Ratios — Mathematics, 11–13 years
Compare quantities fairly by keeping track of how many parts of one thing match another. Mathematics, 11–13 years.
A ratio compares parts
A ratio tells how two quantities match, rather than simply how large either one is. If a paint mix has 2 cups of blue for every 3 cups of white, its ratio is 2:3; multiplying both numbers keeps the same recipe.
Why ratios were needed
A total alone can hide an important difference: 10 red beads and 10 blue beads is not the same mix as 100 red and 10 blue. Ratios grew from practical needs such as mixing, map-making and comparing speeds, where the relationship matters.
Scaling a ratio
A drink uses syrup and water in the ratio 1:4. For 15 cups altogether, the recipe has 5 equal parts, so each part is 15 ÷ 5 = 3 cups. Use 3 cups of syrup and 12 cups of water: 3:12 simplifies back to 1:4.
Do not compare totals alone
It is tempting to say that a 2:3 mix and a 4:5 mix are nearly the same because their numbers look close. They are not: 2 out of 5 parts is 40%, while 4 out of 9 parts is about 44%. The whole must be considered too.
Ratios in real life
Maps use ratios to shrink real distances: a scale of 1:50,000 means 1 centimetre on the map represents 50,000 centimetres outside it. Sports statistics also compare shots, wins or points fairly when players have taken different numbers of attempts.
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