What is a Fraction?
A fraction represents a part of a whole. It's written as:
numerator / denominator = a/b
The numerator (top number) tells you how many parts you have.
The denominator (bottom number) tells you how many equal parts the whole is split into.
Think of it this way: if you cut a pizza into 8 slices and eat 3 of them, you've eaten 3/8 of the pizza. The 3 is what you have, and the 8 is the total number of parts.
Proper vs. Improper Fractions:
A fraction is proper (less than 1) if the numerator is smaller than the denominator, like 3/8 or 2/5. It's improper (greater than or equal to 1) if the numerator is bigger or equal, like 5/3 or 7/7.
How do I Find a Fraction of an Amount?
There are three methods—use whichever feels most natural to you.
Method 1: Divide, then multiply
To find 2/5 of 60:
Step 1: Divide by the denominator: 60 ÷ 5 = 12
Step 2: Multiply by the numerator: 12 × 2 = 24
Method 2: Convert to decimal, then multiply
To find 9/10 of 15:
Step 1: Turn 9/10 into 0.9
Step 2: Multiply: 0.9 × 15 = 13.5
Method 3: Multiply fractions
To find 5/6 of 8:
Rewrite 8 as 8/1, then multiply: (5/6) × (8/1) = 40/6 = 20/3
Exam Tip: Method 1 is fastest for most people in an exam. If you're comfortable with decimals, Method 2 is also quick. Practice the one that feels easiest!
What are Equivalent Fractions?
Equivalent fractions are different fractions that represent the same amount. They're just different ways of writing the same thing.
For example, 1/2, 2/4, 3/6, and 50/100 are all equivalent—they all represent "half."
How to Find an Equivalent Fraction:
Multiply (or divide) both the numerator AND the denominator by the same number. This keeps the fraction's value unchanged because you're multiplying by 1 in a clever way. For example: (5/6) × (2/2) = 10/12. Both represent the same amount, just with different-sized pieces.
Why does this work? When you multiply the top and bottom by the same number, you're not actually changing the value—you're just splitting the pieces smaller (or combining them bigger). Imagine cutting each of your 6 pizza slices in half to get 12 smaller slices; you still have the same amount of pizza.
5/6 = (5×2)/(6×2) = 10/12 = (5×3)/(6×3) = 15/18
All three fractions equal the same amount.
How do I Simplify Fractions?
Simplifying means writing a fraction using the smallest possible numbers. It's the opposite of equivalent fractions—you're making the numbers smaller, not bigger.
To simplify, divide both the numerator and denominator by a common factor (a number that divides evenly into both).