Question

find three rational numbers between 1/4 and 1/2

Answer 1

Step-by-step explanation:

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Answer 2

Given: Two rational numbers $\frac{1}{4}$ and $\frac{1}{2}$

To find: Three rational numbers between the given numbers

Solution: The given rational numbers have different denominators. First we need to make their denominator same.

LCM of their denominators 4 and 2 = 4.

To convert these rational numbers with same denominators, we have

$\frac{1}{4} = \frac{1}{4}$ × $\frac{1}{1} = \frac{1}{4}$ and $\frac{1}{2} = \frac{1}{2}$ × $\frac{2}{2} = \frac{2}{4}$

To insert three rational numbers, multiply both numerator and denominator of each rational number with 3 + 1 i.e., 4.

We have, $\frac{1}{4} = \frac{1}{4}$ × $\frac{4}{4} = \frac{4}{16}$ and $\frac{2}{4} = \frac{2}{4}$ × $\frac{4}{4} = \frac{8}{16}$

∵ $4 < 5 < 6 < 7 < 8$

∴ $\frac{4}{16} < \frac{5}{16} < \frac{6}{16} < \frac{7}{16} < \frac{8}{16}$

Hence, three rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$ are:

$\frac{5}{16}, \frac{6}{16} \ and \ \frac{7}{16}$.