Ratio and proportion · KS3 Maths

Ratio

A ratio compares amounts: 3 : 2. Simplify by dividing by the HCF: 12 : 18 = 2 : 3.
To write a ratio in the form 1 : n, divide both parts by the first part: 5 : 20 = 1 : 4.
In the ratio 3 : 5, there are 8 parts, so the first amount is 3/8 of the total.

Add the parts, find one part, then multiply: share £40 in the ratio 3 : 5. There are 8 parts, so 1 part = £5, and the shares are £15 and £25.
If you know one amount: red to blue is 3 : 4 and there are 12 red, so 1 part = 4 and there are 16 blue.

Direct proportion: find one first (the unitary method). If 4 pens cost £3, 1 pen costs 75p, so 10 pens cost £7.50.
Recipes: a recipe for 4 uses 200 g of flour, so a recipe for 6 uses 300 g.
Best buys: compare the price per gram or per item: 500 g for £2.00 is 0.4p per gram; 750 g for £2.70 is 0.36p per gram, so the larger pack is better value.
Inverse proportion: as one amount goes up, the other goes down. If 4 people take 6 days, 8 people take 3 days.

A map scale of 1 : 50 000 means 1 cm on the map is 50 000 cm (500 m) in real life.
Speed = distance ÷ time: 150 miles in 3 hours is 50 miles per hour.

Ratio: A comparison of two or more amounts, written like 3 : 2.
Simplest form: A ratio that can't be divided any further by a common factor.
Proportion: A part of the whole, or a relationship where amounts change together.
Direct proportion: When one amount doubles, the other doubles too.
Inverse proportion: When one amount doubles, the other halves.
Unitary method: Finding the value of one item first.
Scale: The ratio of a length on a map or drawing to the real length.
Best buy: The option that gives the most for your money.