Guide library
Learn Ratios
Start with the concept you need. Six guides cover what ratios mean, how to simplify and scale them, how a ratio differs from a proportion, and how to prove an answer is right.
- Compare
- Simplify
- Scale
- Apply
- Check
Start here
If ratio notation itself is the question, read this one first.
Work with ratios
Changing the numbers without changing the relationship.
How to Simplify Ratios
“How do I reduce a ratio without changing what it means?”
Dividing every part by the greatest common divisor, why the reduced ratio is equivalent, how decimal and fractional inputs are handled, and how to verify the result.
Read the guideHow to Scale a Ratio Up or Down
“How do I make a ratio larger or smaller and keep the relationship?”
One common factor applied to every part — chosen directly, derived from a known component, or derived from a target total, including multi-part ratios and scaling back down.
Read the guide
Understand the concepts
Where ratio questions are usually misread rather than miscalculated.
Ratio vs Proportion
“What is the difference between a ratio and a proportion?”
A ratio compares quantities. A proportion is the statement that two ratios are equal — a claim you can test, which is why cross-multiplication belongs to proportions and not to ratios.
Read the guideHow Mixing Ratios Work
“What does one “part” mean in a mixing ratio?”
Parts, total parts and the value of one part; sizing a batch from any single known quantity; three-component ratios; and why a volume basis is not automatically a mass basis.
Read the guide
Check your work
You already have an answer and want to know whether to trust it.
Which guide do I need?
| If you need to… | Read |
|---|---|
| Understand what 3:2 means | What Is a Ratio? |
| Reduce 18:24 to its simplest form | How to Simplify Ratios |
| Turn 2:3 into a larger or smaller batch | How to Scale a Ratio Up or Down |
| Tell a ratio apart from a proportion | Ratio vs Proportion |
| Work out what “4 parts to 1 part” means | How Mixing Ratios Work |
| Confirm an answer you already have | How to Check a Ratio Answer Is Right |
Each situation has one canonical guide — nothing here is covered twice across the library.
Need the answer rather than the explanation?
The guides explain the reasoning. These tools do the arithmetic and show the working.