QUESTION 2
Easy
Find six rational numbers between 3 and 4.
SOLUTION
1
Write the numbers as fractions
\( \frac{3}{1} \) and \( \frac{4}{1} \)
2
Multiply both numerator and denominator by a number greater than 6(we choose 7)
3 = \( \frac{3 × 7}{1 × 7} \) = \( \frac{21}{7} \)
4 = \( \frac{4 × 7}{1 × 7} \) = \( \frac{28}{7} \)
3
Write does the six rational numbers between \( \frac{21}{7} \) and \( \frac{28}{7} \)
\( \frac{22}{7} \), \( \frac{23}{7} \), \( \frac{24}{7} \), \( \frac{25}{7} \), \( \frac{26}{7} \), \( \frac{27}{7} \)
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Final Answer : \( \frac{22}{7} \), \( \frac{23}{7} \), \( \frac{24}{7} \), \( \frac{25}{7} \), \( \frac{26}{7} \), \( \frac{27}{7} \)
Concept Note
To find n rational numbers between two numbers with the same denominator, multiply numerator and denominator of both fractions by any number > n. This ensures the numerator gap is large enough to insert n rational numbers between them.