Samacheer Kalvi Class 5 Maths Solutions Term 3 Chapter 6 Fractions Exercise 6.1

Samacheer Kalvi 5th Maths Guide Term 3 Chapter 6 Fractions Ex 6.1

Question 1. Write the fraction shown by the shaded parts.
(i)
(ii)
(iii)
Answer:
(i) \( \frac{5}{12} \)
(ii) \( \frac{2}{6} \)
(iii) \( \frac{3}{9} \) In each figure, the total parts make up the denominator, and the shaded parts form the numerator.
In simple words: To find a fraction from a picture, count all the parts as the bottom number (denominator) and the shaded parts as the top number (numerator).

🎯 Exam Tip: Always count all equal parts carefully to get the correct denominator, and then count the specific shaded or indicated parts for the numerator.

Question 2. Write the fractions for the following and find the numerator and the denominator.
(i) Sheeki got 12 marks out of 20 marks in science.
(ii) Six fruits are rotten out of forty fruits in a basket.
(iii) In a colony of 50 houses. 17 houses are not occupied.
Answer:
(i) Sheeki's marks can be written as the fraction \( \frac{12}{20} \). Here, the Numerator is 12 and the Denominator is 20.
(ii) The fraction of rotten fruits is \( \frac{6}{40} \). So, the Numerator is 6 and the Denominator is 40.
(iii) The fraction of unoccupied houses is \( \frac{17}{50} \). This means the Numerator is 17 and the Denominator is 50.
In simple words: When you have a "part out of a whole," the "part" is the numerator (top number) and the "whole" is the denominator (bottom number) of the fraction.

🎯 Exam Tip: Remember that the numerator shows how many parts you have, and the denominator shows the total number of parts in the whole.

Question 3. Find out which is greater in the following fractions.
(i) \( \frac { 5 }{ 12 } \) and \( \frac { 7 }{ 12 } \)
(ii) \( \frac { 22 }{ 48 } \) and \( \frac { 17 }{ 48 } \)
(iii) \( \frac { 11 }{ 56 } \) and \( \frac { 27 }{ 56 } \)
Answer:
(i) For \( \frac{5}{12} \) and \( \frac{7}{12} \), since the denominators are the same (12), we compare the numerators. Since \( 5 < 7 \), it means that \( \frac{5}{12} < \frac{7}{12} \). Therefore, \( \frac{7}{12} \) is greater.
(ii) For \( \frac{22}{48} \) and \( \frac{17}{48} \), the denominators are the same (48). Comparing the numerators, we see that \( 22 > 17 \). So, \( \frac{22}{48} > \frac{17}{48} \). Therefore, \( \frac{22}{48} \) is greater.
(iii) For \( \frac{11}{56} \) and \( \frac{27}{56} \), the denominators are the same (56). By comparing the numerators, we find that \( 11 < 27 \). This means \( \frac{11}{56} < \frac{27}{56} \). Therefore, \( \frac{27}{56} \) is greater.
In simple words: When two fractions have the same bottom number (denominator), the fraction with the bigger top number (numerator) is the larger fraction.

🎯 Exam Tip: When denominators are equal, comparing fractions becomes as simple as comparing their numerators. The larger numerator means a larger fraction.

Question 4. Which is smaller in the following fraction?
(i) \( \frac { 10 }{42} \) and \( \frac { 21 }{ 42 } \)
(ii) \( \frac { 31 }{ 37 } \) and \( \frac { 15 }{ 37 } \)
Answer:
(i) For \( \frac{10}{42} \) and \( \frac{21}{42} \), the denominators are the same (42). We compare the numerators: \( 10 < 21 \). So, \( \frac{10}{42} < \frac{21}{42} \). Therefore, \( \frac{10}{42} \) is the smaller fraction.
(ii) For \( \frac{31}{37} \) and \( \frac{15}{37} \), the denominators are the same (37). Comparing the numerators, we see that \( 15 < 31 \). So, \( \frac{15}{37} < \frac{31}{37} \). Therefore, \( \frac{15}{37} \) is the smaller fraction.
In simple words: When the bottom numbers (denominators) of two fractions are the same, the fraction with the smaller top number (numerator) is the smaller fraction.

🎯 Exam Tip: Always check if the denominators are the same first. If they are, just look at the numerators to decide which fraction is smaller or larger.