An Introduction to Proportionality

1. An Introduction to Proportionality Slideshow 24, Mathematics Mr Richard Sasaki Room 307

2. Objectives • Learn the meaning of proportionality • Understand the meaning of “direct proportion” and notation describing this

3. Proportion Chapter 4 is all about proportion. What is proportion? Proportion literally means that as one thing changes, another thing does. It is a very loose meaning without further definition. So if two things (let’s say and ) relate to each other, we say “ is proportional to ”. (Or “ is proportional to ”, doesn’t matter which.)

4. Proportion For two things to vary, they cannot be fixed. So unknowns will have different values in different situations.Here is an example. Total number of legs on a group of sheep 2 3 4 0 1 0 4 12 16 8 We can easily see that as the number of sheep goes up bv 1, the number of legs goes up by 4.

5. Proportion Another very important point, for two things and to be proportional… When , must = 0. When there is a constant between them, they are not proportional.

6. Proportion Check for each equation whether and are proportional. Yes! Yes! Yes! Yes! No… No… Yes!

7. Please try the worksheet! Proportion Check for each expression whether the two items in discussion are proportional. Yes! A rectangles width and its area. No… A man’s height and his wife’s height. Yes! A young boy’s age and his height. Yes!(loosely…) A car’s engine size and its top speed.

8. Yes Yes Yes No Both okay. Yes There isn’t a strict numerical link between his height and age. Also a 0 day old baby isn’t 0cm. Numbers on dice? Number of hexagons and number of sides? Yes No Yes When . Yes No Yes, it’s a relationship and when y tends to . No

9. Direct Proportion So far, mainly we’ve just been using proportion as a test to see whether two things are related or not. A big part of proportion with strictly related variables (i.e. when we can draw a table) is called direct proportion. What is direct proportion? Direct proportion is when two things are related and only a coefficient exists between them.

10. It is often shown as too. Direct Proportion So if two things can be written in the form (or ) where and are variables and is a regular number, they are directly proportional. All of the tables we have made so far have involved two variables that are directly proportional. If two variables and are directly proportional, this is denoted… ( is directly proportional to .)

11. 150 2 = 450 Yen No as will have a rate that changes. Also, it can’t be written in the form . The pencils cost the same amount. seconds Yes, as (k=) He (magically) ran at the same speed always. seconds As increases by 1, increases by 4 and as always when so . The cat eats at the same speed at all times.