Equivalent Fractions (Grade 3)
Equivalent fractions are fractions that look different but represent the same amount. For example, 1/2 and 2/4 cover the same part of a whole — they are equivalent.
In Class 3, you learn to recognise equivalent fractions using pictures, and you start to see the pattern of multiplying or dividing both numerator and denominator by the same number.
What is Equivalent Fractions - Class 3 Maths (Fractions)?
Equivalent fractions are fractions that have the same value even though their numerators and denominators are different.
Multiply (or divide) the numerator and denominator by the SAME number to get an equivalent fraction.
Example: 1/2 = 2/4 = 3/6 = 4/8 (all equivalent to one-half).
Solved Examples
Example 1: Using Pictures
Question: Show that 1/2 and 2/4 are equivalent using shapes.
Think:
- Draw a rectangle, divide into 2 equal parts, shade 1 → 1/2.
- Draw the same rectangle, divide into 4 equal parts, shade 2 → 2/4.
- Both have the same amount shaded.
Answer: 1/2 = 2/4. They represent the same part of the whole.
Example 2: Multiply to Find Equivalent
Question: Find a fraction equivalent to 2/3 with denominator 9.
Think:
- 3 × 3 = 9 (denominator multiplied by 3)
- Multiply numerator by 3 too: 2 × 3 = 6
Answer: 2/3 = 6/9.
Example 3: Multiply to Find Equivalent — Another
Question: Write two fractions equivalent to 1/4.
Think:
- Multiply by 2: (1×2)/(4×2) = 2/8
- Multiply by 3: (1×3)/(4×3) = 3/12
Answer: 1/4 = 2/8 = 3/12.
Example 4: Divide to Simplify
Question: Is 4/8 equivalent to 1/2?
Think:
- Divide numerator and denominator by 4: (4÷4)/(8÷4) = 1/2
Answer: Yes, 4/8 = 1/2.
Example 5: Check Equivalence
Question: Are 3/5 and 6/10 equivalent?
Think:
- Multiply 3/5 by 2/2: (3×2)/(5×2) = 6/10
- They match!
Answer: Yes, 3/5 = 6/10.
Example 6: Not Equivalent
Question: Are 2/3 and 4/9 equivalent?
Think:
- 2/3 with denominator 9: (2×3)/(3×3) = 6/9
- 6/9 ≠ 4/9
Answer: No. 2/3 = 6/9, not 4/9.
Example 7: Word Problem
Question: Ria eats 2/6 of a cake. Meera eats 1/3 of the same cake. Did they eat the same amount?
Think:
- 1/3 = 2/6 (multiply by 2/2)
Answer: Yes, 2/6 = 1/3. They ate the same amount.
Example 8: Fill in the Missing Number
Question: 3/4 = ?/8. Find the missing number.
Think:
- 4 × 2 = 8 (denominator multiplied by 2)
- 3 × 2 = 6 (numerator also multiplied by 2)
Answer: 3/4 = 6/8.
Example 9: Visual Fraction Wall
Question: Using a fraction wall, name fractions equivalent to 1/2.
Think:
- Look at rows that line up exactly with the halfway mark: 2/4, 3/6, 4/8, 5/10.
Answer: 1/2 = 2/4 = 3/6 = 4/8 = 5/10.
Key Points to Remember
- Equivalent fractions show the same value with different numbers.
- Multiply both numerator and denominator by the same number to create an equivalent fraction.
- Divide both by the same number to simplify.
- Use pictures or fraction walls to verify equivalence visually.
- 1/2 = 2/4 = 3/6 = 4/8 — these all mean half.
- A fraction is in simplest form when you cannot divide both parts by the same number anymore.
Practice Problems
- Write two fractions equivalent to 1/3.
- Is 2/6 equivalent to 1/3? Show why.
- Fill in the blank: 2/5 = __/10.
- Are 3/4 and 9/12 equivalent?
- Simplify 6/8 to its simplest form.
- Dev says 1/2 and 3/5 are equivalent. Is he correct? Why?
- Find a fraction equivalent to 4/6 with denominator 3.
Frequently Asked Questions
Q1. What are equivalent fractions?
Equivalent fractions are fractions that represent the same amount of a whole but have different numerators and denominators. For example, 1/2 and 2/4 are equivalent.
Q2. How do I make an equivalent fraction?
Multiply (or divide) both the numerator and denominator by the same number. For example, 2/3 × 2/2 = 4/6.
Q3. How do I check if two fractions are equivalent?
Simplify both to their simplest form. If they are the same, they are equivalent. Or cross-multiply: if a/b and c/d are equivalent, then a × d = b × c.
Q4. What is the simplest form of a fraction?
The simplest form is when the numerator and denominator have no common factor other than 1. For example, 2/4 simplified is 1/2.
Q5. Can I use pictures to check equivalence?
Yes. Draw two identical shapes, divide them differently, shade the fractions, and see if the shaded areas match.
Q6. Are 2/3 and 3/2 equivalent?
No. 2/3 is less than 1, and 3/2 is greater than 1. They are not the same value.
Q7. How many equivalent fractions can a fraction have?
Infinitely many. You can keep multiplying by 2/2, 3/3, 4/4, and so on, to get new equivalent fractions.
Q8. Is this topic covered in NCERT Class 3?
Yes. NCERT Class 3 Maths introduces equivalent fractions through visual activities like paper folding and shading shapes.
