CBSE Class 6 Mathematics Fractions Practice Paper Worksheet Set 09 with Answers

Class 6 Maths Ganita Prakash Chapter 7 Fractions Practice Paper 20 (CBSE) is a full 40-mark test with 20 questions across Sections A to E, and every question is answered below step by step. This paper focuses on fair sharing of rotis and juice bottles, fractional units on paper strips, marking twelfths on a number line from 0 to 2, improper fractions and mixed numbers such as 26/8 and 15/12, reducing 84/108 to simplest form, and adding and subtracting fractions like 3/5 + 2/3 + 7/15 and 5/6 − 2/9.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. A paper strip of length 1 unit is folded into 6 equal parts. What is the fractional unit? Represent 4 such units.
Answer:
The strip is folded into 6 equal parts, so the fractional unit is \( \frac{1}{6} \).
4 such units = \( \frac{1}{6} \) + \( \frac{1}{6} \) + \( \frac{1}{6} \) + \( \frac{1}{6} \) = \( \frac{4}{6} \) (= \( \frac{2}{3} \)) of the strip, shown shaded:

In simple words: Each fold-part is one-sixth; shading 4 of the 6 parts shows four-sixths.

Teacher's Note:
1. 4 times the unit \( \frac{1}{6} \) is \( \frac{4}{6} \).
2. \( \frac{4}{6} \) and \( \frac{2}{3} \) cover the same length of the strip.

Question 12. Write \( \frac{26}{8} \) as a mixed number.
Answer:
Divide 26 by 8: 26 = 8 × 3 + 2, so the quotient is 3 and the remainder is 2.
\( \frac{26}{8} \) = \( 3\frac{2}{8} \).
Simplify the fraction part: \( \frac{2}{8} \) = \( \frac{1}{4} \), so \( \frac{26}{8} \) = \( 3\frac{1}{4} \).
In simple words: 26 eighths make 3 wholes (24 eighths) and 2 eighths, which is a quarter.

Teacher's Note:
1. You may first reduce \( \frac{26}{8} \) = \( \frac{13}{4} \) and then convert: 13 = 4 × 3 + 1.
2. Check: 3 × 8 + 2 = 26.

Question 13. Add: \( \frac{1}{3} \) + \( \frac{2}{9} \) using equivalent fractions.
Answer:
The LCM of 3 and 9 is 9.
\( \frac{1}{3} \) = \( \frac{1 \times 3}{3 \times 3} \) = \( \frac{3}{9} \).
\( \frac{3}{9} \) + \( \frac{2}{9} \) = \( \frac{5}{9} \).
In simple words: Change thirds into ninths and add the ninths.

Teacher's Note:
1. 9 is a multiple of 3, so only \( \frac{1}{3} \) needs changing.
2. 5 and 9 have no common factor, so \( \frac{5}{9} \) is final.

Question 14. Reduce \( \frac{84}{108} \) to simplest form.
Answer:
Find the HCF: 84 = 2² × 3 × 7 and 108 = 2² × 3³, so HCF = 2² × 3 = 12.
\( \frac{84 \div 12}{108 \div 12} \) = \( \frac{7}{9} \).
So the simplest form is \( \frac{7}{9} \).
In simple words: Divide top and bottom by 12, the largest number that divides both.

Teacher's Note:
1. Step by step: divide by 2, by 2, then by 3.
2. 7 and 9 have no common factor except 1.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Show whether \( \frac{6}{8} \) and \( \frac{9}{12} \) are equivalent fractions.
Answer:
Reduce each to lowest terms.
\( \frac{6}{8} \) = \( \frac{6 \div 2}{8 \div 2} \) = \( \frac{3}{4} \).
\( \frac{9}{12} \) = \( \frac{9 \div 3}{12 \div 3} \) = \( \frac{3}{4} \).
Both equal \( \frac{3}{4} \), so yes, \( \frac{6}{8} \) and \( \frac{9}{12} \) are equivalent.
Cross-check: 6 × 12 = 72 and 8 × 9 = 72 are equal.
In simple words: Both fractions simplify to three-quarters.

Teacher's Note:
1. Equivalent fractions reduce to the same lowest form.
2. Or write both with denominator 24: \( \frac{18}{24} \) and \( \frac{18}{24} \).

Question 16. Add \( \frac{3}{5} \) + \( \frac{2}{3} \) + \( \frac{7}{15} \).
Answer:
The LCM of 5, 3 and 15 is 15.
\( \frac{3}{5} \) = \( \frac{9}{15} \), \( \frac{2}{3} \) = \( \frac{10}{15} \), \( \frac{7}{15} \) = \( \frac{7}{15} \).
Sum = \( \frac{9 + 10 + 7}{15} \) = \( \frac{26}{15} \).
26 = 15 × 1 + 11, so the sum is \( 1\frac{11}{15} \) (= \( \frac{26}{15} \)).
In simple words: Change everything into fifteenths, add, then write as a mixed number.

Teacher's Note:
1. 15 is already a multiple of 5 and 3, so it is the common denominator.
2. Rough check: 0.6 + 0.67 + 0.47 is about 1.73.

Question 17. Subtract: \( \frac{5}{6} \) − \( \frac{2}{9} \) using the common denominator method.
Answer:
The LCM of 6 and 9 is 18.
\( \frac{5}{6} \) = \( \frac{15}{18} \) and \( \frac{2}{9} \) = \( \frac{4}{18} \).
\( \frac{15}{18} \) − \( \frac{4}{18} \) = \( \frac{11}{18} \).
11 is prime and does not divide 18, so the answer is \( \frac{11}{18} \).
In simple words: Turn both fractions into eighteenths and subtract the numerators.

Teacher's Note:
1. The LCM 18 is smaller than 6 × 9 = 54, so it keeps numbers small.
2. Keep the denominator; subtract only the numerators.

Section D: Long Answer Question (5 Marks)

Question 18. A number line from 0 to 2 is divided into 24 equal parts (12 equal parts between 0 and 1 and 12 between 1 and 2).
(a) What is the size of one part?
(b) Mark \( \frac{5}{12} \) on the number line.
(c) Express \( \frac{15}{12} \) as a mixed number.
(d) Are \( \frac{5}{12} \) and \( \frac{10}{24} \) equivalent? Prove.
(e) Is \( \frac{15}{12} \) > \( \frac{11}{12} \)? Why?
Answer:
(a) Each unit (0 to 1, and 1 to 2) has 12 equal parts, so one part is \( \frac{1}{12} \).
(b) Count 5 parts from 0 to reach \( \frac{5}{12} \). The figure also shows \( \frac{11}{12} \) and \( \frac{15}{12} \), which are used in (e):

(c) 15 = 12 × 1 + 3, so \( \frac{15}{12} \) = \( 1\frac{3}{12} \) = \( 1\frac{1}{4} \).
(d) \( \frac{10}{24} \) = \( \frac{10 \div 2}{24 \div 2} \) = \( \frac{5}{12} \). Yes, they are equivalent.
(e) Yes. Both have denominator 12 and 15 > 11. Also \( \frac{15}{12} \) is more than 1 while \( \frac{11}{12} \) is less than 1; on the number line \( \frac{15}{12} \) lies to the right of \( \frac{11}{12} \).
In simple words: Each small gap is one-twelfth; fifteen-twelfths is past 1, so it is bigger than eleven-twelfths.

Teacher's Note:
1. The size of one part is (length of one unit) ÷ (parts in one unit).
2. On a number line, the number further to the right is greater.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1:
A farmer divides 3 identical sugarcane juice bottles equally among his 4 children. Each child drinks his share, and later the children compare how much they drank using fractional units. The youngest child wants to convert the fraction into simplest form, while the eldest wants to know how to represent it on a number line. They also check whether the fractional unit is \( \frac{1}{3} \) or \( \frac{1}{4} \) and discuss their reasoning using examples from the textbook.
Based on the above, answer the following questions:
(a) Fraction per child?
(b) Write its one equivalent fraction.
(c) Represent it on a number line.
(d) Is \( \frac{3}{4} \) greater than 1? Explain.
Answer:
(a) 3 bottles shared by 4 children: 3 ÷ 4 = \( \frac{3}{4} \) of a bottle per child. (Already in simplest form; the fractional unit is \( \frac{1}{4} \).)
(b) \( \frac{3 \times 2}{4 \times 2} \) = \( \frac{6}{8} \) (others: \( \frac{9}{12} \), \( \frac{12}{16} \)).
(c) Divide 0 to 1 into 4 equal parts and count 3 parts from 0:

(d) No. In \( \frac{3}{4} \) the numerator 3 is less than the denominator 4, so it is a proper fraction and less than 1. It is \( \frac{1}{4} \) short of a whole bottle.
In simple words: Each child gets three-quarters of a bottle, which is less than one full bottle.

Teacher's Note:
1. Sharing 3 wholes among 4 gives \( \frac{3}{4} \) each; the fractional unit is \( \frac{1}{4} \), not \( \frac{1}{3} \).
2. A proper fraction always lies between 0 and 1 on the number line.

Question 20. Case Study 2:
A class prepares a fruit salad using 5 rotis of sweet bread cut into equal pieces. The teacher divides all pieces equally among 15 students. Later, 5 more students join, and the teacher redistributes the same amount of pieces. Students compare both situations, find equivalent fractions, and reason which group got a larger share. They connect this with the rule “more children → smaller share”.
Based on the above, answer the following questions:
(a) Fraction of a roti per child in the first group.
(b) Fraction of a roti per child in the second group.
(c) Which group gets more?
(d) Explain using equivalent fractions.
Answer:
(a) 5 rotis shared by 15 students: 5 ÷ 15 = \( \frac{5}{15} \) = \( \frac{1}{3} \) of a roti per child.
(b) 5 rotis shared by 15 + 5 = 20 students: 5 ÷ 20 = \( \frac{5}{20} \) = \( \frac{1}{4} \) of a roti per child.
(c) The first group (15 students) gets more per child.
(d) With denominator 12: \( \frac{1}{3} \) = \( \frac{4}{12} \) and \( \frac{1}{4} \) = \( \frac{3}{12} \). Since 4 > 3, \( \frac{1}{3} \) > \( \frac{1}{4} \).
This agrees with the rule: more children, smaller share.
In simple words: A third of a roti each for 15 children, but only a quarter each when 20 share.

Teacher's Note:
1. For the same numerator, the larger denominator gives the smaller fraction.
2. Common denominator 12 makes the two shares easy to compare.