Fractions
See fractions as one number, not two
The single most important shift: a fraction like 3/4 is one number — not "3 out of 4" separate things.
See It in Action
The Problem
Which is larger: 3/8 or 2/5?
Common Mistake
3/8. Because 3 > 2, and 8 > 5, so 3/8 must be bigger.
This applies whole-number thinking. Bigger digits do not mean bigger fractions. Eighths are smaller pieces than fifths, so you need more of them to make the same amount.
Correct Approach
Find a common denominator. The LCM of 8 and 5 is 40. Convert: 3/8 = 15/40. Convert: 2/5 = 16/40. Now compare: 16/40 > 15/40. So 2/5 > 3/8.
Answer: 2/5 is larger
As a decimal: 3/8 = 0.375, 2/5 = 0.4. Since 0.4 > 0.375, confirmed: 2/5 is larger. ✓
The Core Concept
Most fraction mistakes come from treating the numerator (top) and denominator (bottom) as two separate whole numbers. They're not. A fraction is a single number that lives somewhere on the number line between whole numbers. 3/4 is one number: three quarters.
The denominator tells you how many equal pieces the whole is cut into. The numerator tells you how many of those pieces you have. So 3/4 means: cut the whole into 4 equal pieces, take 3. This also means a bigger denominator = smaller pieces = a smaller fraction. That's why 1/5 is smaller than 1/4, even though 5 > 4.
For equivalent fractions, the key is that multiplying or dividing both numerator and denominator by the same number creates the same-sized piece from a different-sized whole. 2/4 = 1/2 because if you double both the pieces and the pieces-needed, you get the same amount of the whole.
Common Mistakes to Avoid
Comparing fractions by their digits alone
The denominator changes everything. 1/10 < 1/2, even though 10 > 2. Always convert to a common denominator or use decimals to compare.
Adding fractions by adding numerators AND denominators separately
1/3 + 1/3 ≠ 2/6. You need a common denominator first. 1/3 + 1/3 = 2/3, not 2/6.
Forgetting to simplify
6/8 is correct but 3/4 is the simplified form. Always check if numerator and denominator share a common factor you can divide out.
"Of" means multiply
"3/4 of 20" means 3/4 × 20 = 15. The word "of" always signals multiplication. Don't add or subtract.
Try It Yourself
A bag of 24 marbles is 3/8 red. How many marbles are red?
Hint: "3/8 of 24" — the word "of" means multiply. What is 24 ÷ 8 × 3?
Key Tips
Draw a rectangle and divide it when comparing or adding fractions — pictures make fraction size obvious.
Remember: "of" = multiply. "3/4 of 20" = 3/4 × 20.
To find a fraction of a quantity: divide by the denominator first, then multiply by the numerator.
Ready to practise Fractions?
Reading is the start. The Maths Gym has exercises designed around this skill — with instant feedback and progress tracking.