What it does
A ratio like 2 : 3 says how much of one thing there is for every so much of another. The easiest way to feel what a ratio means is to mix something. This page has two jars. You add equal parts (cups, spoons, tins) of blue and yellow paint, or of lemon syrup and water, and the jar shows the colour of the mix.
The key idea: the colour depends only on the ratio, not on how much you make. 2 : 3 and 4 : 6 give exactly the same green, because in both, blue is 2 out of every 5 parts. But 2 : 3 and 3 : 4 are different greens, even though one is just “one more of each”.
The page also shows each ratio in simplest form, the share of the first ingredient as a fraction and a percentage, a cross-multiplication test that says which mix is bluer (or which lemonade is stronger), and how to scale a mix up to any amount.
It fits Class 8 Mathematics, proportional reasoning (ratios, equivalent ratios and sharing in a ratio), and is good revision for any class that uses ratios. To find the common factor that simplifies a ratio, use HCF and LCM; equal ratios come back in geometry as similar triangles.
How to use it
- Pick Blue and yellow paint or Lemonade at the top.
- Use the − and + buttons to set the parts in mix A and mix B (0 to 20 of each). The squares above each jar show every part; the jar shows the colour of the whole mix.
- The quick buttons load useful pairs: an equal pair (2 : 3 and 4 : 6), a close pair (2 : 3 and 3 : 4) and others.
- Under the picture you get each ratio in simplest form, its share as a percentage, the cross-multiplication, and a verdict.
- In Make more of mix A, type how much you want in all. The page finds the size of one part and the amount of each ingredient, and lists the first five multiples of the ratio.
A worked example
The page starts with mix A = 2 blue : 3 yellow and mix B = 4 blue : 6 yellow.
- A is already in simplest form. Blue is 2/5 of it = 40%.
- B = 4 : 6 = 2 : 3 after dividing both by 2. Blue is 4/10 = 40%.
- Cross-multiply: 2 × 6 = 12 and 3 × 4 = 12. Equal, so the ratios are equal: the jars are the same colour.
Now change B to 3 : 4. Cross-multiply: 2 × 4 = 8 and 3 × 3 = 9. The 9 belongs to B, so B is bluer (3/7 ≈ 42.9% blue against 40%).
To make 30 cups of mix A: 2 + 3 = 5 parts, so one part is 30 ÷ 5 = 6 cups. Blue = 2 × 6 = 12 cups, yellow = 3 × 6 = 18 cups.
Why cross-multiplying works
Mix A has a share a₁/(a₁ + a₂) of blue and mix B has b₁/(b₁ + b₂). Comparing those fractions is the same as comparing a₁ × b₂ with a₂ × b₁ (multiply both sides by the two positive bottoms and cancel). So you never need decimals: two multiplications decide it.
Check yourself
Five fresh questions each time: simplest form, a missing term, sharing a total, a percentage, and which mix is bluer. Type the answer, press Check, and open the worked answer if you need it. Nothing is saved.
FAQ
Why is adding one of each not the same ratio? Multiplying both parts by the same number keeps the share the same. Adding the same number changes it: 1 : 2 (one third blue) plus one of each is 2 : 3 (two fifths blue).
Is the colour exactly what real paint would do? No. Real paints mix in complicated ways. The jar uses a simple model that keeps the key fact true: the same ratio always gives the same colour.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Ratios, equivalent ratios, the unitary method and comparing ratios by cross-multiplication are standard school arithmetic. Wording, pictures and examples are fibub's own.
- The paint colour is a simple model (a weighted geometric mean of the red, green and blue values), chosen so that blue and yellow make green. It shows the idea, not the exact shade of a real paint.
- Checked by hand-worked examples and by comparing every pair of mixes up to 12 parts with exact fractions.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.