Ratios compare one part to another part (not part to whole — that's fractions).
Order matters. Whoever/whatever is mentioned first goes first in the ratio.
Add the parts of a ratio together to find the total number of parts in the whole.
Equivalent ratios are made by multiplying or dividing every part by the same number.
A ratio is simplified when all parts are integers with no common factor left.
Sharing an amount = find 1 part → multiply it by however many parts you need.
Two two-part ratios can be linked into one three-part ratio via a shared quantity.
Direct proportion: both quantities scale the same way. Inverse: one goes up, the other goes down by the same factor.
Think of a ratio as a recipe instruction. If a cake recipe says "mix flour and butter
in the ratio 2 : 1," it's telling you exactly how the two ingredients relate to each other — for every
2 scoops of flour, you need 1 scoop of butter. It doesn't tell you the total amount of cake mixture;
it just tells you the balance between the two ingredients.
That's the core idea: a ratio compares one part of a whole to another part — not a part
to the whole (that job belongs to fractions, which we'll get to in a second).
Order Matters — Always
In any ratio question, whoever or whatever gets mentioned first in the sentence takes
the first position in the ratio. This trips up more students than anything else in this
topic, so get it locked in now.
Example
"Flour and butter in the ratio 2 : 1" → Flour = 2, Butter = 1
If the question said "butter and flour," the ratio would flip to 1 : 2. Same numbers, completely different meaning if you get the order wrong.
Parts of a Whole
The numbers in a ratio tell you how many "parts" each quantity is made of. Add them up to find the total number of parts in the whole thing.
Rule
Ratio 4 : 3 → 4 + 3 = 7 total parts
Ratio 2 : 5 : 3 → 2 + 5 + 3 = 10 total parts
Try It
A fruit punch is made from orange juice and lemonade in the ratio 5 : 3. How many total "parts" make up the whole punch?
This is where a lot of the confusion in this topic actually lives, so let's nail the distinction with a
picture in your head: imagine a pizza cut into 8 slices, shared between two people —
the first person gets 5 slices, the second gets 3.
Fraction vs Ratio
A fraction compares a part to the whole: the first person gets 5⁄8 of the pizza, the second gets 3⁄8.
A ratio compares one part to another part: the ratio of slices (person 1 to person 2) is 5 : 3.
never
appears inside the ratio itself