Ratio
A ratio compares two quantities of the same kind.
Ratios are written in the form:
2 : 1 this is read as a ratio of two to one.
Examples

In words

In numbers

There are 10 boys in a class and 20 girls. 
number of boys : number of girls

10 : 20

Pink paint has to have 5 parts red and two parts white. 
red paint : white paint

5 : 2

Simplifying ratios
Ratios should be written in their simplest form.
Ratios can be simplified like fractions. e.g. 50 : 25 can be reduced to 2 : 1.
For the two examples above:
In words

In numbers

Simplest form

number of boys : number of girls 
10 : 20 (divide both by 10)

1 : 2

red paint : white paint 
5 : 2 (already in simplest form)

5 : 2

Before simplifying a ratio, each quantity should be in the same units. e.g. $4 to $2 or 60 minutes to 30 minutes.
Ratios as Fractions and Percentages
A ratio can be expressed in several forms. e.g. A ratio of 1 to 2 can be written 1 : 2 or or 50%.
Percentage


1 : 2

^{1}⁄_{2}

50%

15 : 20 
^{15}⁄_{20} = ^{3}⁄_{4} 
^{15}⁄_{20} = ^{75}⁄_{100} = 75%

Problems using Ratios
Often quantities have to be split up using ratios.
For example:
You might want to split up a pizza so that you get twice as much as someone else.
So altogether the pizza is being split into 2 + 1 parts. i.e. Three parts = Thirds You get two thirds of the pizza and they get one third. 
Another example:

To split up $1000 for two people in ratio of 7 : 3
The first person gets seven tenths and the second person gets three tenths. (Alway check that the split amounts add up to the original amount. 
Rates
A rate compares two quantities of a different kind.
The units for rates are like fractions. The line of the fraction is read as "per"
Rates are also usually written in their simplest form with the second unit being reduced to one.
Examples
Speed = kilometre per hour (km/h)
If a car travels 100 km in 2 hours it would travel 50 km in one hour so its speed is 50 km / h
Wage rate = Dollars per week ($/week)
If I earn $1000 in two weeks, I would earn $500 in one week so I earn $500 / h
A woman earns $425 in 50 hours. 
Rate of pay = ^{425}⁄_{50} = $8.50/week 
A motorist travels 85 km in 2 hours. 
Speed = ^{85}⁄_{2} = 42.5 km/hr 