Concept · Fractions
What Is a Ratio? A Plain Explanation
A ratio is a comparison, not a count. 2:3 says nothing about the actual sizes involved — only that the second is always one and a half times the first.
A comparison, not a count
A ratio compares two or more quantities by division rather than by subtraction. Saying a classroom has a 2:3 ratio of boys to girls says nothing about how many students there are in total — only that for every 2 boys there are 3 girls, whatever the actual class size turns out to be.
That distinction matters. 'Two more girls than boys' is a difference, fixed at 2 regardless of class size. '3:2' is a relationship, the same whether the class has 10 students or 500.
Why 2:3 and 4:6 are the same ratio
A ratio describes a relationship, and many different pairs of numbers can describe the same relationship. 4:6 simplifies to 2:3 for the same reason 4/6 simplifies to 2/3 — both say the second quantity is one and a half times the first.
- 4:6the first ratio
- 4 ÷ 2 = 2, 6 ÷ 2 = 3divide both terms by their common factor, 2
- 2:3the same relationship, in simplest form
Ratios written this way — 4:6, 2:3, 100:150 — are called equivalent ratios. None of them is more correct than another; simplest form is just the most useful one to read at a glance.
Part-to-part versus part-to-whole
A ratio can compare a part to another part, or a part to the whole. In a fruit bowl with 3 apples and 5 oranges, the ratio of apples to oranges is 3:5 — part to part. The ratio of apples to all the fruit is 3:8 — part to whole, since the whole bowl has 3 + 5 = 8 pieces.
| Comparison | Ratio | Kind |
|---|---|---|
| apples to oranges | 3:5 | part to part |
| apples to all fruit | 3:8 | part to whole |
| oranges to all fruit | 5:8 | part to whole |
Mixing these up is a common source of error: a percentage question usually wants the part-to-whole version, and reading off the part-to-part ratio instead gives a number that looks plausible but answers a different question.
Ratios with more than two terms
A ratio can compare any number of quantities at once. A recipe calling for flour, sugar and butter in the ratio 4:6:8 simplifies to 2:3:4 the same way a two-term ratio does — divide every term by their shared greatest common factor, which is 2 here.
The extension is direct: it is the same operation, applied to more numbers simultaneously, and every term still has to be divided by the same factor to keep the relationship intact.
How a ratio relates to a fraction and a scale factor
For a two-term ratio a:b, the fraction a/b carries exactly the same information — 3:4 and 3/4 are two notations for one idea. This is why a ratio calculator and a fraction calculator use the same simplification method underneath.
A scale factor is a ratio applied to resize something while keeping its proportions: a map at a 1:100,000 scale means every unit on the map represents 100,000 of the same unit in reality — the ratio between the drawing and the real world stays constant everywhere on the map.
What a ratio does not tell you
A ratio alone never gives actual quantities, only the relationship between them. Knowing a paint mix is 2:3 blue to yellow tells you nothing about how much paint exists until a total amount — a can size, a quantity of one colour — is also given. That is exactly the missing piece a proportion, or a total to split, supplies.
Questions about what is a ratio
What is a ratio in simple terms?
A comparison between two or more quantities by division. 2:3 means the second quantity is always 1.5 times the first, regardless of the actual sizes involved.
What is the difference between a ratio and a fraction?
For two terms, none — 3:4 and 3/4 carry the same information and simplify the same way. A ratio can also compare three or more quantities at once, which a single fraction cannot represent.
Why are 2:3 and 4:6 considered the same ratio?
Because they describe the same relationship — the second quantity is 1.5 times the first in both cases. Dividing 4:6 by their common factor, 2, gives 2:3 back.
What is the difference between part-to-part and part-to-whole?
Part-to-part compares two pieces directly, like apples to oranges. Part-to-whole compares one piece to everything combined, like apples to all the fruit — a different number from the part-to-part version.