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Ratios Direct Proportion Including

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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.

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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

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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

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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

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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

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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.

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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.

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£ 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!!

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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?

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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!!!

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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!!

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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

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

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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?

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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.

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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.

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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

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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

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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

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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.

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

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