Fractions Revision (Grade 5)
Fractions revision in Class 5 consolidates everything students learned about fractions in earlier grades — types of fractions, equivalent fractions, comparing fractions, and converting between mixed numbers and improper fractions.
A strong revision of these basics is essential before moving to operations with unlike fractions, which form the core of Grade 5 fraction work.
In Classes 3 and 4, students were introduced to fractions as parts of a whole, learned to identify like and unlike fractions, and practised adding and subtracting like fractions. Before Class 5 takes fractions to the next level (adding/subtracting unlike fractions, multiplying fractions), this revision ensures every student has a solid foundation.
What this revision covers:
- Types of fractions: proper, improper, mixed, unit, like, and unlike
- Converting between mixed numbers and improper fractions
- Finding equivalent fractions
- Simplifying fractions to lowest terms
- Comparing and ordering fractions
- Finding a fraction of a number
What is Fractions Revision - Class 5 Maths (Fractions)?
A fraction represents a part of a whole. It is written as:
Numerator / Denominator
Numerator = number of parts taken
Denominator = total equal parts the whole is divided into
- Proper fraction: Numerator < Denominator (e.g., 3/7). Value is less than 1.
- Improper fraction: Numerator ≥ Denominator (e.g., 9/4). Value is 1 or more.
- Mixed number: A whole number + a proper fraction (e.g., 2 1/4). Represents a value greater than 1.
- Unit fraction: Numerator is 1 (e.g., 1/5, 1/8).
- Like fractions: Same denominator (e.g., 2/9 and 5/9).
- Unlike fractions: Different denominators (e.g., 3/4 and 5/6).
Fractions Revision (Grade 5) Formula
Mixed to Improper: a b/c = (a × c + b) / c
Improper to Mixed: Divide numerator by denominator.
Quotient = whole part, Remainder = numerator of fraction part.
Equivalent Fractions: a/b = (a × n) / (b × n) for any non-zero n
Types and Properties
Two fractions are equivalent if they represent the same value. Multiply or divide both numerator and denominator by the same number.
- 1/2 = 2/4 = 3/6 = 4/8 = 5/10
- 2/3 = 4/6 = 6/9 = 8/12
Simplest Form (Lowest Terms):
A fraction is in simplest form when the numerator and denominator have no common factor other than 1 (they are co-prime). Divide both by their HCF.
- 12/18: HCF = 6, so 12/18 = 2/3
- Like fractions (same denominator): Compare numerators. Larger numerator = larger fraction.
- Unlike fractions: Convert to like fractions using LCM of denominators, then compare.
- Cross multiplication: Compare a/b and c/d by checking a × d vs c × b.
Solved Examples
Example 1: Example 1: Identifying Fraction Types
Problem: Classify each fraction as proper, improper, or mixed: 5/8, 11/4, 3 2/5, 7/7.
Solution:
- 5/8: Numerator (5) < Denominator (8) → Proper fraction
- 11/4: Numerator (11) > Denominator (4) → Improper fraction
- 3 2/5: Has a whole number part (3) and a fraction part (2/5) → Mixed number
- 7/7: Numerator = Denominator → Improper fraction (equal to 1)
Example 2: Example 2: Converting Mixed to Improper
Problem: Convert 4 3/7 to an improper fraction.
Solution:
Step 1: Multiply whole number by denominator: 4 × 7 = 28
Step 2: Add the numerator: 28 + 3 = 31
Step 3: Write over the same denominator: 31/7
Answer: 4 3/7 = 31/7
Example 3: Example 3: Converting Improper to Mixed
Problem: Convert 23/5 to a mixed number.
Solution:
Step 1: Divide: 23 ÷ 5 = 4 remainder 3
Step 2: Quotient = 4 (whole part), Remainder = 3 (numerator)
Step 3: Mixed number = 4 3/5
Answer: 23/5 = 4 3/5
Example 4: Example 4: Finding Equivalent Fractions
Problem: Write three equivalent fractions for 3/4.
Solution:
Step 1: Multiply numerator and denominator by 2: (3×2)/(4×2) = 6/8
Step 2: Multiply by 3: (3×3)/(4×3) = 9/12
Step 3: Multiply by 5: (3×5)/(4×5) = 15/20
Answer: Three equivalent fractions of 3/4 are 6/8, 9/12, and 15/20.
Example 5: Example 5: Simplifying a Fraction
Problem: Simplify 36/48 to its lowest terms.
Solution:
Step 1: Find HCF of 36 and 48.
36 = 2 × 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3
HCF = 2 × 2 × 3 = 12
Step 2: Divide both by HCF: 36 ÷ 12 = 3; 48 ÷ 12 = 4
Answer: 36/48 in simplest form = 3/4
Example 6: Example 6: Comparing Unlike Fractions
Problem: Which is greater: 3/5 or 4/7?
Solution:
Method: Cross multiplication
Step 1: Cross multiply: 3 × 7 = 21 and 4 × 5 = 20
Step 2: Compare: 21 > 20
Step 3: Since 3 × 7 > 4 × 5, we get 3/5 > 4/7.
Answer: 3/5 is greater than 4/7.
Example 7: Example 7: Ordering Fractions
Problem: Arrange in ascending order: 2/3, 5/8, 7/12.
Solution:
Step 1: LCM of 3, 8, 12 = 24.
Step 2: Convert to like fractions:
- 2/3 = (2 × 8)/(3 × 8) = 16/24
- 5/8 = (5 × 3)/(8 × 3) = 15/24
- 7/12 = (7 × 2)/(12 × 2) = 14/24
Step 3: Order: 14/24 < 15/24 < 16/24
Answer: Ascending order: 7/12 < 5/8 < 2/3
Example 8: Example 8: Word Problem
Problem: Neha ate 3/8 of a pizza. Ria ate 2/8 of the same pizza. Who ate more? What fraction of the pizza is left?
Solution:
Step 1: These are like fractions (same denominator 8).
Step 2: Compare: 3/8 > 2/8 → Neha ate more.
Step 3: Total eaten = 3/8 + 2/8 = 5/8
Step 4: Left = 1 − 5/8 = 8/8 − 5/8 = 3/8
Answer: Neha ate more. 3/8 of the pizza is left.
Example 9: Example 9: Finding a Fraction of a Number
Problem: Aman has ₹240. He spends 3/4 of it on books. How much did he spend?
Solution:
Step 1: 3/4 of 240 = (3 × 240) / 4
Step 2: 240 ÷ 4 = 60
Step 3: 60 × 3 = 180
Answer: Aman spent ₹180 on books.
Example 10: Example 10: Checking Equivalence
Problem: Are 4/6 and 14/21 equivalent fractions?
Solution:
Step 1: Simplify 4/6: HCF(4, 6) = 2; 4/6 = 2/3
Step 2: Simplify 14/21: HCF(14, 21) = 7; 14/21 = 2/3
Step 3: Both simplify to 2/3.
Answer: Yes, 4/6 and 14/21 are equivalent fractions.
Real-World Applications
Where fractions appear in daily life:
- Cooking: Measuring ingredients — "add 3/4 cup of rice"
- Time: Half an hour (1/2), quarter of an hour (1/4)
- Money: Splitting bills, calculating discounts (e.g., 1/4 off = 25% discount)
- Sharing: Dividing food equally — "each person gets 2/5 of the cake"
- Measurement: Reading rulers marked in fractions of a centimetre
Key Points to Remember
- A fraction = numerator / denominator, representing parts of a whole.
- Proper fraction: numerator < denominator (value < 1).
- Improper fraction: numerator ≥ denominator (value ≥ 1).
- Mixed number = whole number + proper fraction.
- To convert mixed to improper: (whole × denominator + numerator) / denominator.
- To convert improper to mixed: divide numerator by denominator; quotient is whole, remainder is new numerator.
- Equivalent fractions: multiply or divide numerator and denominator by the same number.
- Simplest form: divide numerator and denominator by their HCF.
- To compare unlike fractions: convert to like fractions using LCM, or use cross multiplication.
Practice Problems
- Classify these fractions as proper, improper, or mixed: 7/3, 2/9, 5 1/6, 12/12.
- Convert 5 2/3 to an improper fraction.
- Convert 37/8 to a mixed number.
- Write four equivalent fractions for 5/6.
- Simplify 42/56 to its lowest terms.
- Arrange in descending order: 3/4, 5/6, 7/8.
- Priya drank 2/5 of a litre of milk in the morning and 1/5 at night. What fraction did she drink in total? What fraction is left?
- Dev has ₹500. He gives 3/5 to his sister. How much does his sister get?
Frequently Asked Questions
Q1. What is the difference between a proper and an improper fraction?
In a proper fraction, the numerator is less than the denominator (e.g., 3/5), so the value is less than 1. In an improper fraction, the numerator is greater than or equal to the denominator (e.g., 7/4), so the value is 1 or more.
Q2. How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and write the result over the same denominator. For example, 3 2/5 = (3 × 5 + 2)/5 = 17/5.
Q3. What are equivalent fractions?
Equivalent fractions represent the same value but have different numerators and denominators. You get them by multiplying or dividing both parts by the same number. For example, 1/2 = 2/4 = 3/6.
Q4. How do I simplify a fraction?
Find the HCF of the numerator and denominator, then divide both by the HCF. For example, 18/24: HCF is 6, so 18/24 = 3/4.
Q5. How do I compare fractions with different denominators?
Convert them to like fractions by finding the LCM of the denominators. Then compare the numerators. Alternatively, use cross multiplication: for a/b and c/d, compare a × d with c × b.
Q6. What is a unit fraction?
A unit fraction has 1 as its numerator. Examples: 1/2, 1/3, 1/7, 1/10. Unit fractions are the building blocks of all fractions — 3/5 is just 1/5 taken 3 times.
Q7. Why is 0 not allowed as a denominator?
Division by 0 is undefined in mathematics. A fraction means dividing into equal parts, and you cannot divide something into 0 parts. So the denominator must always be a non-zero number.
Q8. What is the fraction of a whole?
A whole is represented as a fraction where the numerator equals the denominator: 3/3 = 1, 8/8 = 1, 100/100 = 1. Any fraction equal to 1 represents one whole.
Q9. Is this revision important for Class 5?
Yes. Class 5 introduces operations with unlike fractions and mixed numbers, which require a solid understanding of equivalent fractions, simplification, and comparison. This revision ensures students are ready.
Related Topics
- Fractions (Grade 4)
- Adding Unlike Fractions
- Subtracting Unlike Fractions
- Adding Mixed Numbers
- Subtracting Mixed Numbers
- Multiplying Fractions
- Multiplying a Fraction by a Whole Number
- Fraction of a Number
- Reciprocal of a Fraction
- Dividing Fractions
- Fraction Word Problems (Grade 5)
- Proper, Improper and Mixed Fractions
