Ratios

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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