revision: CH 1 - Ratio and proportion

Ratio is used to describe a fraction.
If the ratio of a boy's heright to his father's height is 4:5, then he is 4/5 as tall as his father.

[Change the ratio 2:5 in the form of]
a) 1:n
a) 2:5 = 1: 5/2
           = 1: 2.5
b) m:1
b) 2:5 = 2/5:1
          = 0.4:1
Just remember - for ratios, letters are stronger, so the number on the side of the letter will go on top of the number of the other side.*


Example 1 -
Divide $60 between 2 people, A and B in the ratio of 5:7.
Consider $60 as 12 equal parts because of 5+7 (due to ratio being 5:7).
A receives 5 parts and B receives 7 parts.

- A receives 5/12 of $60 = $25
- B receives 7/12 of $60 = $35

Because ratio is 5:7, to find the total, add them together - 5 + 7 = 12.
Then to find the ratio, you find 5/12 of 60 and 7/12 of 60 to get 25:35.

It is the same when they are asking you to divide a certain number by a ratio.


Example 2 -
Divide 200kg in the ratio 1:3:4
First, add the ratio - 1 + 3 + 4 = 8.
The parts are now 1/8, 3/8 and 4/8.
Find:
- 1/8 of 200 = 25
- 3/8 of 200 = 75
- 4/8 of 200 = 100

PROPORTION -
The majority of problems where proportion is involved are usually problems solved by finding the value of a unit quality.

If a wire of length 2 meters cost $10, find the cost of a wire length 35cm.
First, this means 200cm = 1000cents.

- 1cm = 1000/20 cents = 5 cents.
- 35cm = 5 cents x 35 cm = 175 cents or $1.75