Learning Objectives
- Compare fractions with the same numerator or the same denominator.
- Find a fraction of a group of objects.
- Understand equivalent fractions.
- Identify like and unlike fractions.
- Add fractions with the same denominator.
Let Us Begin!
In Class 3, you learned that a fraction is a part of a whole. You learned about halves, thirds, and quarters. Now in Class 4, we will go deeper!
Imagine your mother cuts a roti into 4 equal pieces and you eat 1 piece. You ate 1/4 of the roti. But what if she cuts another roti into 8 equal pieces and you eat 2 pieces? You ate 2/8. Surprise -- both are the same amount! These are called equivalent fractions. Let us explore more.
Comparing Fractions
Rule 1: Same Denominator -- When the denominators are the same, the fraction with the bigger numerator is greater.
Example 1: Compare 3/7 and 5/7
Both have denominator 7. Since 5 > 3, we get 5/7 > 3/7.
Rule 2: Same Numerator -- When the numerators are the same, the fraction with the smaller denominator is greater (bigger pieces).
Example 2: Compare 2/5 and 2/9
Both have numerator 2. Since 5 < 9, the pieces in 2/5 are bigger. So 2/5 > 2/9.
Think: If you get 1/3 of a cake and your friend gets 1/6, who gets the bigger piece?
Fraction of a Group
To find a fraction of a group, divide the total by the denominator and multiply by the numerator.
Example 3: Find 1/3 of 12 marbles
Divide 12 by 3 = 4. So 1/3 of 12 = 4 marbles.
Example 4: Find 2/5 of 20 pencils
Divide 20 by 5 = 4. Multiply 4 x 2 = 8. So 2/5 of 20 = 8 pencils.
Equivalent Fractions
Equivalent fractions look different but show the same amount. You get an equivalent fraction by multiplying (or dividing) both the numerator and denominator by the same number.
Example 5: Find an equivalent fraction of 1/2
Multiply numerator and denominator by 2: (1 x 2) / (2 x 2) = 2/4.
Multiply by 3: (1 x 3) / (2 x 3) = 3/6.
So 1/2 = 2/4 = 3/6. They are all equivalent.
Think: Can you find two equivalent fractions for 2/3?
[Image: Equivalent Fractions — Three circles side by side showing 1/2 = 2/4 = 4/8. Each circle divided differently but same amount shaded. Title: "Equivalent Fractions — Same Amount, Different Names"]
Like and Unlike Fractions
Like fractions have the same denominator. Example: 2/7, 5/7, 1/7.
Unlike fractions have different denominators. Example: 1/3, 2/5, 3/8.
Adding Fractions with the Same Denominator
When fractions have the same denominator, simply add the numerators. The denominator stays the same.
Example 6: Add 2/9 + 4/9
Add numerators: 2 + 4 = 6. Denominator stays 9. Answer: 6/9.
Example 7: Add 3/8 + 1/8
Add numerators: 3 + 1 = 4. Denominator stays 8. Answer: 4/8 (which equals 1/2).
Key Words
| Word | Meaning |
|---|
| Numerator | The top number of a fraction (parts taken) |
| Denominator | The bottom number of a fraction (total equal parts) |
| Equivalent Fractions | Fractions that represent the same value |
| Like Fractions | Fractions with the same denominator |
| Unlike Fractions | Fractions with different denominators |
⭐ Key Points to Remember:
- Same denominator: bigger numerator = bigger fraction.
- Same numerator: smaller denominator = bigger fraction.
- To find a fraction of a group: divide by denominator, multiply by numerator.
- Equivalent fractions are made by multiplying or dividing both parts by the same number.
- To add like fractions: add numerators, keep the denominator.
Practice Questions
A. Fill in the Blanks
1. In the fraction 5/8, the numerator is and the denominator is .
2. 1/4 of 20 = .
3. An equivalent fraction of 2/3 is .
4. 3/10 + 5/10 = .
5. Fractions with the same denominator are called fractions.
B. Compare Using >, < or =
1. 3/5 1/5
2. 4/7 4/11
3. 2/6 1/3
4. 5/9 7/9
C. Find the Fraction of a Group
1. 1/4 of 24 =
2. 2/3 of 15 =
3. 3/5 of 30 =
4. 1/6 of 42 =
D. Multiple Choice Questions
1. Which fraction is greater: 3/8 or 5/8?
(a) 3/8(b) 5/8(c) Both are equal(d) Cannot tell
2. An equivalent fraction of 1/2 is:
(a) 2/3(b) 3/6(c) 1/4(d) 2/5
3. What is 2/7 + 3/7?
(a) 5/14(b) 5/7(c) 6/7(d) 1/7
E. Short Answer Questions
1. Write three equivalent fractions for 1/4.
2. Ravi has 18 sweets. He gives 1/3 of them to his sister. How many sweets does his sister get?
3. Priya ate 2/6 of a pizza and her brother ate 3/6. What fraction of the pizza did they eat together?
🎨 Fun Activity — Equivalent Fraction Chains
Start with the given fraction. Find equivalent fractions by multiplying both the numerator and denominator by 2, then by 3, then by 4. Complete the chain!
| Start | x 2 | x 3 | x 4 |
|---|
| 1/3 | | | |
| 2/5 | | | |
| 3/4 | | | |