Solve 2/8<1/8+4/24<3/8

$$\frac { 2 } { 8 } < \frac { 1 } { 8 } + \frac { 4 } { 24 } < \frac { 3 } { 8 }$$

Verify

Solution Steps

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

$$\frac{1}{4}<\frac{1}{8}+\frac{4}{24}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}<\frac{1}{8}+\frac{1}{6}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{1}{6} to fractions with denominator 24.

$$\frac{1}{4}<\frac{3}{24}+\frac{4}{24}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Since \frac{3}{24} and \frac{4}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}<\frac{3+4}{24}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Add 3 and 4 to get 7.

$$\frac{1}{4}<\frac{7}{24}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Least common multiple of 4 and 24 is 24. Convert \frac{1}{4} and \frac{7}{24} to fractions with denominator 24.

$$\frac{6}{24}<\frac{7}{24}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Compare \frac{6}{24} and \frac{7}{24}.

$$\text{true}\text{ and }\frac{1}{8}+\frac{4}{24}<\frac{3}{8}$$

Reduce the fraction \frac{4}{24} to lowest terms by extracting and canceling out 4.

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

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{1}{6} to fractions with denominator 24.

$$\text{true}\text{ and }\frac{3}{24}+\frac{4}{24}<\frac{3}{8}$$

Since \frac{3}{24} and \frac{4}{24} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{3+4}{24}<\frac{3}{8}$$

Add 3 and 4 to get 7.

$$\text{true}\text{ and }\frac{7}{24}<\frac{3}{8}$$

Least common multiple of 24 and 8 is 24. Convert \frac{7}{24} and \frac{3}{8} to fractions with denominator 24.

$$\text{true}\text{ and }\frac{7}{24}<\frac{9}{24}$$

Compare \frac{7}{24} and \frac{9}{24}.

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

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

$$\text{true}$$