Chapter 7 Fractions from the Class 6 NCERT book introduces new concepts that are covered in this class. But, nothing to worry about as we have 21 questions selected for you to practice once you have completed the chapter in class. These questions are a bit challenging. If you are stuck somewhere, we have an answer key at the end with hints on how to solve the questions.
Class 6 Mathematics – Worksheet, Chapter 7: Fractions (NCERT) | Practice Set: Challenging
A. Fractional Units, Reading Fractions, and Basic Ideas
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In the fraction 5/6, write:
- (a) Numerator = ________
- (b) Denominator = ________
- (c) Fractional unit = ________
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Write each fraction as “numerator times (fractional unit)“:
- (a) 3/4 = ________ times ________
- (b) 7/10 = ________ times ________
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A whole roti is divided into 8 equal parts. Riya eats 5 parts.
- (a) What fraction of the roti did she eat?
- (b) Write it as “5 times 1/8”.
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Fill the table for 1/4 like a “times table” of a fractional unit:
1 × (1/4) = ____ , 2 × (1/4) = ____ , 3 × (1/4) = ____ , … , 9 × (1/4) = ____ -
You have a strip showing 1/3 of a unit. Without using a ruler,
explain how you can make 1/6 using this strip. (Write 2–3 lines.)
B. Fractions on the Number Line
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The distance from 0 to 1 is divided into 5 equal parts.
- (a) What fraction is one part?
- (b) Which point represents 3/5?
- (c) Write a fraction for the point just before 1.
- Write three fractions between 0 and 1 that have denominator 10.
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True or False (give one-line reason):
“There are only 9 fractions between 0 and 1.” -
Arrange in increasing order:
1/2, 3/10, 4/5, 7/10
C. Equivalent Fractions and Lowest Terms
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Make equivalent fractions with the given denominator:
- (a) 2/3 = ____/12
- (b) 5/6 = ____/24
- (c) 7/8 = ____/40
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Fill the blanks:
- (a) 3/4 = (3×___)/(4×___) = 15/___
- (b) 6/10 = 3/___ (reduce to lowest terms)
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Reduce to simplest form:
- (a) 12/18
- (b) 16/24
- (c) 21/35
D. Comparing Fractions (Using Same Fractional Unit)
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Compare using <, > or = :
- (a) 3/4 ____ 2/3
- (b) 5/8 ____ 7/12
- (c) 9/10 ____ 17/20
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Arrange in decreasing order:
5/6, 7/9, 3/4, 11/12
E. Mixed Fractions
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Convert to mixed fraction:
- (a) 13/4
- (b) 29/6
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Convert to improper fraction:
- (a) 3 1/5
- (b) 7 2/3
F. Addition and Subtraction (Brahmagupta’s Method)
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Add (same denominator):
- (a) 5/8 + 3/8
- (b) 7/9 + 1/9
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Subtract (same denominator):
- (a) 7/9 − 5/9
- (b) 10/27 − 1/27
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Add (different denominators) using common denominator:
- (a) 2/5 + 4/15
- (b) 1/6 + 3/8
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Subtract (different denominators) using common denominator:
- (a) 3/4 − 2/3
- (b) 8/15 − 1/6
G. Fraction Puzzle (From the Chapter)
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Find three different fractional units (unit fractions) that add up to 1.
Write one correct set and show the addition.
Class 6 Mathematics – Answer Key
A. Fractional Units, Reading Fractions, and Basic Ideas
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(a) Numerator = 5
(b) Denominator = 6
(c) Fractional unit = 1/6 -
(a) 3/4 = 3 times 1/4
(b) 7/10 = 7 times 1/10 -
(a) Fraction eaten = 5/8
(b) = 5 times 1/8 -
1×(1/4)=1/4, 2×(1/4)=2/4, 3×(1/4)=3/4, 4×(1/4)=1,
5×(1/4)=5/4, 6×(1/4)=6/4, 7×(1/4)=7/4, 8×(1/4)=2, 9×(1/4)=9/4 -
Fold the 1/3 strip into 2 equal parts. Each half becomes 1/6 of the whole.
(Because 1/3 divided into 2 equal parts gives 1/6.)
B. Fractions on the Number Line
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(a) One part = 1/5
(b) 3/5 is the third tick after 0 (0, 1/5, 2/5, 3/5, 4/5, 1)
(c) Just before 1 is 4/5 - Any three: 1/10, 3/10, 7/10 (many answers possible).
- False. There are infinitely many fractions between 0 and 1.
- Increasing order: 3/10 < 1/2 < 7/10 < 4/5
C. Equivalent Fractions and Lowest Terms
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(a) 2/3 = 8/12
(b) 5/6 = 20/24
(c) 7/8 = 35/40 -
(a) 3/4 = (3×5)/(4×5) = 15/20
(b) 6/10 = 3/5 -
(a) 12/18 = 2/3
(b) 16/24 = 2/3
(c) 21/35 = 3/5
D. Comparing Fractions
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(a) 3/4 > 2/3 (since 3/4 = 9/12 and 2/3 = 8/12)
(b) 5/8 > 7/12 (since 5/8 = 15/24 and 7/12 = 14/24)
(c) 9/10 > 17/20 (since 9/10 = 18/20) - Decreasing order: 11/12 > 5/6 > 7/9 > 3/4
E. Mixed Fractions
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(a) 13/4 = 3 1/4
(b) 29/6 = 4 5/6 -
(a) 3 1/5 = 16/5
(b) 7 2/3 = 23/3
F. Addition and Subtraction (Common Denominator)
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(a) 5/8 + 3/8 = 8/8 = 1
(b) 7/9 + 1/9 = 8/9 -
(a) 7/9 − 5/9 = 2/9
(b) 10/27 − 1/27 = 9/27 = 1/3 -
(a) 2/5 + 4/15 = 6/15 + 4/15 = 10/15 = 2/3
(b) 1/6 + 3/8 = 4/24 + 9/24 = 13/24 -
(a) 3/4 − 2/3 = 9/12 − 8/12 = 1/12
(b) 8/15 − 1/6 = 16/30 − 5/30 = 11/30
G. Fraction Puzzle
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One correct set is: 1/2 + 1/3 + 1/6 = 1
Because 1/2 = 3/6, 1/3 = 2/6, 1/6 = 1/6, so total = (3+2+1)/6 = 6/6 = 1.
