1. Ratios Direct Proportion Including

2. Ratios This relates one quantity to another (or several others if a recipe). Ratios are given a bit like a fraction, but they are given as A : B rather than It is important that the units are the same for both parts. For example a drink is diluted with water in the ratio 1 : 6 means 1 part of concentrate to 6 parts of water. The units could be pints, litres, gallons, etc. It does not matter as long as the units are the same for both parts.

3. Ratios Ratios are normally given as 1 : something or something : 1 Occasionally they give other whole numbers such as 3 : 4 It is rare to give fractions or decimals in a ratio BUT this may occur. If asked to simplify a ratio, you treat it in the same way as a fraction. That is you divide (or multiply) both sides by the same numbers!!! Example: Simplify the ratio 12 : 4 Dividing both sides by four gives 3 : 1

4. Simplify these ratios 1.2:8 2.3:6 3.7:21 4.4:6 5.5:20 6.42:49 7.15:30 8.8:4 1:4 1:2 1:3 2:3 1:4 6:7 1:2 2:1

5. Now consider the ratio: 16 Kg : 800 g To simplify this ratio we MUST get all the “bits” into the same units. There are 1000 g in 1 Kg So 16 Kg = 16 x 1000 g = 16000 g The ratio becomes 16000: 800 simplifies to 160 : 8 and then finally 20:1

6. You try these 1. £2 : 40p 2.10 mm : 1 m 3. 55 g : 2 Kg 4. £2.80 : £3.50 5. 10 cm : 2 mm 6.800 cm : 4 Km 5 : 1 1 : 100 11 : 400 4 : 5 50 : 1 1 : 500

7. Ratios Another way of looking at ratios is when a sum of money is shared out between several people in a ratio according to either how much they paid or their ages.

8. Example: £6000 Lottery win is shared out between 4 people according to how much they paid for their portion of the tickets. They paid in the ratio 5 : 4 : 3 : 3 Add the ratios together: 5 + 4 + 3 + 3 = 15 This means that there are 15 ‘shares’ to be handed out. One share is worth £6000  15 = £400 We now multiply £400 by each of the ratios in turn.

9. £ 6000 Lottery win is shared out between 4 people according to how much they paid for their portion of the tickets. They paid in the ratio 5 : 4 : 3 : 3 1 Share is worth £400 So: 5 shares are worth 5 x £400 = £2000 As a final check, add up all the winnings to make sure that they give £6000!! 3 shares are worth 3 x £400 = £1200 And the final 3 shares are also worth £1200 4 shares are worth 4 x £400 = £1600 £2000 + £1600 + £1200 + £1200 = £6000 Yes the calculation is correct!!

10. Try this one for yourselves Three children are given £800 for Christmas to be shared out according to their ages. They are 16, 10 and 6 years old. How much does each receive?

11. Ratios Add the ages together: 16 + 10 + 6 = 32 Now divide the £800 by 32 = £25 £25 is the amount of 1 share (or each year of age) Now multiply each of the ages by £25 We get £400, £250 and £150 Finally check that the £400 + £250 + £150 add up to the £800 to be shared out. It does!!!

12. Another everyday example of ratios is a recipe from a cook-book. If we need to increase the amount of food made we multiply all the ingredients by the same number. If a recipe makes 15 cakes and we want 60, we need to think of what multiple of 15 makes 60!! 60 is 4 times 15 so each of the ingredients need to be multiplied by 4!!

13. Ratios 500 g self raising flour 250 g margarine 150 g sugar 200 g mixed dried fruit 2 eggs Makes 16 small cakes We want 56 cakes for a party, so what number do we need to multiply 16 by to make 56? 3.5 So we multiply each of the ingredients by 3.5!! 1750 g flour 875 g margarine 525 g sugar 700 g fruit 7 eggs Makes 56 small cakes

14. Ratios Any recipe variations will use this type of calculation!!! Try the next recipe calculation for yourselves.

15. Ratios A casserole for 10 people consists of: 1000 g Beef (diced) 250 g onions (chopped) 250 g carrots (chopped) 100 g plain flour 1000 g potato (cubed) 2 litres beef stock We need to cater for 65 people, how much of each do we need? 65 is 10 x 6.5 so we need to multiply the ingredients by 6.5 6500 g (6.5 Kg) 1625 g 650 g 6500 g (6.5 Kg) 13 litres What do we need to multiply 10 by to get 65?

16. There is always a question involving this type of proportion ratio based on a recipe type question in the exam!!! So make sure you can increase a recipe from a cookbook as an exercise.

17. Direct Proportion This is where we have a cost of a number of items and we need to find the cost of a different number of items. Example: 4 books cost £19.96 How much will 17 books cost? We use the unit method. Find the cost of 1 item then multiply out to find the cost of the number required.

18. Just remember : Find out the cost of 1. Then the cost of the number required!!! Direct Proportion 4 books cost £19.96 So: 1 book costs £19.96  4 = £4.99 And 17 books cost £4.99 x 17 = So what’s hard about this? £84.83

19. Direct Proportion Try the following for yourselves 1.6 cakes cost £1.20, how much for 15 cakes? 2.20 pencils cost 80p, how much will 75 pencils cost? 3.4 tee-shirts cost £15, how much will 7 tee-shirts cost? 4.18 pairs of trainers cost £630, how much will 4 pairs of trainers cost? £3.00 £26.25 £140.00

20. You are working for a building firm and call in at the suppliers for 37 paving slabs; you notice that they are priced up as £8.50 for 5. The supplier (Honest Joe) tells you that he'll give you 37 for the special price of £65. Do you pay him they money - or try to work out whether you're being done or not? If 5 slabs cost £8.50 Then 1 slab costs £8.50 ÷ 5 = £1.70 And 37 slabs cost £1.70 x 37 = £62.90

21. Easy isn't it - and by doing a little maths you've just managed you save yourself £2.10 by not going for his offer, which is not bad for a small amount of time spent doing a calculation.

22. Direct Proportion With direct proportion, the thing to remember is that both parts increase. As the number of items increases, so does the cost!!!