__
Proportion__

Question)

If I drive 10 miles, I burn 6 litres of
petrol. If I drive 20 miles I burn 12 litres of petrol. How many miles can I
drive with 50 litres?

Answer)

This is a directly proportional relationship so if I call
distance D and litres L, D α L

1) D α L

2) D=kL where k is some constant

3) 10 = k x 6

4) k = 10/6

5) k = 5/3

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Now that you know what k is, put it in to
see what D is when L = 50

1) D = kL

2) D = ^{5}/_{3} x 50

3) D = 250/3

4) D is 83^{1}/_{3}

So I can drive 83^{1}/_{3}
miles on 50 litres of petrol

**Types of proportion**

Direct)
a α b; when one doubles so does the other

a α b^{2}; a is directly proportional to the square of b so when a
doubles, b^{2} doubles, not b!

Inverse)
a α b^{-1} or a α ^{1}/_{b}; when
a doubles, b halves

a α b^{-2} or a α ^{1}/(_{b}2); when a doubles, b^{2}
halves

NB a α b^{-1 }means that a = ^{
k}/_{b}