Solve 2/5<1/5+5/15<3/5

$$\frac { 2 } { 5 } < \frac { 1 } { 5 } + \frac { 5 } { 15 } < \frac { 3 } { 5 }$$

Verify

Solution Steps

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{2}{5}<\frac{1}{5}+\frac{1}{3}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{1}{3} to fractions with denominator 15.

$$\frac{2}{5}<\frac{3}{15}+\frac{5}{15}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Since \frac{3}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}<\frac{3+5}{15}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Add 3 and 5 to get 8.

$$\frac{2}{5}<\frac{8}{15}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Least common multiple of 5 and 15 is 15. Convert \frac{2}{5} and \frac{8}{15} to fractions with denominator 15.

$$\frac{6}{15}<\frac{8}{15}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Compare \frac{6}{15} and \frac{8}{15}.

$$\text{true}\text{ and }\frac{1}{5}+\frac{5}{15}<\frac{3}{5}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

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

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{1}{3} to fractions with denominator 15.

$$\text{true}\text{ and }\frac{3}{15}+\frac{5}{15}<\frac{3}{5}$$

Since \frac{3}{15} and \frac{5}{15} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{3+5}{15}<\frac{3}{5}$$

Add 3 and 5 to get 8.

$$\text{true}\text{ and }\frac{8}{15}<\frac{3}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{8}{15} and \frac{3}{5} to fractions with denominator 15.

$$\text{true}\text{ and }\frac{8}{15}<\frac{9}{15}$$

Compare \frac{8}{15} and \frac{9}{15}.

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

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

$$\text{true}$$