ 5 } < \frac{ 1 }{ 5 } + \frac{ 6 }{ 25 } < \frac{ 3 }{ 5 }$$

Verify

Solution Steps

Least common multiple of 5 and 25 is 25. Convert \frac{1}{5} and \frac{6}{25} to fractions with denominator 25.

$$\frac{2}{5}<\frac{5}{25}+\frac{6}{25}\text{ and }\frac{1}{5}+\frac{6}{25}<\frac{3}{5}$$

Since \frac{5}{25} and \frac{6}{25} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}<\frac{5+6}{25}\text{ and }\frac{1}{5}+\frac{6}{25}<\frac{3}{5}$$

Add 5 and 6 to get 11.

$$\frac{2}{5}<\frac{11}{25}\text{ and }\frac{1}{5}+\frac{6}{25}<\frac{3}{5}$$

Least common multiple of 5 and 25 is 25. Convert \frac{2}{5} and \frac{11}{25} to fractions with denominator 25.

$$\frac{10}{25}<\frac{11}{25}\text{ and }\frac{1}{5}+\frac{6}{25}<\frac{3}{5}$$

Compare \frac{10}{25} and \frac{11}{25}.

$$\text{true}\text{ and }\frac{1}{5}+\frac{6}{25}<\frac{3}{5}$$

Least common multiple of 5 and 25 is 25. Convert \frac{1}{5} and \frac{6}{25} to fractions with denominator 25.

$$\text{true}\text{ and }\frac{5}{25}+\frac{6}{25}<\frac{3}{5}$$

Since \frac{5}{25} and \frac{6}{25} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{5+6}{25}<\frac{3}{5}$$

Add 5 and 6 to get 11.

$$\text{true}\text{ and }\frac{11}{25}<\frac{3}{5}$$

Least common multiple of 25 and 5 is 25. Convert \frac{11}{25} and \frac{3}{5} to fractions with denominator 25.

$$\text{true}\text{ and }\frac{11}{25}<\frac{15}{25}$$

Compare \frac{11}{25} and \frac{15}{25}.

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

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

$$\text{true}$$