Ratio & proportion tools
What Is a Ratio?
A ratio compares quantities in parts. That single idea explains everything else.
Writing 3:2 says: for every three of the first thing, there are two of the second. It does not say how many there are in total — only how the quantities relate. That is why the same ratio describes 3 and 2, 30 and 20, or 4.5 and 3.
3 : 2 drawn to scale
Parts and the whole
Add the parts and you get the total: 3 + 2 = 5 parts. The first quantity is three-fifths of the whole (60%) and the second is two-fifths (40%). Once you know the value of one part, every other quantity follows by multiplication.
Order matters
3:2 and 2:3 are different ratios. Always keep the order the same as the labels you wrote down — concentrate first, water second, or whichever order your source uses.
Ratios and fractions
A ratio compares part to part; a fraction usually compares part to whole. In 3:2 the first part is 3/2 of the second, but 3/5 of the total. Confusing the two is the most common source of wrong answers.