Fractions Made Easy
Fractions are just parts of a whole. Think of a pizza cut into slices — if you eat 3 slices out of 8, you have eaten 3/8 of the pizza. The top number (numerator) is how many slices you have. The bottom number (denominator) is how many equal slices there are in total.
Understanding Fractions — The Pizza Way
Imagine a whole pizza cut into 4 equal slices. If you take 1 slice, you have 1/4 (one quarter). Take 2 slices and you have 2/4, which simplifies to 1/2 (one half). See? Fractions are just counting slices!
Equivalent fractions are different ways of writing the same amount. 1/2 = 2/4 = 3/6 = 4/8. You multiply (or divide) the top AND bottom by the same number.
Key Rules
- Adding/Subtracting: make the denominators the same first
- Multiplying: top x top, bottom x bottom
- Dividing: Keep, Flip, Change (KFC) — keep the first, flip the second, change ÷ to ×
- Simplifying: divide top and bottom by their highest common factor
Adding and Subtracting Fractions
You can only add or subtract fractions when the denominators (bottom numbers) are the same. If they are not the same, you need to find a common denominator first. The easiest way? Multiply the two denominators together — or find the lowest common multiple.
Worked Examples
Example 1 — Adding: 1/4 + 2/4
The denominators are already the same (both 4), so just add the tops:
- 1 + 2 = 3
- Keep the denominator: 3/4
Answer: 3/4
Think: 1 pizza slice + 2 pizza slices = 3 slices out of 4 ✓
Example 2 — Different denominators: 1/3 + 1/4
- Find a common denominator: 3 × 4 = 12
- Convert 1/3 → multiply top and bottom by 4 → 4/12
- Convert 1/4 → multiply top and bottom by 3 → 3/12
- Now add: 4/12 + 3/12 = 7/12
Answer: 7/12
Example 3 — Dividing with KFC: 3/5 ÷ 2/3
- Keep the first fraction: 3/5
- Flip the second fraction: 2/3 becomes 3/2
- Change ÷ to ×: 3/5 × 3/2
- Multiply tops: 3 × 3 = 9. Multiply bottoms: 5 × 2 = 10
Answer: 9/10
KFC = Keep, Flip, Change. Works every time! ✓
Example 4 — Simplifying: 12/18
- Find the highest common factor (HCF) of 12 and 18 → 6
- Divide top by 6: 12 ÷ 6 = 2
- Divide bottom by 6: 18 ÷ 6 = 3
Answer: 2/3
Mixed Numbers and Improper Fractions
A mixed number has a whole part and a fraction part, like 2 1/3. An improper fraction has a bigger top than bottom, like 7/3. To convert: multiply the whole number by the denominator, add the numerator. So 2 1/3 = (2 × 3 + 1)/3 = 7/3. To go back: divide the top by the bottom — the answer is the whole part, the remainder goes on top.
Practice Questions
- 3/8 + 2/8
- 1/2 + 1/5
- 4/7 − 2/7
- 2/3 × 5/6
- 5/8 ÷ 1/4 (use KFC!)
Answers: 1) 5/8 2) 7/10 3) 2/7 4) 10/18 = 5/9 5) 5/2 = 2 1/2