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… understand ratio
We use ratios to make comparisons between two things. It’s a way of
comparing the relationship between the quantity or amount of one thing and
another.
For example, a joiner makes 7 sash windows for every 10 casement windows.
We can write this:

in words. When we express ratios in words, we use the word ‘to’. The
ratio of sash to casement windows is ‘seven to ten’.

as a ratio. When expressed as a ratio, it uses the ‘:’ symbol. In our
example, the ratio of sash to casement windows is 7:10.
We can also swap the ratio (and the order in which we write the objects)
around:

the ratio of casement to sash windows is 10:7.
Simplifying ratios
In a workshop, the ratio of softwood to hardwood doors made is 70 to 20,
so the ratio of softwood to hardwood is 70:20.
We can simplify this ratio by dividing both numbers by 10 to give a ratio of
7:2.
Ratios and fractions
A workshop discovers that the ratio of teak to oak doors made is 3:4. In
other words, for every 7 hardwood doors made, 3 will be teak and 4 will be
oak.
We can write this result as a fraction:
3
/7 of the doors are teak.
4
/7 of the doors are oak.
If the workshop made 21 hardwood doors, then we can estimate that:
3
x 21 = 9 will be teak
7
4
x 21 = 12 will be oak
7
Try these!
What’s the ratio of softwood to hardwood?
Key
Softwood
Hardwood
What fraction of the wood used is hardwood?
Ratios and proportion
If the ratio of two items stays the same even when the quantities increase
or decrease, then they are in direct proportion to each other.
For example, a company may add a £10 mark-up for every £30 of materials.
If you double the quantities, you’d charge £20 on £60 worth of materials.
Try these!
Fitting an interior door requires:
1 door
2 hinges
2 door handles
12 screws
15 panes of glass
 What is the ratio of hinges to screws?
 What is the ratio of screws to hinges?
 How many screws would you use with 30 hinges?
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