Equivalent Fractions (Grade 4)
Equivalent fractions are fractions that look different but represent the same value. For example, 1/2 and 2/4 are equivalent because both represent the same part of a whole.
You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number.
What is Equivalent Fractions - Class 4 Maths (Fractions)?
Equivalent fractions are two or more fractions that have the same value, even though they have different numerators and denominators.
a/b = (a × n) / (b × n) — multiply both by the same number
a/b = (a ÷ n) / (b ÷ n) — divide both by the same number
Example: 1/3 = 2/6 = 3/9 = 4/12 (all equivalent)
Solved Examples
Example 1: Example 1: Generate Equivalent Fractions by Multiplying
Problem: Write 3 equivalent fractions of 2/5.
Solution:
Step 1: Multiply numerator and denominator by 2: (2×2)/(5×2) = 4/10
Step 2: Multiply by 3: (2×3)/(5×3) = 6/15
Step 3: Multiply by 4: (2×4)/(5×4) = 8/20
Answer: 2/5 = 4/10 = 6/15 = 8/20
Example 2: Example 2: Check if Fractions Are Equivalent
Problem: Are 3/4 and 9/12 equivalent?
Solution:
Method 1 (Cross multiply): 3 × 12 = 36 and 4 × 9 = 36. Since both are equal, the fractions are equivalent.
Method 2: 3/4 × 3/3 = 9/12. Yes, multiplying both by 3 gives 9/12.
Answer: Yes, 3/4 and 9/12 are equivalent fractions.
Example 3: Example 3: Find the Missing Number
Problem: 4/7 = ?/21. Find the missing number.
Solution:
Step 1: Denominator changed from 7 to 21. Multiply: 7 × 3 = 21.
Step 2: Multiply the numerator by the same number: 4 × 3 = 12.
Answer: 4/7 = 12/21
Example 4: Example 4: Generate by Dividing
Problem: Write an equivalent fraction of 8/12 by dividing.
Solution:
Step 1: Find a common factor of 8 and 12. Both are divisible by 4.
Step 2: Divide: (8÷4)/(12÷4) = 2/3.
Answer: 8/12 = 2/3
Example 5: Example 5: Check Non-Equivalent Fractions
Problem: Are 2/3 and 4/9 equivalent?
Solution:
Step 1: Cross multiply: 2 × 9 = 18 and 3 × 4 = 12.
Step 2: 18 ≠ 12.
Answer: No, 2/3 and 4/9 are not equivalent.
Example 6: Example 6: Find the Missing Numerator
Problem: 15/20 = ?/4. Find the missing number.
Solution:
Step 1: Denominator changed from 20 to 4. Divide: 20 ÷ 5 = 4.
Step 2: Divide numerator by the same number: 15 ÷ 5 = 3.
Answer: 15/20 = 3/4
Example 7: Example 7: Word Problem
Problem: Priya ate 2/6 of a chocolate bar. Aman ate 1/3 of an identical bar. Did they eat the same amount?
Solution:
Step 1: Check if 2/6 = 1/3.
Step 2: 2/6 simplified: (2÷2)/(6÷2) = 1/3.
Answer: Yes, 2/6 = 1/3, so Priya and Aman ate the same amount.
Example 8: Example 8: Multiple Equivalent Fractions
Problem: Which of these fractions are equivalent to 1/2? Options: 3/6, 4/7, 5/10, 2/5.
Solution:
- 3/6: 3÷3 = 1, 6÷3 = 2 → 1/2 ✓
- 4/7: Cross multiply: 1×7 = 7, 2×4 = 8 → 7 ≠ 8 ✗
- 5/10: 5÷5 = 1, 10÷5 = 2 → 1/2 ✓
- 2/5: Cross multiply: 1×5 = 5, 2×2 = 4 → 5 ≠ 4 ✗
Answer: 3/6 and 5/10 are equivalent to 1/2.
Example 9: Example 9: Visual Proof
Problem: Show that 2/4 and 3/6 are equivalent using a visual method.
Solution:
Step 1: Draw a rectangle divided into 4 equal parts. Shade 2 parts → 2/4 is shaded.
Step 2: Draw another identical rectangle divided into 6 equal parts. Shade 3 parts → 3/6 is shaded.
Step 3: Both shaded areas cover exactly half the rectangle.
Answer: 2/4 = 3/6 = 1/2. Both represent the same portion of the whole.
Key Points to Remember
- Equivalent fractions represent the same value but have different numerators and denominators.
- Multiply or divide both numerator and denominator by the same non-zero number to get an equivalent fraction.
- Cross multiplication can verify if two fractions are equivalent (if a×d = b×c, then a/b = c/d).
- Every fraction has infinitely many equivalent fractions.
- Equivalent fractions occupy the same point on a number line.
- Simplifying a fraction means finding an equivalent fraction with the smallest numerator and denominator.
Practice Problems
- Write 4 equivalent fractions of 3/8.
- Are 5/6 and 15/18 equivalent? Check using cross multiplication.
- Find the missing number: 6/9 = ?/3.
- Meera says 3/5 = 6/15. Is she correct? Explain.
- Which of these are equivalent to 2/3: 4/6, 6/8, 8/12, 10/15?
- Simplify 12/16 to its equivalent fraction with the smallest numbers.
- Arjun ate 4/8 of his tiffin and Kavi ate 3/6 of his identical tiffin. Did they eat the same amount?
Frequently Asked Questions
Q1. What are equivalent fractions?
Equivalent fractions are fractions that have the same value even though they look different. For example, 1/2, 2/4, and 3/6 are all equivalent because they all represent the same amount.
Q2. How do you find equivalent fractions?
Multiply or divide both the numerator and the denominator by the same non-zero number. For example, 2/3 x 4/4 = 8/12, so 2/3 and 8/12 are equivalent.
Q3. How do you check if two fractions are equivalent?
Use cross multiplication. For fractions a/b and c/d, if a x d = b x c, they are equivalent. Or simplify both fractions and see if they reduce to the same simplest form.
Q4. Can you divide to get equivalent fractions?
Yes. If both numerator and denominator share a common factor, divide both by that factor. For example, 6/8 divided by 2/2 = 3/4. This is called simplifying.
Q5. Why are equivalent fractions important?
They are essential for comparing fractions, adding and subtracting fractions with different denominators, and simplifying fractions to their lowest terms.
Q6. How many equivalent fractions does a fraction have?
Every fraction has infinitely many equivalent fractions. You can keep multiplying the numerator and denominator by 2, 3, 4, 5, and so on to get more.
Q7. What is the simplest form of a fraction?
The simplest form is the equivalent fraction where the numerator and denominator have no common factor other than 1. For example, the simplest form of 6/8 is 3/4.
Q8. Do equivalent fractions look the same on a number line?
Yes. Equivalent fractions represent the same point on a number line. For example, 1/2, 2/4, and 3/6 all fall at the same point, exactly halfway between 0 and 1.
Q9. Is this topic in the NCERT Class 4 syllabus?
Yes. Equivalent fractions are a key topic in Class 4 Maths under the Fractions chapter. Students learn to find, verify, and use equivalent fractions.
Related Topics
- Fractions (Grade 4)
- Simplifying Fractions
- Comparing 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)
