What is a ratio?
A ratio compares two amounts of the same kind. If a basket has 3 apples and 2 oranges, we write the ratio of apples to oranges as 3 : 2. We read this as “three to two”. Order matters, so 3 : 2 is not the same as 2 : 3. A ratio does not use units; it only tells us how the amounts compare.
Simplifying a ratio
To write a ratio in its simplest form, divide both numbers by the same number (their common factor) until you cannot divide any more. A simplest form is neater and easier to compare, just like a fraction in its lowest terms.
Key idea
Divide both sides of the ratio by the same number to simplify. This does not change what the ratio means.
Worked example
Simplify 12 : 8.
Both numbers can be divided by 4.
12 ÷ 4 = 3 and 8 ÷ 4 = 2.
So 12 : 8 = 3 : 2.
Remember
- Keep the order the question asks for.
- Divide both numbers by the same value.
- Stop when no common factor is left.