Working with Ratios

Number

A ratio compares the sizes of two or more quantities that together make up a whole
The quantities are separated by a colon, and two or three parts are usual
- 4 : 5 and 3 : 4 : 5 are both ratios
Order follows the question: whichever quantity is named first belongs to the first number
- Cement and sand mixed 1 : 6 means one part cement to six parts sand
Labelling each part in the working prevents the two quantities being swapped later

Each number counts parts, and the whole is the sum of the parts
- In 3 : 5 there are 8 parts altogether
A fraction compares a part against the whole, whereas a ratio compares parts against each other
- Where red and blue counters are in the ratio 3 : 5, the fraction that is red is 3/8
The total never appears in the ratio itself, which is the usual source of error
- 1 : 4 is not another way of writing 1/4, because 1 : 4 means one part in five