Ratio and Proportion

Ratios are used only to compare quantities. They do not give information about actual values.

The ratio's 3:4, 6:8, 9:12... are different forms of the same ratio. They are called equivalent ratio's. They can be found by multiplying/ dividing each part of the ratio by the same number.
To simplify a ratio divide both numbers in the ratio by the same number. A ratio with a whole number that cannot be simplified is in its simplist form.

Sharing in a given ratio. EXAMPLE - James and Sally share £20 in the ratio 3:2. How much do they each get?

Add the numbers in the ratio. 3 + 2 = 5.
For every £5 shared: James gets £3, Sally gets £2.
20 / 5 = 4 There are 4 shares of £5 in £20. James gets £3 x 4 = 12. Sally gets £2 x 4 = £8. So James gets £12 and Sally gets £8.

Direct Proportion.    When a motorist buys fuel, the more he buys the greater the cost. In this situation the quantities can change but the ratio between the quantities stays the same. As one quantity increases, so does the other. The quantities are in direct proportion.
Inverse proportion.     By using more people to deliver a batch of leaflets, the time taken to complete the task is reduced. In this situation, as one quantity increases the other quantity decreases. The quantities are in inverse proportion.

• 4 cakes cost £1.20. Find the cost of 7 cakes.
  4 cakes cost £1.20     1 cake costs £1.20 / 4 = 30p     7 cakes cost 30p x 7 = £2.10 So, 7 cakes cost £2.10. (this is sometimes called the unitary method.)
  
• 3 people take 8 hours to deliver some leaflets. How long would it take 4 people? 3 people take 8 hours.     1 person takes: 8 hours x 3 = 24 hours.     4 people take: 24 hours / 4 = 6 hours. So, 4 people would take 6 hours. (This shows that the time is inversely proportional to the  number of people.)