Fractions — Class 4 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 4 Mathematics. Parts of a whole, types of fractions, equivalent fractions, and operations on like fractions.
1. What a fraction is
Every number you have met so far answered the question "how many?" A fraction answers a different one: "how much of one thing?"
Cut a chapati into 4 equal pieces and take 1. You have taken one quarter, written 1/4.
The word equal is doing real work there. Four pieces of different sizes are not quarters. A fraction only makes sense when the whole has been divided into parts of the same size.
2. Numerator and denominator
A fraction has two numbers with a line between them.
- The denominator is the bottom number. It says how many equal parts the whole was cut into.
- The numerator is the top number. It says how many of those parts you have.
In 3/4, the whole was cut into 4 equal parts and you have 3 of them.
A useful way to remember which is which: the denominator is down.
3. Three types of fraction
| Type | Rule | Examples |
|---|---|---|
| Proper | Numerator smaller than denominator | 3/4, 2/5, 1/8 |
| Improper | Numerator equal to or bigger than denominator | 5/3, 7/4, 6/6 |
| Mixed | A whole number together with a proper fraction | 1 1/2, 2 3/4 |
A proper fraction is always less than one whole. An improper fraction is one whole or more — which is why it can be rewritten as a mixed fraction. Seven quarters, 7/4, is one whole (4/4) with 3/4 left over, so 7/4 = 1 3/4.
4. Equivalent fractions
Different-looking fractions can mean exactly the same amount.
Half a pizza can be cut as 1/2, or 2/4, or 3/6, or 4/8. Every one of those is the same quantity of pizza — the slices are just thinner and more numerous.
To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same number.
- 1/2 = (1 × 3)/(2 × 3) = 3/6
- 4/8 = (4 ÷ 4)/(8 ÷ 4) = 1/2
Both parts must be treated the same way. Change only the top and you have changed the amount.
5. Comparing fractions
When the denominators match, the parts are the same size, so just compare the numerators. Five eighths is more than three eighths:
3/8 < 5/8
When the numerators match, think about the size of each part. The more pieces you cut a whole into, the smaller each piece must be. So a bigger denominator means a smaller fraction:
3/5 > 3/7
This is where the most common mistake in the chapter lives. Children see 1/3 and 1/2 and reason that 3 is bigger than 2, so 1/3 must be bigger. But a third of a chapati is smaller than half of it. 1/2 > 1/3.
6. Adding and subtracting like fractions
Fractions with the same denominator are called like fractions. They are easy to combine, because the parts are already the same size.
Add or subtract the numerators and keep the denominator unchanged.
- 3/8 + 2/8 = 5/8
- 7/9 − 4/9 = 3/9, which simplifies to 1/3
- 2/7 + 3/7 = 5/7
Why does the denominator stay? Because you are counting eighths. Three eighths plus two eighths is five eighths — the type of part has not changed, only how many you have. Adding the denominators to get 5/16 would be like saying three apples plus two apples equals five oranges.
When the answer comes out improper, turn it into a mixed fraction: 4/5 + 3/5 = 7/5 = 1 2/5.
7. Worked examples
Example 1. In 5/9, name the numerator and the denominator.
Solution: Numerator 5, denominator 9. The whole was cut into 9 equal parts and 5 were taken.
Example 2. Classify 7/4, 2/5 and 6/6.
Solution: 7/4 is improper (7 > 4). 2/5 is proper (2 < 5). 6/6 is improper, and equals one whole.
Example 3. Find the missing number: 1/2 = ?/6.
Solution: The denominator was multiplied by 3, so the numerator must be too. 1 × 3 = 3, giving 3/6.
Example 4. Which is greater, 3/5 or 3/7?
Solution: The numerators match, so compare the parts. Fifths are bigger than sevenths, so 3/5 is greater.
Example 5. Add 3/7 + 2/7.
Solution: Add the numerators and keep the denominator: 5/7.
Example 6. Subtract 5/9 − 2/9.
Solution: 5 − 2 = 3, so the answer is 3/9, which simplifies to 1/3.
Example 7. Write 5/3 as a mixed fraction.
Solution: 3/3 makes one whole and 2/3 is left, so 5/3 = 1 2/3.
8. Practice
- In 4/9, which number is the denominator?
- Is 8/5 a proper or an improper fraction?
- Find the missing number: 3/4 = ?/8.
- Which is bigger, 1/2 or 1/3?
- Add 4/11 + 3/11.
- Subtract 8/11 − 3/11.
- Write 2/5 as an equivalent fraction with denominator 10.
- Write 7/4 as a mixed fraction.
- Arrange in order, smallest first: 5/8, 1/8, 3/8.
9. Answers
- 9 is the denominator, the bottom number.
- Improper, because 8 is bigger than 5.
- The denominator doubled, so the numerator doubles: 6/8.
- 1/2. The bigger the denominator, the smaller each part.
- 7/11.
- 5/11.
- Multiply both parts by 2: 4/10.
- One whole (4/4) with 3/4 left, so 1 3/4.
- 1/8 < 3/8 < 5/8.
10. Summary
- A fraction shows a part of a whole that has been divided into equal parts.
- The denominator (down) is how many parts; the numerator is how many you have.
- Proper fractions are less than one; improper fractions are one or more; mixed fractions pair a whole with a proper fraction.
- Multiply or divide both parts by the same number to get an equivalent fraction.
- With the same denominator, the bigger numerator wins.
- With the same numerator, the smaller denominator wins, because fewer parts means bigger parts.
- To add or subtract like fractions, work on the numerators and leave the denominator alone.
