StudyOSStudyOS CBSE Study Material, Class 5–12

Fractions

NCERT Class 6 · Mathematics Based on NCERT Class 6 Mathematics textbook · Free CBSE study kit

Everything you need to ace this chapter, in one place.
Notes · Mind Map · Quiz · Assertion-Reason · Case Studies · Question Bank · Past Papers

Get Full Study Kit →
Studying with friends? Send them this chapter.

Chapter Notes

Overview
This chapter introduces the concept of fractions as equal shares of a whole. It explains fractional units, how to represent fractions on a number line, and how to compare, add, and subtract them. The one big idea a student must walk away with is that a fraction represents a part of a whole, and operations on fractions require a common denominator (same fractional unit).
Key Concepts (11)
Fraction
A number that represents a part of a whole or a part of a group, obtained when a whole number of things is shared equally among some number of people.
e.g. If one roti is divided equally between two children, each child gets half a roti, written as 1/2.
Fractional Unit (Unit Fraction)
When one whole unit is divided into several equal parts, each part is called a fractional unit. It has numerator 1.
e.g. 1/2, 1/3, 1/4, 1/5, 1/100 are all fractional units.
Numerator
The top number in a fraction that tells how many fractional units are taken.
e.g. In 5/6, 5 is the numerator.
Denominator
The bottom number in a fraction that tells into how many equal parts the whole is divided.
e.g. In 5/6, 6 is the denominator.
Mixed Fraction (Mixed Number)
A number that contains a whole number part and a fractional part that is less than 1.
e.g. 2 2/3 is a mixed fraction meaning 2 whole units and 2/3 of another unit.
Equivalent Fractions
Fractions that represent the same share or the same length on a number line, but are expressed using different fractional units.
e.g. 1/2 = 2/4 = 4/8 = 3/6 are all equivalent fractions.
Simplest Form (Lowest Terms)
A fraction is in its simplest form when its numerator and denominator have no common factor other than 1.
e.g. 4/5 is the simplest form of 16/20 because 4 and 5 have no common factor other than 1.
Comparing Fractions
Determining which fraction is greater or smaller by converting them to equivalent fractions with the same denominator, then comparing numerators.
e.g. To compare 4/5 and 7/9, convert to 36/45 and 35/45. Since 36 > 35, 4/5 > 7/9.
Brahmagupta's Method for Addition
Convert fractions to equivalent fractions with a common denominator, then add the numerators and keep the denominator the same.
e.g. 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
Brahmagupta's Method for Subtraction
Convert fractions to equivalent fractions with a common denominator, then subtract the numerators and keep the denominator the same.
e.g. 3/4 - 2/3 = 9/12 - 8/12 = 1/12.
Fraction Wall
A visual tool showing equivalent fractions by aligning strips of the same length divided into different numbers of equal parts.
e.g. The fraction wall shows that 1/2 = 2/4 = 4/8.
Formulas & Equations (6)
Fraction = Number of parts taken / Total number of equal parts
Reads as: Fraction equals number of parts taken divided by total number of equal parts
Variables: Numerator = number of parts taken; Denominator = total number of equal parts
Use when: Writing a fraction from a real-life sharing or division situation
⚠ Students often reverse numerator and denominator, e.g., writing 4/1 instead of 1/4 for one roti shared among 4 children.
To find equivalent fractions: Multiply or divide numerator and denominator by the same non-zero number.
Reads as: To find equivalent fractions, multiply or divide numerator and denominator by the same number
Variables: a/b = (a × k)/(b × k) = (a ÷ k)/(b ÷ k)
Use when: Finding equivalent fractions or simplifying fractions to lowest terms
⚠ Students multiply or divide only the numerator or only the denominator, not both.
To compare fractions: a/b and c/d → convert to (a×d)/(b×d) and (c×b)/(d×b), then compare numerators.
Reads as: To compare a over b and c over d, convert to a times d over b times d and c times b over d times b, then compare numerators
Variables: a, b, c, d are integers; b, d ≠ 0
Use when: Comparing any two fractions with different denominators
⚠ Students compare numerators directly without making denominators equal, e.g., saying 4/5 > 7/9 because 4 > 7 is wrong.
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Reads as: a over b plus c over d equals a times d plus c times b over b times d
Variables: a, b, c, d are integers; b, d ≠ 0
Use when: Adding two fractions with different denominators
⚠ Students add numerators and denominators directly, e.g., 1/4 + 1/3 = 2/7 instead of 7/12.
Subtraction: a/b - c/d = (a×d - c×b) / (b×d)
Reads as: a over b minus c over d equals a times d minus c times b over b times d
Variables: a, b, c, d are integers; b, d ≠ 0
Use when: Subtracting one fraction from another with different denominators
⚠ Students subtract numerators and denominators directly, e.g., 3/4 - 2/3 = 1/1 instead of 1/12.
Mixed fraction to improper fraction: Whole × Denominator + Numerator over Denominator
Reads as: Whole number times denominator plus numerator, all over denominator
Variables: Whole = whole number part; Numerator = numerator of fractional part; Denominator = denominator of fractional part
Use when: Converting a mixed number to an improper fraction for addition or subtraction
⚠ Students forget to multiply the whole number by the denominator, e.g., 3 1/4 becomes 4/4 instead of 13/4.
How It Works
Finding equivalent fractions using a fraction wall
  1. Take a strip of paper as one unit.
  2. Fold it into equal parts to create fractional units (e.g., halves, quarters, eighths).
  3. Compare lengths: e.g., 1/2 aligns with 2/4 and 4/8, showing they are equal.
  4. Conclude that fractions representing the same length are equivalent.
💡 Equivalent fractions have different numerators and denominators but represent the same value.
Comparing two fractions with different denominators
  1. Find a common denominator (e.g., product of the two denominators).
  2. Convert each fraction to an equivalent fraction with that common denominator.
  3. Compare the numerators of the equivalent fractions.
  4. The fraction with the larger numerator is greater.
💡 Never compare fractions directly without making denominators equal first.
Adding fractions with different denominators (Brahmagupta's method)
  1. Find a common denominator (e.g., LCM or product of denominators).
  2. Convert each fraction to an equivalent fraction with that denominator.
  3. Add the numerators of the equivalent fractions.
  4. Keep the common denominator.
  5. Simplify the result to lowest terms if possible.
💡 Only add numerators after denominators are made equal. Never add denominators.
Subtracting fractions with different denominators (Brahmagupta's method)
  1. Find a common denominator (e.g., LCM or product of denominators).
  2. Convert each fraction to an equivalent fraction with that denominator.
  3. Subtract the numerators of the equivalent fractions.
  4. Keep the common denominator.
  5. Simplify the result to lowest terms if possible.
💡 Only subtract numerators after denominators are made equal. Never subtract denominators.
Expressing a fraction in lowest terms (simplest form)
  1. Find the highest common factor (HCF) of the numerator and denominator.
  2. Divide both numerator and denominator by the HCF.
  3. The resulting fraction has no common factor other than 1.
💡 You can also simplify step by step by dividing by common factors repeatedly.
Converting a mixed number to an improper fraction
  1. Multiply the whole number part by the denominator.
  2. Add the numerator to this product.
  3. Write the result over the original denominator.
💡 The denominator stays the same; only the numerator changes.
Exam Traps — Don't Make These Mistakes
⚠ Thinking 1/9 is greater than 1/5 because 9 > 5
✗ 1/9 > 1/5 because 9 is bigger than 5.
→ For unit fractions, the larger the denominator, the smaller the fraction because the whole is divided into more parts.
✓ 1/9 < 1/5 because when sharing one roti among more children, each child gets a smaller share.
⚠ Adding fractions by adding numerators and denominators directly
✗ 1/4 + 1/3 = 2/7
→ You cannot add denominators directly. Fractions must first be converted to equivalent fractions with a common denominator.
✓ 1/4 + 1/3 = 3/12 + 4/12 = 7/12
⚠ Subtracting fractions by subtracting numerators and denominators directly
✗ 3/4 - 2/3 = 1/1
→ You cannot subtract denominators directly. Fractions must first be converted to equivalent fractions with a common denominator.
✓ 3/4 - 2/3 = 9/12 - 8/12 = 1/12
⚠ Comparing fractions by comparing numerators only
✗ 4/5 > 7/9 because 4 > 7 is false, but some write 7/9 > 4/5 because 7 > 4.
→ You cannot compare numerators directly unless denominators are equal. Convert to common denominator first.
✓ 4/5 = 36/45, 7/9 = 35/45. Since 36/45 > 35/45, 4/5 > 7/9.
⚠ Forgetting to simplify the final answer
✗ 3/6 as final answer for 1/6 + 1/3
→ 3/6 can be simplified further because 3 and 6 have a common factor of 3.
✓ 3/6 = 1/2 after dividing numerator and denominator by 3.
⚠ Confusing numerator and denominator when writing a fraction from a word problem
✗ 4/1 for one roti shared among 4 children
→ The denominator should be the number of equal parts (4), and numerator should be the number of parts taken (1).
✓ Each child gets 1/4 roti.
Compare & Contrast
Numerator value
Fractional Unit (Unit Fraction)
General Fraction
A fractional unit always has numerator 1 (e.g., 1/2, 1/3). A general fraction can have any numerator (e.g., 3/4, 5/6).
Comparison of numerator and denominator
Proper Fraction
Improper Fraction
In a proper fraction, numerator is less than denominator (e.g., 3/4, value < 1). In an improper fraction, numerator is greater than or equal to denominator (e.g., 5/2, value ≥ 1).
Exam Focus
Marks pattern: 2 MCQs (1 mark each), 1 SA (3 marks) on comparing or adding fractions, 1 LA (5 marks) on word problems involving addition/subtraction of fractions
Most asked: Identifying and writing fractions from real-life situations · Comparing fractions using common denominator · Addition and subtraction of fractions (like and unlike denominators) · Converting between mixed numbers and improper fractions · Finding equivalent fractions and simplifying to lowest terms
Don't skip: Word problems involving addition or subtraction of fractions with different denominators; Comparing two fractions and justifying the answer
One-Line Revision (read aloud before the exam)
  1. A fraction represents a part of a whole, written as numerator/denominator.
  2. A unit fraction has numerator 1, e.g., 1/2, 1/3.
  3. The larger the denominator in a unit fraction, the smaller the value.
  4. Equivalent fractions represent the same value, e.g., 1/2 = 2/4 = 4/8.
  5. To compare fractions, convert them to a common denominator first.
  6. To add or subtract fractions, first make denominators equal, then add or subtract numerators.
  7. A mixed number has a whole part and a fractional part, e.g., 2 2/3.
  8. To convert a mixed number to an improper fraction: multiply whole by denominator, add numerator, write over denominator.
  9. A fraction is in simplest form when numerator and denominator have no common factor other than 1.
  10. Brahmagupta's method: for addition/subtraction, find common denominator, then operate on numerators.
  11. Fractions greater than 1 have numerator larger than denominator.
  12. Fractions less than 1 have numerator smaller than denominator.
  13. A fraction wall visually shows equivalent fractions.
  14. When sharing equally, the number of shares is the denominator, and each share is a unit fraction.
  15. Always simplify your final answer to lowest terms.

MCQs — 10 Questions with Answers

Q1. If 1 roti is shared equally among 4 children, how much roti will each child get?

  • A. 1/4 roti ✓
  • B. 1/2 roti
  • C. 4/1 roti
  • D. 1/5 roti

Answer: A — When 1 roti is divided equally among 4 children, each child's share is 1/4 roti.

Q2. In the fraction 7/9, what does the number 7 represent?

  • A. Total number of equal parts
  • B. Number of parts we take ✓
  • C. How many children share the roti
  • D. The whole amount

Answer: B — The top number (numerator) tells us how many equal parts we take, so 7 represents the parts we take.

Q3. Which fraction is greater: 1/6 or 1/10?

  • A. 1/10
  • B. 1/6 ✓
  • C. Both are equal
  • D. Cannot be compared

Answer: B — 1/6 is greater because when 1 roti is shared among 6 children instead of 10, each child gets a larger piece.

Q4. If a paper strip is folded into 8 equal parts and you take 3 parts, what fraction do you have?

  • A. 8/3
  • B. 3/8 ✓
  • C. 1/8
  • D. 5/8

Answer: B — When you take 3 parts out of 8 equal parts, the fraction is 3/8 (numerator 3, denominator 8).

Q5. A wholesale merchant packed 1 kg of rice equally in 5 packets. What is the weight of each packet?

  • A. 1/5 kg ✓
  • B. 1/4 kg
  • C. 5/1 kg
  • D. 2/5 kg

Answer: A — When 1 kg is divided equally into 5 packets, each packet weighs 1/5 kg.

Q6. What is 5 times 1/3?

  • A. 1/3
  • B. 5/3 ✓
  • C. 3/5
  • D. 1/5

Answer: B — Multiplying the fractional unit: 5 times 1/3 = 5/3.

Q7. Look at a number line from 0 to 1 divided into 4 equal parts. What is the length of the blue line marked from 0 to the second division mark?

  • A. 1/4
  • B. 2/4 ✓
  • C. 3/4
  • D. 4/4

Answer: B — The blue line covers 2 divisions out of 4, so its length is 2/4.

Q8. Which of these is a fractional unit?

  • A. 2/5
  • B. 3/7
  • C. 1/8 ✓
  • D. 4/9

Answer: C — A fractional unit (unit fraction) has 1 as the numerator, so 1/8 is a fractional unit.

Q9. Three friends ordered 2 glasses of sugarcane juice and shared equally. How much did each friend drink?

  • A. 1/3 glass
  • B. 2/3 glass ✓
  • C. 3/2 glass
  • D. 1/2 glass

Answer: B — When 2 glasses are shared equally among 3 friends, each friend gets 2/3 glass.

Q10. The big fish weighs 1/2 kg and the small fish weighs 1/4 kg. Together, they weigh ____ kg.

  • A. 1/6 kg
  • B. 2/4 kg
  • C. 3/4 kg ✓
  • D. 1 kg

Answer: C — 1/2 kg + 1/4 kg = 2/4 kg + 1/4 kg = 3/4 kg.

Flashcards

What is a fraction?

A fraction shows how much each person gets when one whole thing is divided equally among several people.

What is a fractional unit or unit fraction?

A fractional unit is one equal part of a whole, written as 1/n, such as 1/2, 1/3, 1/4, 1/5, etc.

In the fraction 5/8, what is the numerator and what is the denominator?

5 is the numerator (how many parts we take) and 8 is the denominator (total equal parts in the whole).

Which is bigger: 1/5 or 1/9?

1/5 is bigger because if you share 1 roti among 5 children instead of 9, each child gets a larger piece.

If one roti is shared equally among 3 children, how much does each child get?

Each child gets 1/3 roti.

What does 4 times 1/6 equal?

4 times 1/6 equals 4/6.

How do you read the fraction 3/4?

You can read it as 'three quarters' or 'three upon four' or '3 times 1/4.'

If you fold a paper strip into 4 equal parts, what fractional unit does each part represent?

Each part represents 1/4 of the whole paper strip.

Two guavas together weigh 1 kg and are the same size. How much does each guava weigh?

Each guava weighs 1/2 kg.

On a number line from 0 to 1, if the distance is divided into 6 equal parts, what is the length of one part?

The length of one part is 1/6 unit.

Important Board Questions

What is meant by a fractional unit? Give one example. [1 mark]

A fractional unit is one equal part of a whole, written as 1/n. Example: 1/3 means one part when a whole is divided into 3 equal parts.

If one pizza is divided equally among 6 friends, how much pizza does each friend get? Write the answer as a fraction. [2 marks]

When 1 whole is shared equally among 6 people, each person's share is 1 ÷ 6. Express this as a fraction with numerator 1 and denominator 6.

Four friends ordered 3 glasses of juice and shared equally. Using the concept of fractional units, explain how much juice each friend drank. Show your working. [3 marks]

3 glasses ÷ 4 friends means 3 fractional units of 1/4 glass each. Write as: 3 times 1/4 = 3/4 glass per friend. Explain why the numerator is 3 (glasses) and denominator is 4 (friends).

On a number line from 0 to 1, show how you would mark the fractions 1/5, 2/5, 3/5, and 4/5. Draw and label the number line clearly. Explain why you divided the distance between 0 and 1 into 5 equal parts. [5 marks]

Divide the distance from 0 to 1 into 5 equal parts (because denominator is 5). Each part is 1/5. Mark the first mark at 1/5, second at 2/5, third at 3/5, fourth at 4/5. Explain: the denominator tells us how many equal divisions to make; the numerator tells us which division to mark.

True or False: 1/100 is larger than 1/10. Give a reason for your answer. [2 marks]

False. When the numerator is 1, a larger denominator means the whole is cut into more pieces, so each piece is smaller. Since 100 > 10, each piece of 1/100 is much smaller than each piece of 1/10.

Assertion-Reason Questions for Fractions

Q1. Assertion (A):

The fraction 1/8 is smaller than the fraction 1/5.

Reason (R):

When a whole is divided into more equal parts, each part becomes smaller.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true. When 1 whole is divided into 8 parts (1/8), each part is smaller than when divided into 5 parts (1/5). The reason correctly explains why 1/8 < 1/5.

Q2. Assertion (A):

The fraction 3/4 can be read as '3 times 1/4'.

Reason (R):

The denominator tells us the fractional unit, and the numerator tells us how many times we have that unit.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both assertion and reason are true and correctly connected. 3/4 = 3 × (1/4), where 1/4 is the fractional unit and we have 3 of them. The reason perfectly explains the assertion.

Q3. Assertion (A):

If you fold a paper strip in half once, each part will be 1/4 of the original strip.

Reason (R):

Folding a paper strip in half creates two equal parts.

Answer: D — A is false but R is true — The assertion is false—folding once creates 1/2, not 1/4. You need to fold twice to get 1/4 parts. The reason is true (folding once does create two parts), but it doesn't match the false assertion, so the answer is C.

Unlock more Assertion-Reason questions in Premium — unlock →

Case-Based Questions (CBQ) for Fractions

Case Study:

Meena's mother made a delicious sweet called barfi for Diwali. She cut the whole barfi into 8 equal pieces. Meena ate 2 pieces, her brother ate 3 pieces, and they gave 2 pieces to their grandmother. The remaining piece was kept for their father.

Q1. What fraction of the barfi did Meena eat?

  • A. 2/8 ✓
  • B. 3/8
  • C. 2/6
  • D. 1/8

Answer: A

Q2. What fraction of the barfi did Meena and her brother eat together?

  • A. 2/8
  • B. 3/8
  • C. 5/8 ✓
  • D. 8/8

Answer: C

Q3. What fraction of the barfi was left for their father?

  • A. 1/8 ✓
  • B. 2/8
  • C. 3/8
  • D. 4/8

Answer: A

Unlock more case studies in Premium — unlock →

Next chapterPlaying with Constructions →
Found this useful? Share it with your class group.

You've seen the free preview. Open the full interactive study kit — mind map, instant-graded quiz, progress tracking — free, no sign-in required.

Open Full Study Kit — Free →

Premium unlocks the full Question Bank, Daily Practice Papers, Chapter Quiz and Full Mock Papers for every chapter.