QUESTION 3
Easy
Find five rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \).
SOLUTION
1
Multiply both numerator and denominator by a number greater than 5(we choose 6)
\( \frac{3}{5} \) = \( \frac{3 × 6}{5 × 6} \) = \( \frac{18}{30} \)
\( \frac{4}{5} \) = \( \frac{4 × 6}{5 × 6} \) = \( \frac{24}{30} \)
2
Write the numbers between \( \frac{18}{30} \) and \( \frac{24}{30} \)
\( \frac{19}{30} \), \( \frac{20}{30} \), \( \frac{21}{30} \), \( \frac{22}{30} \), \( \frac{23}{30} \)
Or after simplifying
\( \frac{19}{30} \), \( \frac{2}{3} \), \( \frac{7}{10} \), \( \frac{11}{15} \), \( \frac{23}{30} \)
3
Write the five rational numbers
\( \frac{19}{30} \), \( \frac{2}{3} \), \( \frac{7}{10} \), \( \frac{11}{15} \), \( \frac{23}{30} \)
🏆
Final Answer : \( \frac{19}{30} \), \( \frac{2}{3} \), \( \frac{7}{10} \), \( \frac{11}{15} \), \( \frac{23}{30} \)
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.