Simplifying Fractions (Grade 5)
Simplifying fractions (also called reducing fractions) means writing a fraction in its lowest terms by dividing both the numerator and denominator by their Highest Common Factor (HCF). A simplified fraction has no common factor other than 1 between its numerator and denominator.
For example, 12/18 can be simplified to 2/3 because both 12 and 18 are divisible by 6. The value of the fraction does not change — 12/18 and 2/3 represent the same amount.
What is Simplifying Fractions - Class 5 Maths (Fractions)?
A fraction is in its simplest form (or lowest terms) when the HCF of the numerator and denominator is 1. This means no number other than 1 divides both evenly.
Methods to simplify:
- Method 1 — HCF method: Find the HCF of numerator and denominator, then divide both by it.
- Method 2 — Step-by-step division: Keep dividing both by common factors (2, 3, 5...) until no common factor remains.
Simplifying Fractions (Grade 5) Formula
Simplified Fraction = Numerator ÷ HCF / Denominator ÷ HCF
Solved Examples
Example 1: Example 1: Simplify using HCF
Problem: Simplify 18/24.
Solution:
Step 1: Find HCF of 18 and 24. Factors of 18: 1,2,3,6,9,18. Factors of 24: 1,2,3,4,6,8,12,24. HCF = 6.
Step 2: Divide both by 6: 18÷6 / 24÷6 = 3/4.
Answer: 18/24 = 3/4
Example 2: Example 2: Step-by-step simplification
Problem: Simplify 36/48.
Solution:
Step 1: Both are even → divide by 2: 36/48 = 18/24
Step 2: Both are even → divide by 2: 18/24 = 9/12
Step 3: Both divisible by 3: 9/12 = 3/4
Step 4: HCF of 3 and 4 is 1. Done.
Answer: 36/48 = 3/4
Example 3: Example 3: Already in simplest form
Problem: Is 7/12 in its simplest form?
Solution:
Factors of 7: 1, 7 (prime number)
Factors of 12: 1, 2, 3, 4, 6, 12
HCF = 1. No common factor other than 1.
Answer: Yes, 7/12 is already in simplest form.
Example 4: Example 4: Simplifying a large fraction
Problem: Simplify 45/75.
Solution:
HCF of 45 and 75: Both divisible by 5 → 9/15. Both divisible by 3 → 3/5.
Or directly: HCF of 45 and 75 = 15. So 45÷15 / 75÷15 = 3/5.
Answer: 45/75 = 3/5
Example 5: Example 5: Simplifying after an operation
Problem: Add 1/6 + 1/4 and simplify.
Solution:
Step 1: LCM of 6 and 4 = 12
Step 2: 1/6 = 2/12, 1/4 = 3/12
Step 3: 2/12 + 3/12 = 5/12
Step 4: HCF of 5 and 12 = 1. Already simplified.
Answer: 5/12
Example 6: Example 6: Simplify an improper fraction
Problem: Simplify 28/8.
Solution:
Step 1: HCF of 28 and 8 = 4
Step 2: 28÷4 / 8÷4 = 7/2
Step 3: As a mixed fraction: 7/2 = 3 1/2
Answer: 28/8 = 7/2 = 3 1/2
Example 7: Example 7: Word problem — Recipe
Problem: A recipe needs 8/12 cup of sugar. Express this in simplest form.
Solution:
HCF of 8 and 12 = 4
8÷4 / 12÷4 = 2/3
Answer: The recipe needs 2/3 cup of sugar.
Example 8: Example 8: Multiple fractions to simplify
Problem: Simplify: 6/10, 15/25, 14/21.
Solution:
- 6/10: HCF = 2, so 3/5
- 15/25: HCF = 5, so 3/5
- 14/21: HCF = 7, so 2/3
Answer: 6/10 = 3/5, 15/25 = 3/5, 14/21 = 2/3
Notice: 6/10 and 15/25 are equivalent fractions (both simplify to 3/5).
Example 9: Example 9: Word problem — Exam marks
Problem: Aman scored 36 out of 48 in a test. Express his score as a fraction in simplest form.
Solution:
Score = 36/48. HCF of 36 and 48 = 12.
36÷12 / 48÷12 = 3/4
Answer: Aman scored 3/4 of the total marks.
Key Points to Remember
- A fraction is in simplest form when HCF of numerator and denominator is 1.
- To simplify: divide both numerator and denominator by their HCF.
- Alternatively, divide step by step using common factors (2, 3, 5, 7...).
- Simplifying does not change the value of a fraction — 6/8 and 3/4 are equal.
- If the numerator is a prime number and does not divide the denominator, the fraction is already in simplest form.
- Always simplify the final answer after performing operations on fractions.
- Equivalent fractions simplify to the same lowest-term fraction.
Practice Problems
- Simplify 24/36.
- Simplify 35/56.
- Is 11/15 in its simplest form? Explain.
- Simplify 42/63.
- Priya answered 30 out of 45 questions correctly. Express as a fraction in simplest form.
- Simplify the improper fraction 54/12 and write as a mixed fraction.
- Which of these fractions are equivalent: 4/6, 8/12, 6/10, 10/15?
- Simplify 72/96.
Frequently Asked Questions
Q1. What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their Highest Common Factor (HCF). The value remains the same — only the numbers become smaller and easier to work with.
Q2. How do I find the HCF to simplify a fraction?
List the factors of both numbers and find the largest one they share. For example, factors of 18 are 1,2,3,6,9,18 and factors of 24 are 1,2,3,4,6,8,12,24. The HCF is 6, so divide both by 6.
Q3. Can I simplify in multiple steps?
Yes. If you cannot immediately find the HCF, divide both by any common factor and repeat. For example, 48/72 → divide by 2 → 24/36 → divide by 2 → 12/18 → divide by 6 → 2/3. The result is the same as dividing by HCF (24) at once.
Q4. How do I know if a fraction is in simplest form?
A fraction is in simplest form when the only common factor of the numerator and denominator is 1. Quick check: if the numerator is prime and does not divide the denominator, the fraction is already simplified.
Q5. Does simplifying change the value of a fraction?
No. Simplifying only changes the way the fraction looks, not its value. 6/8 and 3/4 represent the same amount. They are equivalent fractions.
Q6. Why should I always simplify my answers?
Simplified fractions are easier to understand and compare. In exams, answers are usually expected in simplest form. It also helps avoid errors in further calculations.
Q7. Can I simplify before multiplying fractions?
Yes! This is called cancellation. When multiplying a/b × c/d, you can cancel common factors between any numerator and any denominator before multiplying. This keeps numbers small and makes calculation easier.
Q8. What if the numerator is larger than the denominator?
You can still simplify an improper fraction the same way. For example, 15/10 → HCF = 5 → 3/2. You can then convert to a mixed fraction: 1 1/2.
Related Topics
- Fractions Revision (Grade 5)
- HCF by Prime Factorisation
- 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)
