Simplifying Fractions
Simplifying fractions means reducing a fraction to its simplest form (also called lowest terms). A fraction is in its simplest form when the numerator and denominator have no common factor other than 1.
For example, 6/8 can be simplified to 3/4 by dividing both numerator and denominator by 2.
What is Simplifying Fractions - Class 4 Maths (Fractions)?
A fraction is in its simplest form (or lowest terms) when the HCF of the numerator and denominator is 1. To simplify a fraction, divide both the numerator and denominator by their HCF.
Simplified Fraction = Numerator ÷ HCF / Denominator ÷ HCF
Solved Examples
Example 1: Example 1: Simplify by Dividing by HCF
Problem: Simplify 8/12.
Solution:
Step 1: Find HCF of 8 and 12. Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. HCF = 4.
Step 2: Divide both by 4: 8÷4 = 2, 12÷4 = 3.
Answer: 8/12 = 2/3
Example 2: Example 2: Simplify a Fraction
Problem: Simplify 15/25.
Solution:
Step 1: HCF of 15 and 25. Factors of 15: 1, 3, 5, 15. Factors of 25: 1, 5, 25. HCF = 5.
Step 2: Divide: 15÷5 = 3, 25÷5 = 5.
Answer: 15/25 = 3/5
Example 3: Example 3: Already in Simplest Form
Problem: Simplify 7/10.
Solution:
Step 1: Factors of 7: 1, 7. Factors of 10: 1, 2, 5, 10.
Step 2: HCF = 1 (no common factor other than 1).
Answer: 7/10 is already in simplest form.
Example 4: Example 4: Step-by-Step Division
Problem: Simplify 24/36.
Solution:
Method (Step-by-step):
24/36 → divide both by 2 → 12/18
12/18 → divide both by 2 → 6/9
6/9 → divide both by 3 → 2/3
Answer: 24/36 = 2/3
Alternatively, HCF of 24 and 36 = 12. So 24÷12 / 36÷12 = 2/3 (in one step).
Example 5: Example 5: Simplify a Large Fraction
Problem: Simplify 18/27.
Solution:
Step 1: HCF of 18 and 27 = 9.
Step 2: 18÷9 = 2, 27÷9 = 3.
Answer: 18/27 = 2/3
Example 6: Example 6: Simplify to Check Equivalence
Problem: Are 6/10 and 9/15 equivalent? Simplify both to check.
Solution:
Step 1: Simplify 6/10: HCF(6,10) = 2 → 6÷2 / 10÷2 = 3/5.
Step 2: Simplify 9/15: HCF(9,15) = 3 → 9÷3 / 15÷3 = 3/5.
Step 3: Both simplify to 3/5.
Answer: Yes, 6/10 and 9/15 are equivalent (both = 3/5).
Example 7: Example 7: Word Problem
Problem: Aditi scored 16 out of 20 in a test. Express her score as a fraction in simplest form.
Solution:
Step 1: Fraction = 16/20.
Step 2: HCF of 16 and 20 = 4.
Step 3: 16÷4 = 4, 20÷4 = 5.
Answer: Aditi scored 4/5 in the test.
Example 8: Example 8: Simplify by Common Factor
Problem: Simplify 14/21.
Solution:
Step 1: Both 14 and 21 are divisible by 7.
Step 2: 14÷7 = 2, 21÷7 = 3.
Answer: 14/21 = 2/3
Example 9: Example 9: Word Problem
Problem: A ribbon is 12 cm long. Meera cut 8 cm from it. What fraction of the ribbon did she cut? Write in simplest form.
Solution:
Step 1: Fraction cut = 8/12.
Step 2: HCF of 8 and 12 = 4.
Step 3: 8÷4 = 2, 12÷4 = 3.
Answer: Meera cut 2/3 of the ribbon.
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.
- You can also simplify step-by-step by dividing by any common factor repeatedly.
- Simplifying does not change the value of the fraction.
- If no common factor exists (other than 1), the fraction is already in simplest form.
- Simplifying fractions makes them easier to compare, add, and subtract.
Practice Problems
- Simplify 10/15.
- Simplify 20/28.
- Is 5/9 in its simplest form? Explain.
- Simplify 30/45.
- Rahul got 12 out of 18 questions correct. Express as a fraction in simplest form.
- Simplify 36/48 using step-by-step division.
- Priya says 4/6 and 6/9 are the same. Is she right? Simplify both to check.
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 simplified fraction has the same value as the original.
Q2. How do you know if a fraction is in simplest form?
A fraction is in simplest form when the numerator and denominator share no common factor other than 1. In other words, their HCF is 1.
Q3. Does simplifying change the value of the fraction?
No. Simplifying produces an equivalent fraction with smaller numbers. For example, 6/8 and 3/4 represent the same value.
Q4. Can you simplify a fraction in multiple steps?
Yes. You can divide by any common factor repeatedly until no common factor remains. For example, 12/18 -> 6/9 -> 2/3. The result is the same as dividing by the HCF directly.
Q5. What if the numerator and denominator are the same?
If numerator = denominator, the fraction equals 1. For example, 5/5 = 1. In simplest form, it is written as 1.
Q6. Can an improper fraction be simplified?
Yes. Simplify the same way by dividing both parts by their HCF. For example, 9/6: HCF = 3, so 9/6 = 3/2.
Q7. Why is simplifying fractions useful?
Simplified fractions are easier to understand, compare, and use in calculations. It is also the standard way to express final answers in maths.
Q8. Is 1 the simplest form of all fractions where numerator equals denominator?
Yes. Any fraction like 4/4, 7/7, or 100/100 equals 1. They are all equivalent and simplify to 1.
Q9. Is simplifying fractions in the NCERT Class 4 syllabus?
Yes. Simplifying fractions is taught in Class 4 under the Fractions chapter. Students learn to use the HCF to reduce fractions to their lowest terms.
Related Topics
- Equivalent Fractions (Grade 4)
- Comparing Fractions (Grade 4)
- Fractions (Grade 4)
- Ordering Fractions
- Addition of Fractions (Grade 4)
- Subtraction of Fractions (Grade 4)
- Mixed Numbers and Improper Fractions
- Fraction Word Problems (Grade 4)
- Fractions on a Number Line (Grade 4)
- Proper and Improper Fractions
- Fraction of a Number (Grade 4)
