Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.4

Question 1. Write the proper symbol from <, >, or = in the box
(i) \( \frac{3}{5} \) ___ \( \frac{2}{5} \)
(ii) \( \frac{2}{8} \) ___ \( \frac{1}{8} \)
(iii) \( \frac{2}{11} \) ___ \( \frac{10}{11} \)
(iv) \( \frac{3}{15} \) ___ \( \frac{10}{30} \)
(v) \( \frac{3}{8} \) ___ \( \frac{3}{7} \)
(vi) \( \frac{4}{7} \) ___ \( \frac{4}{11} \)
(vii) \( \frac{5}{12} \) ___ \( \frac{1}{6} \)
(viii) \( \frac{4}{9} \) ___ \( \frac{4}{9} \)
(ix) \( \frac{3}{7} \) ___ \( \frac{5}{9} \)
(x) \( \frac{4}{11} \) ___ \( \frac{1}{5} \)
Answer:
(i) Since the denominators are the same, we compare the numerators: \( 3 > 2 \). So, \( \frac{3}{5} > \frac{2}{5} \). This is because a larger numerator with the same denominator means a bigger fraction.
(ii) Since the denominators are the same, we compare the numerators: \( 2 > 1 \). So, \( \frac{2}{8} > \frac{1}{8} \).
(iii) Since the denominators are the same, we compare the numerators: \( 2 < 10 \). So, \( \frac{2}{11} < \frac{10}{11} \).
(iv) To compare \( \frac{3}{15} \) and \( \frac{10}{30} \), we make their denominators the same.
Multiply the numerator and denominator of \( \frac{3}{15} \) by 2: \( \frac{3 \times 2}{15 \times 2} = \frac{6}{30} \).
Now compare \( \frac{6}{30} \) and \( \frac{10}{30} \). Since \( 6 < 10 \), we have \( \frac{6}{30} < \frac{10}{30} \).
Therefore, \( \frac{3}{15} < \frac{10}{30} \).
(v) To compare \( \frac{3}{8} \) and \( \frac{3}{7} \), we make their denominators the same by finding the least common multiple (LCM) of 8 and 7, which is 56.
For \( \frac{3}{8} \): multiply numerator and denominator by 7: \( \frac{3 \times 7}{8 \times 7} = \frac{21}{56} \).
For \( \frac{3}{7} \): multiply numerator and denominator by 8: \( \frac{3 \times 8}{7 \times 8} = \frac{24}{56} \).
Now compare \( \frac{21}{56} \) and \( \frac{24}{56} \). Since \( 21 < 24 \), we have \( \frac{21}{56} < \frac{24}{56} \).
Therefore, \( \frac{3}{8} < \frac{3}{7} \).
(vi) To compare \( \frac{4}{7} \) and \( \frac{4}{11} \), we make their denominators the same by finding the LCM of 7 and 11, which is 77.
For \( \frac{4}{7} \): multiply numerator and denominator by 11: \( \frac{4 \times 11}{7 \times 11} = \frac{44}{77} \).
For \( \frac{4}{11} \): multiply numerator and denominator by 7: \( \frac{4 \times 7}{11 \times 7} = \frac{28}{77} \).
Now compare \( \frac{44}{77} \) and \( \frac{28}{77} \). Since \( 44 > 28 \), we have \( \frac{44}{77} > \frac{28}{77} \).
Therefore, \( \frac{4}{7} > \frac{4}{11} \).
(vii) To compare \( \frac{5}{12} \) and \( \frac{1}{6} \), we make their denominators the same.
Multiply the numerator and denominator of \( \frac{1}{6} \) by 2: \( \frac{1 \times 2}{6 \times 2} = \frac{2}{12} \).
Now compare \( \frac{5}{12} \) and \( \frac{2}{12} \). Since \( 5 > 2 \), we have \( \frac{5}{12} > \frac{2}{12} \).
Therefore, \( \frac{5}{12} > \frac{1}{6} \).
(viii) Both fractions are exactly the same. So, \( \frac{4}{9} = \frac{4}{9} \). When the numerator and denominator are identical, the fractions are equal.
(ix) To compare \( \frac{3}{7} \) and \( \frac{5}{9} \), we make their denominators the same by finding the LCM of 7 and 9, which is 63.
For \( \frac{3}{7} \): multiply numerator and denominator by 9: \( \frac{3 \times 9}{7 \times 9} = \frac{27}{63} \).
For \( \frac{5}{9} \): multiply numerator and denominator by 7: \( \frac{5 \times 7}{9 \times 7} = \frac{35}{63} \).
Now compare \( \frac{27}{63} \) and \( \frac{35}{63} \). Since \( 27 < 35 \), we have \( \frac{27}{63} < \frac{35}{63} \).
Therefore, \( \frac{3}{7} < \frac{5}{9} \).
(x) To compare \( \frac{4}{11} \) and \( \frac{1}{5} \), we make their denominators the same by finding the LCM of 11 and 5, which is 55.
For \( \frac{4}{11} \): multiply numerator and denominator by 5: \( \frac{4 \times 5}{11 \times 5} = \frac{20}{55} \).
For \( \frac{1}{5} \): multiply numerator and denominator by 11: \( \frac{1 \times 11}{5 \times 11} = \frac{11}{55} \).
Now compare \( \frac{20}{55} \) and \( \frac{11}{55} \). Since \( 20 > 11 \), we have \( \frac{20}{55} > \frac{11}{55} \).
Therefore, \( \frac{4}{11} > \frac{1}{5} \).
In simple words: To compare fractions, make their bottom numbers (denominators) the same. Then, look at the top numbers (numerators). The fraction with the bigger top number is the larger one. If the denominators are already the same, just compare the numerators directly.

🎯 Exam Tip: When comparing fractions with different denominators, always find a common denominator first, usually the least common multiple (LCM), to avoid errors. Cross-multiplication is also a quick method for comparing two fractions.