## Big Idea

Ratios allow us to compare the relative sizes of two quantities.

## Background points for teaching

An understanding of ratios involves understanding the following:

__Ratios can compare a part to the whole.__

An example of a part to a whole ratio is the number of females in a class to the number of students in the class. If there are 8 females in the class of 20 students the ratio of girls to students can be expressed 8:20 (females to students). Because this ratio is relating a part to a whole it can also be expressed as a fraction (8/20) or as a percentage (40%).__Ratios can compare parts to parts.__

An example of a part to a part ratio is where the number of females in a class is compared to the number of males. If there are 8 females in a class of 20 the ratio of females to males is 8:12. It is important when using ratios to clearly state what the comparison is made in relation to. One of the most common uses of part-to-part ratios are odds. The odds of an event happening is a ratio of the number of ways an event can happen to the number of ways it cannot happen.__Ratios can also be a rate.__

Part-to-whole and part-to-part ratios compare two quantities of the same thing. Rates on the other hand are examples of ratios where a comparison is made between quantities of different things. In rates the measuring units are different for the quantities being compared and the rate is expressed as one quantity**per**the other quantity. For example the value of food can be expressed as price per kilogram, fuel efficiency can be expressed as litres per 100 km.__A proportion expresses the relationship between two ratios.__

A proportion is a statement of the equality between two rations. For example if it takes 10 balls of wool to make 15 beanies, 6 beanies will take 4 balls of wool. In this example the ratio of 2:3 (balls to beanies) can be applied to each situation. Solving proportional problems involves applying a known ratio to situations that are proportionally related and finding one of the measures when the other is given. For example, in the beanie situation the ratio of 2:3 (balls to beanies) can be applied to the problem where you want to find out how many balls of wool are needed to make 33 beanies.

2:3 = ?:33,

? = 22