CBSE Class 6 Mathematics Fractions Practice Paper Assignment Set 12 with Answers

This is CBSE Class 6 Maths Ganita Prakash Chapter 7 Fractions Practice Paper 19, a 40-mark paper of 20 questions in Sections A to E, solved here with step-by-step answers. It tests fractional units from equal sharing of rotis, chikki and guavas, reading and marking fractions on a number line, mixed numbers, lowest terms, equivalent fractions, and adding and subtracting unlike fractions such as 2/3 + 5/6 + 1/4 and 7/8 − 1/3.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. Three guavas together weigh 1 kg. Find the weight of each guava.
Answer:
Assume the three guavas are of equal weight.
Weight of each guava = 1 kg ÷ 3.
So each guava weighs \( \frac{1}{3} \) kg.
In simple words: 1 kg shared equally by 3 guavas gives one-third of a kilogram each.

Teacher's Note:
1. Dividing 1 whole into 3 equal parts gives the fractional unit \( \frac{1}{3} \).
2. \( \frac{1}{3} \) kg is a little more than 333 g.

Question 12. Represent \( \frac{5}{8} \) on a number line.
Answer:
Draw a number line and mark 0 and 1.
Divide the gap from 0 to 1 into 8 equal parts; each part is \( \frac{1}{8} \).
Count 5 parts from 0. That point is \( \frac{5}{8} \), shown in red.

In simple words: Cut 0 to 1 into 8 equal pieces and stop after the 5th piece.

Teacher's Note:
1. The denominator tells how many equal parts to make between 0 and 1.
2. The numerator tells how many parts to count from 0.

Question 13. Write \( \frac{11}{4} \) as a mixed number.
Answer:
Divide 11 by 4: 11 = 4 × 2 + 3, so the quotient is 2 and the remainder is 3.
Quotient = whole number, remainder = new numerator, denominator stays 4.
\( \frac{11}{4} \) = \( 2\frac{3}{4} \).
In simple words: Eleven quarters make 2 wholes (8 quarters) and 3 quarters left over.

Teacher's Note:
1. Check: 2 × 4 + 3 = 11.
2. The denominator never changes when converting.

Question 14. Express \( \frac{40}{60} \) in lowest terms.
Answer:
HCF of 40 and 60 = 20.
\( \frac{40 \div 20}{60 \div 20} \) = \( \frac{2}{3} \).
So \( \frac{40}{60} \) in lowest terms is \( \frac{2}{3} \).
In simple words: Divide top and bottom by 20, the biggest number that divides both.

Teacher's Note:
1. You may also go step by step: divide by 10, then by 2.
2. 2 and 3 have no common factor except 1, so we stop.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Check using equivalent fractions whether \( \frac{4}{6} \) and \( \frac{6}{9} \) are equivalent.
Answer:
Reduce each fraction to lowest terms.
\( \frac{4}{6} \) = \( \frac{4 \div 2}{6 \div 2} \) = \( \frac{2}{3} \).
\( \frac{6}{9} \) = \( \frac{6 \div 3}{9 \div 3} \) = \( \frac{2}{3} \).
Both are equal to \( \frac{2}{3} \), so yes, \( \frac{4}{6} \) and \( \frac{6}{9} \) are equivalent.
Cross-check: 4 × 9 = 36 and 6 × 6 = 36 are equal.
In simple words: Both fractions simplify to two-thirds, so they show the same amount.

Teacher's Note:
1. Reducing both fractions to lowest terms is a sure test.
2. You can also write both with denominator 18: \( \frac{12}{18} \) and \( \frac{12}{18} \).

Question 16. Add: \( \frac{2}{3} \) + \( \frac{5}{6} \) + \( \frac{1}{4} \)
Answer:
The LCM of 3, 6 and 4 is 12.
\( \frac{2}{3} \) = \( \frac{8}{12} \), \( \frac{5}{6} \) = \( \frac{10}{12} \), \( \frac{1}{4} \) = \( \frac{3}{12} \).
Sum = \( \frac{8 + 10 + 3}{12} \) = \( \frac{21}{12} \).
Simplify: \( \frac{21}{12} \) = \( \frac{7}{4} \) (dividing by 3) = \( 1\frac{3}{4} \).
In simple words: Change all three fractions into twelfths, add the twelfths, then simplify.

Teacher's Note:
1. Always simplify the final answer and change it to a mixed number if it is improper.
2. Rough check: 0.67 + 0.83 + 0.25 is about 1.75.

Question 17. Subtract using common denominators: \( \frac{7}{8} \) − \( \frac{1}{3} \).
Answer:
The LCM of 8 and 3 is 24.
\( \frac{7}{8} \) = \( \frac{21}{24} \) and \( \frac{1}{3} \) = \( \frac{8}{24} \).
\( \frac{21}{24} \) − \( \frac{8}{24} \) = \( \frac{13}{24} \).
13 is prime and does not divide 24, so the answer is \( \frac{13}{24} \).
In simple words: Write both fractions in twenty-fourths and subtract the numerators.

Teacher's Note:
1. 8 and 3 are co-prime, so their LCM is 8 × 3 = 24.
2. Subtract numerators only; keep the common denominator.

Section D: Long Answer Question (5 Marks)

Question 18. A paper strip of length 1 unit is folded to make 8 equal parts.
(a) What is the fractional length of one part?
(b) What is 6 times \( \frac{1}{8} \)?
(c) Convert \( \frac{6}{8} \) into lowest terms.
(d) Show \( \frac{7}{8} \) on a number line.
(e) Is \( \frac{6}{8} \) equal to \( \frac{3}{4} \)? Explain.
Answer:
(a) 1 unit is folded into 8 equal parts, so one part is \( \frac{1}{8} \) unit long.
(b) 6 times \( \frac{1}{8} \) = \( \frac{1}{8} \) + \( \frac{1}{8} \) + \( \frac{1}{8} \) + \( \frac{1}{8} \) + \( \frac{1}{8} \) + \( \frac{1}{8} \) = \( \frac{6}{8} \).
(c) HCF of 6 and 8 is 2: \( \frac{6 \div 2}{8 \div 2} \) = \( \frac{3}{4} \).
(d) Divide 0 to 1 into 8 equal parts and count 7 parts from 0. The red point is \( \frac{7}{8} \):

(e) Yes. Dividing the numerator and denominator of \( \frac{6}{8} \) by 2 gives \( \frac{3}{4} \). On strips of the same length, 6 of 8 equal parts covers the same length as 3 of 4 equal parts:

In simple words: One fold-part is one-eighth; six of them make six-eighths, which is the same as three-quarters.

Teacher's Note:
1. n times the unit fraction \( \frac{1}{d} \) is \( \frac{n}{d} \).
2. Equivalent fractions cover the same length of the same whole.
3. \( \frac{7}{8} \) is one part short of 1 on the number line.

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

Question 19. Case Study 1:
Radha and her three cousins visited a fair. They bought a large rectangular chikki and decided to share it equally. The shopkeeper cut the chikki into 12 equal parts, similar to the chikki division. Radha ate 3 parts, while each cousin ate 2 parts. After eating, they compared how much each one had eaten and tried converting their shares into fractional units. Radha wanted to know if she ate more than each cousin and if her share could be written in lowest terms. They also wanted to show their shares on a number line.
Based on the above, answer the following questions:
(a) Fraction of chikki Radha ate.
(b) Fraction each cousin ate.
(c) Who ate more?
(d) Express Radha’s fraction in lowest terms and mark it on a number line.
Answer:
The whole chikki has 12 equal parts, so each part is \( \frac{1}{12} \) of the chikki.
(a) Radha ate 3 parts: \( \frac{3}{12} \) of the chikki.
(b) Each cousin ate 2 parts: \( \frac{2}{12} \) (= \( \frac{1}{6} \)) of the chikki.
(c) Both fractions have denominator 12 and 3 > 2, so \( \frac{3}{12} \) > \( \frac{2}{12} \). Radha ate more than each cousin.
(d) \( \frac{3}{12} \) = \( \frac{3 \div 3}{12 \div 3} \) = \( \frac{1}{4} \). Divide 0 to 1 into 4 equal parts and mark the first point:

In simple words: Radha had 3 of the 12 pieces, which is one-quarter of the chikki, more than a cousin's 2 pieces.

Teacher's Note:
1. With the same denominator, the bigger numerator is the bigger fraction.
2. Together they ate 3 + 2 + 2 + 2 = 9 parts, so \( \frac{3}{12} \) of the chikki was left.

Question 20. Case Study 2:
A school canteen prepared fruit juice for 10 students. The flask had 5 glasses of juice. The teacher planned to distribute the juice equally, similar to the “sharing equally” activity. Later, 5 more students joined, and they again shared the same amount of juice equally. The teacher wanted students to compare the two fractions, understand equivalent fractions, and decide which group received more juice per student. They discussed whether increasing the number of children decreases each share.
(a) Fraction of a glass of juice per child in the first group.
(b) Fraction of a glass of juice per child in the second group.
(c) Which group gets more?
(d) Explain using equivalent fractions.
Answer:
(a) 5 glasses shared by 10 children: 5 ÷ 10 = \( \frac{5}{10} \) = \( \frac{1}{2} \) glass per child.
(b) 5 glasses shared by 10 + 5 = 15 children: 5 ÷ 15 = \( \frac{5}{15} \) = \( \frac{1}{3} \) glass per child.
(c) The first group (10 students) gets more per child.
(d) Write both with denominator 6: \( \frac{1}{2} \) = \( \frac{3}{6} \) and \( \frac{1}{3} \) = \( \frac{2}{6} \). Since 3 > 2, \( \frac{3}{6} \) > \( \frac{2}{6} \), so \( \frac{1}{2} \) > \( \frac{1}{3} \).
So when the same juice is shared by more children, each share becomes smaller.
In simple words: Half a glass each for 10 children, but only a third of a glass each for 15 children.

Teacher's Note:
1. Same amount, more sharers means a smaller share.
2. Equivalent fractions with a common denominator make comparison easy.