Proportion
Maths: Edexcel IGCSE Higher, topic 1.7.2
Proportion
Two pairs of numbers are in proportion if the ratio between the first pair is equivalent to the ratio between the second pair.
Ratios in proportion
- An equals sign between two ratios means that the two ratios are in proportion.
Worded problems
- Worded problems can be converted into proportions.
- ‘The ratio of male to female pupils on a school trip is 5 : 2’
- This can be written as m : f = 5 : 2
Proportions and fractions
- Proportions can be converted into an equation involving fractions.
Direct Proportion
Notation
- This means x is proportional to y.
- This means there is some number k such that x = ky.
Proportional to x²
- If y is proportional to x2 then we write y α x2 and there is some number k such that y = kx2.
Inverse Proportion
3 builders take 12 days to build a wall. How long does it take 4 builders to build an identical wall?
Notation
- We write y α 1⁄x and there is some number k such that y = k⁄x.
- The time taken to complete a job is inversely proportional to the number of people working on the job.
Days taken are inversely proportional to builders
- d = number of days taken
- b = number of builders
We need to find k
It takes 3 builders 12 days to build the wall
Rearrange to find k
Sub k back into the original equation
Sub in b = 4
- We want to know the days taken for 4 builders to build the wall.
It takes them 9 days
Test yourself on Proportion
There are 5 times as many green pens (g) as blue pens (b). Which proportion represents this relationship?
There are 8 times as many green pens (g) as blue pens (b). Which proportion represents this relationship?
There are 3 times as many green pens (g) as blue pens (b). Which proportion represents this relationship?
w : x = y : zWhich equation represents this proportion?
3 : 1 = 6 : 2Which equation represents this proportion?