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Ratios
Fichas del conjunto (12)
- 1Reducing Ratios to their simplest form: To reduce a ratio to a simpler form, divide all numbers in the ratio by the same number (a bit like simplifying a fraction). It is in it's simplest form when there is nothing left you can divide byExample:
Write the ratio 15:18 in its simplest form
For the ratio 15:18, both numbers are factors of 3, so divide them by three
15/3 = 5 and 18/3 = 6
It cannot be divided further so the simplest form of 15:18 is 5:6 - 21) If the ratio contains decimals or fractions - multiply Simply the ratio 2.4:3.6 as far as possible - Multiply both sides by ten to get rid of the decimal parts = 24:36 - Then divide to reduce the ratio 24/12 = 2 and 36/12 = 3 2:32) If the ratio has mixed numbers - convert to the smaller unit
Reduce the ratio 24mm:7.2cm to its simplet form
1) Convert 7.2cm into milimetres
7.2 x 10 = 72
2) Simply the resulting ratio
24/24 = 1 and 72/24 = 3 - 1:3 - 33) To get the form 1:n or n:1 - just divide Reduce 5:54 to the form 1:n Divide both sides by 5 5/5 = 1 and 54/5 = 10.8 1:10.8Scaling up ratios:
If you know the ratio between parts and the actual size of one part, you can scale the ratio up to find the other parts - 4Example: Mortar is made from mixing sand and cement in the ratio 7:2. How many buckets of mortar will be made if 21 buckets of sand are used in the mixture?You need to multiply by 3 to go from 7 to 21 on the left-hand side - so do that to both sides
sand : cement
7x3 = 21 and 2x3 = 6
So 21 buckets of sand and 6 buckets of cement are used
Amount of mortar made = 21 + 6 = 27 - 5The two parts of a ratio are always in direct proportion. So in the example, the sand and cement are in direct proportion, meaning if the amount of sand doubles, the amount of cement doubles.Writing Ratios as Fractions:
1) To write one part as a fraction of anther part - put one number over the other
E.g. if apples and oranges are in the ratio 2:9 then we say there are 2/9 as many apples as oranges or 9/2 times as many oranges as apples - 62) To write one part as a fraction of the total - add up the parts to find the total, then put the part you want over the total E.g. a pie dough is made by mixing flour, butter and water in the ratio 3:2:1 The total number of parts is 3+2+1 = 6 So 3/6 = 1/2 of the dough is flour, 2/6 = 1/3 is butter and 1/6 is waterPart : Whole Ratios:
You may come across a ratio where the left-hand side is included in the right-hand side - these are called part : whole ratios - 7Example: Mrs Miggins owns tabby cats and ginger cats. The ratio of tabby cats to the total number of cats is 3:5. a) What fraction of Mrs Miggins' cats are tabby cats?The ratio tells you that for every 5 cats, 3 are tabby cats
part/whole = 3/5 - 8b) What is the ratio of tabby cats to ginger cats? 3 in every 5 cats are tabby, so 2 in every 5 are ginger. 5-3 = 2 For every 3 tabby cats there are 2 ginger cats tabby:ginger = 3:2c) Mrs Miggins has 12 tabby cats. How many ginger cats does she have?
Scale up the ratio from part b) to find the number of ginger cats
tabby:ginger
12/3 = 4
3x4 = 12 and 2x4 = 8
There are 8 ginger cats - 9Proportional Division: In a proportional division question a total amount is split into parts in a certain ratio The key word here is partsExample:
Jess, Mo and Greg share £9100 in the ratio 2:4:7. How much does Mo get?
1) Add up the parts
The ratio 2:4:7 means there will be a total of 13 parts
2 + 4 + 7 = 13 parts - 102) Divide to find one 'part' Just divide the total amount by the number of parts £9100/13 = £700 = 1 part3) Multiply to find the amounts:
We want to know Mo's share, which is 4 parts
4 parts = 4 x £700 = £2800 - 11Some proportional division questions don't give you the total amount. The usual method cannot be used to work it out.Example:
A baguette is cut into 3 pieces. The second piece is twice as big as the first and the third piece is five times as long as the first - 12a) Find the ratio of the lengths of the 3 pieces. Give your answer in its simplest form. If the first piece is 1 part, then the second piece is 1 x 2 = 2 parts and the third piece is 1 x 5 = 5 parts. So the ratio of the lengths is 1:2:5b) The first piece is 28cm smaller than the third piece. How long is it?
1) Work out how many parts 28cm makes up
28cm = 3rd piece - 1st piece
= 5 parts - 1 part = 4 parts
2) Divide to find one part
28cm/4 = 7cm = 1 part
3) Multiply to find the length of the 2nd piece.
2nd piece = 2 x 7cm = 14cm
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- Maths Fichas sobre Ratios, creado por Liffey Farrell el 13/05/2017.
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- Liffey Farrell
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