Ratios and Proportions
Mixing paint, scaling a recipe, reading a map: ratios are how you keep things in the right proportion. Three short lessons and you'll never get them muddled.
What a ratio is
A ratio compares amounts. A drink mixed 1 : 4 (“one to four”) means 1 part squash for every 4 parts water: 5 parts in total.
Like fractions, ratios can be simplified by dividing every part by the same number: 10 : 15 = 2 : 3.
Order matters. A ratio of boys to girls of 2 : 3 is not the same as girls to boys of 2 : 3.
Sharing in a ratio
- Total parts: 1 + 3 = 4
- One part: $120 ÷ 4 = $30
- 1 part = $30, 3 parts = $90
- $30 and $90
The same method works with any number of parts: add the parts, find one part, multiply.
Scaling up and down
To keep things in proportion, multiply everything by the same scale factor.
- Scale factor: 6 ÷ 4 = 1.5
- 200 g pasta × 1.5 = 300 g
- 2 eggs × 1.5 = 3 eggs
- Multiply every ingredient by 1.5
Maps use ratios too. On a 1 : 25,000 map, 1 cm on paper is 25,000 cm (250 m) in real life, so 4 cm is 1 km.
Cooking caution: ingredients scale, but cooking times and pan sizes don't always. Doubling a cake doesn't mean baking for twice as long.