Solve 2/8<1/8+6/40<3/8

$$\frac { 2 } { 8 } < \frac { 1 } { 8 } + \frac { 6 } { 40 } < \frac { 3 } { 8 }$$

Verify

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}<\frac{1}{8}+\frac{6}{40}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}<\frac{1}{8}+\frac{3}{20}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Least common multiple of 8 and 20 is 40. Convert \frac{1}{8} and \frac{3}{20} to fractions with denominator 40.

$$\frac{1}{4}<\frac{5}{40}+\frac{6}{40}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Since \frac{5}{40} and \frac{6}{40} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}<\frac{5+6}{40}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Add 5 and 6 to get 11.

$$\frac{1}{4}<\frac{11}{40}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Least common multiple of 4 and 40 is 40. Convert \frac{1}{4} and \frac{11}{40} to fractions with denominator 40.

$$\frac{10}{40}<\frac{11}{40}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Compare \frac{10}{40} and \frac{11}{40}.

$$\text{true}\text{ and }\frac{1}{8}+\frac{6}{40}<\frac{3}{8}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$\text{true}\text{ and }\frac{1}{8}+\frac{3}{20}<\frac{3}{8}$$

Least common multiple of 8 and 20 is 40. Convert \frac{1}{8} and \frac{3}{20} to fractions with denominator 40.

$$\text{true}\text{ and }\frac{5}{40}+\frac{6}{40}<\frac{3}{8}$$

Since \frac{5}{40} and \frac{6}{40} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{5+6}{40}<\frac{3}{8}$$

Add 5 and 6 to get 11.

$$\text{true}\text{ and }\frac{11}{40}<\frac{3}{8}$$

Least common multiple of 40 and 8 is 40. Convert \frac{11}{40} and \frac{3}{8} to fractions with denominator 40.

$$\text{true}\text{ and }\frac{11}{40}<\frac{15}{40}$$

Compare \frac{11}{40} and \frac{15}{40}.

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

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

$$\text{true}$$