To find a pair of rational numbers between \( \frac{1}{4} \) and \( \frac{3}{4} \), we can use a systematic approach involving averaging and finding fractions.
Understanding Rational Numbers
- Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero.
- Examples include fractions like \( \frac{1}{2} \) or \( \frac{3}{5} \).
Finding a Common Denominator
- To compare \( \frac{1}{4} \) and \( \frac{3}{4} \), we can use a common denominator.
- The denominators are both 4, so we can express both fractions in a more expanded form:
- \( \frac{1}{4} = \frac{2}{8} \)
- \( \frac{3}{4} = \frac{6}{8} \)
Choosing Rational Numbers
- Now that we have expressed the fractions with a common denominator, we can find rational numbers between \( \frac{2}{8} \) and \( \frac{6}{8} \).
- Possible pairs of rational numbers could include:
- \( \frac{3}{8} \)
- \( \frac{5}{8} \)
Conclusion
- Therefore, the pair of rational numbers between \( \frac{1}{4} \) and \( \frac{3}{4} \) is \( \frac{3}{8} \) and \( \frac{5}{8} \).
- This method can be applied to find rational numbers between any two given fractions by determining a common denominator and selecting suitable numerators.