Ratio
Ratios What is a Ratio?
Direct Proportion Simplifying Ratios
Splitting Ratio Practice Test Question
What is a Ratio? For Introduction to Ratios Video – click here
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There is a relationship between fractions and ratios. Fractions tell us how many parts of a whole we have, ratios compare these parts For example: Look at the pile of fruit. There are 7 fruit in total, 4 oranges and 3 lemons. If we wrote these as fractions we would have: If we were to write these as a ratio this would be: Oranges
4 7
Lemons
:
3 7
This means that for every 4 oranges there are in the group there will be 3 lemons.
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Ratio compares different parts of a whole or the sizes of two or more quantities
Express the ratio of the shaded area to the unshaded area 1a
3a
b
2a
b
b 5a
4a
b
b
Answers: 1a – 1:2, b – 2:6, 2a – 3:2, b – 6:4, 3a – 2:1, b – 4:2, 4a – 2:2, b – 1:1 , 5a – 4:1, b – 5:5
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• Which rows below have the same ratio of
to
?
Answer: 1, 3 & 4
Answer: 2 & 3
• Which rows above have the same ratio of Back
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Direct Proportion For Introduction to Direct Proportion Video – click here
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A common place that many people use ratios in everyday life is when cooking. To make larger quantities of marmalade using the previous ratio we would need to increase the number of oranges and lemons that we used in the same ratio. Oranges
4
Lemons
:
3
X2 XX 5?
X2
8
:
6
X5
If we used 8 oranges, how many lemons Andneed if wetohad 20 oranges? would we use?
20 : 15 Back
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Look at the example below for mixing 3 different shades of green paint: To make green paint we mix blue and yellow paint in the ratios shown. If we have 500ml of blue paint, how much yellow do we need to make each shade correctly? Light Green
Mid Green
Dark Green
Blue : Yellow
Blue : Yellow
Blue : Yellow
1:4
2:3
3:1
500 :
42000ml x 500 or 2l
500 :
3 x 250
(therefore 1 part = 500 รท 2 = 250)
= 750
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500 :
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(therefore 1 part = 500 รท 3 = 166.67)
Recipe for Bread and Butter Pudding • • • • •
6 slices of bread 2 eggs 1 pint of milk 150g raisins 10g margarine
This recipe is enough for 4 people Work out the amounts needed so that there will be enough for 6 people
• • • • •
9 .................................. slices of bread 3 .................................. eggs 1½ .................................. pints of milk 225 .................................. g raisins .................................. g margarine 15 Back
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Simplifying Ratios For Introduction to Simplifying Ratios Video – click here
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Simplifying Ratios Simplifying ratios is similar to simplifying fractions. We need to find the highest factor that goes into both (or all) parts of the ratio. For example: Ratio
÷ 30 =
÷ 30 =
30 1 : 150 5
Both sides are divisible by 30. If you couldn’t spot this you could divide by 10 then by 3. The final answer would be the same it just takes more steps to get there.
And… ÷6=
÷6=
12 2 : 54 9
Both sides are divisible by 6.
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Adapted from Liverpool Community College Maths Flexi Packs
Now try these: Cancel these ratios down to their simplest form 1) 4) 7) 10)
6 : 12 4 : 10 6 : 30 10 : 45
1:2 2:5 1:5 2:9
2) 8 : 24 1 : 3 5) 9 : 12 3 : 4 8) 25 : 150 1 : 6
3) 3 : 21 1 : 7 6) 15 : 25 3 : 5 9) 11 : 33 1 : 3
11) A farmer uses 20 bags of fertilizer for 4 fields. How many bags for each field? 5 12) A recipe for shortbread uses 200g butter, 100 grams sugar and 300 grams flour. Write this as a ratio, then cancel it to its simplest form 2 : 1 : 3 13) A car’s petrol tank holds 9 gallons. On a full tank the car can travel 270 miles. Write this as a ratio of gallons to miles. Then cancel down to find how many miles the car can travel on 1 gallon 1 : 30
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True or false?
• 3:6 = 6:12
Answers: True
• 14:6 = 7:3
True
• 4:5 = 8:11
True
• 5:10:15 = 10:20:30 = 1:2:3
False
False True
• 6:9 = 4:18 • 12:8 = 6:4 = 3:2 Back
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Splitting Ratio For Introduction to Splitting Ratios Video – click here
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Splitting Ratio Sometimes we may know how much of a substance or liquid we want to make, and know the ratio that we need to use to split this amount. How can we calculate the actual amount of each substance that is needed? For example:
We want to make 2 litres of orange drink. We need to mix squash and water in the ratio 1:4, i.e. 4 times as much water as squash. Step321 Multiply this answer by the number Step Step many partsside do we have in total? ofHow parts on each of the ratio: Divide the total amount to be made 1 of squash 4 of= water Squash = 1 x +400 400ml,= 5 parts in into 5 parts to find the value of each total. = 4 x 400 = 1600ml. Water water part. 2000ml รท 5 = 400ml Check - 400ml + 1600 ml water = 2000ml/2 litres. water
400ml
water
400ml
squash
400ml
400ml 2 litres or 2000ml
400ml
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Calculating in a ratio when only part of the information is known
ď ś A paint colour is made by mixing RED, BLUE and YELLOW in the ratio 5:3:2. In the final mix 30 litres of yellow paint are used. For each of the other colours, how much paint is used in the mix? Answer: the 30 litres of YELLOW paint is 2 parts of the mix To find 1 part: 30 á 2 = 15 litres For 3 parts: 3 x 15 For 5 parts: 5 x 15
45 75 So, _______litres of blue paint and ______litres of red paint are used.
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Dividing an amount by a given ratio
Patrick and Emily share £35 in the ratio 3:4 How much does each person get?
Answer: Total number of parts:
3+4=7
To find 1 part: 35 ÷ 7 = 5 For 3 parts: 3 x 5 For 4 parts: 4 x 5 20 So Patrick gets £ _15 __ and Emily £ ___.
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Try yourself
Divide £ 12 in the ratio 1:3 Answer: £3 : £9
60 km in the ratio 3:7 Answer: 18km : 42km
£ 45 in the ratio 7:2 Answer: £35 : £10
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Adapted from Liverpool Community College Maths Flexi Packs
Now try these: 1) Jamie makes 1500mls of lemon squash. The juice is mixed with water in the ratio 3:7. How much of each is needed. 450 : 1050 2) Chris and Les share a lottery win of £ 400 in the ratio of their ticket prices. Chris paid £ 5 and Les paid £ 3. How much will they each win? 250 : 150 3) The ratio of male to female students in a college is 4:5. There are 2070 students altogether. How many men and women are there? 920 : 1150 4) Joe is laying paving in his garden and wants to have bricks in the ratio of 7 grey to every 5 terracotta. He needs 540 bricks altogether. How many of each colour will there be? 315 : 225 5) A roadside is planted with trees in the ratio of 1 oak to every 4 birch. Altogether the farmer wants 65 trees. How many of each will there be? 13 : 52
6) An alloy is made from copper and zinc in the ratio of 5:6. If the alloy weighs 3190 grams, how much of each metal will there be? 1450 : 1740 Back
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Practice Test Questions
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Test A – Q8
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Test A – Q10
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Test A – Q23
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Test B – Q18
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Test B – Q33
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Test B – Q39
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Test C – Q5
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Test C – Q7
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Test C – Q22
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Test N – Q13
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Test N – Q21
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Test N – Q35
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