Solve 2/8<1/8+124/24<3/8

$$\frac { 2 } { 8 } < \frac { 1 } { 8 } + \frac { 124 } { 24 } < \frac { 3 } { 8 }$$

Verify

Solution Steps

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

$$\frac{1}{4}<\frac{1}{8}+\frac{124}{24}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Reduce the fraction \frac{124}{24} to lowest terms by extracting and canceling out 4.

$$\frac{1}{4}<\frac{1}{8}+\frac{31}{6}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{31}{6} to fractions with denominator 24.

$$\frac{1}{4}<\frac{3}{24}+\frac{124}{24}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Since \frac{3}{24} and \frac{124}{24} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}<\frac{3+124}{24}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Add 3 and 124 to get 127.

$$\frac{1}{4}<\frac{127}{24}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Least common multiple of 4 and 24 is 24. Convert \frac{1}{4} and \frac{127}{24} to fractions with denominator 24.

$$\frac{6}{24}<\frac{127}{24}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Compare \frac{6}{24} and \frac{127}{24}.

$$\text{true}\text{ and }\frac{1}{8}+\frac{124}{24}<\frac{3}{8}$$

Reduce the fraction \frac{124}{24} to lowest terms by extracting and canceling out 4.

$$\text{true}\text{ and }\frac{1}{8}+\frac{31}{6}<\frac{3}{8}$$

Least common multiple of 8 and 6 is 24. Convert \frac{1}{8} and \frac{31}{6} to fractions with denominator 24.

$$\text{true}\text{ and }\frac{3}{24}+\frac{124}{24}<\frac{3}{8}$$

Since \frac{3}{24} and \frac{124}{24} have the same denominator, add them by adding their numerators.

$$\text{true}\text{ and }\frac{3+124}{24}<\frac{3}{8}$$

Add 3 and 124 to get 127.

$$\text{true}\text{ and }\frac{127}{24}<\frac{3}{8}$$

Least common multiple of 24 and 8 is 24. Convert \frac{127}{24} and \frac{3}{8} to fractions with denominator 24.

$$\text{true}\text{ and }\frac{127}{24}<\frac{9}{24}$$

Compare \frac{127}{24} and \frac{9}{24}.

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

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

$$\text{false}$$