Ratio
Two different things (or quantities) can be compared in a variety
of ways. Take the Smith brothers for example…
Walter Wilbur
If Walter weighs 50kg and Wilbur weighs 75kg, then we can
compare their weights by saying
Wilbur is heavier than Walter.
Wilbur is 11/2 times as heavy as Walter.
Wilbur is 25kg heavier than Walter.
Another way of comparing their weights is to show them as a ratio.
That’s all ratio is… a way of comparing two things. We can show
their weights as
50:75
Teachers always like you to show this in its simplest form though
and that means cancelling down. What number goes into both 50
and 75? 25! So we divide 50 by 25 to get 2 and 75 by 25 to get 3.
Instead of showing the ratio as
50:75
we can now show it as
2:3
What this tells us is that for every 2kg Walter weighs, Wilbur
weighs 3.
(By the way, Walter and Wilbur both support Sunderland. Ha’way
the Lads!)
We can use ratio to compare lots of things. Suppose that in a
class there are 12 boys and 16 girls and we are asked to find the
ratio of boys to girls. This means find out how many boys there are
for every girl in the class. Remember when we see : we say ‘for
every’, so instead of writing out there are 12 boys for every girl, we
can write 12:16. Less writing so it must be easier! Don’t forget to
cancel down and put the ratio in its simplest form. What number
goes into 12 and 16 exactly? 4! So we divide 12 by 4 to get 3 and
16 by 4 to get 4. We can now write the ratio of boys to girls as
3:4
Sometimes a problem will give you the ratio and ask you to work
out how many of something there is, but don’t let this bamboozle
you, just work through the problem backwards. Suppose you’re
presented with this problem…
Q. It’s Mrs Thompson’s birthday and the children bring her a box
of sweets. The box contains a total of 35 chocolates and toffees in
a ratio of 3:4. How many chocolates are in the box and how many
toffees are in the box?
A. This tells us that there are 3 chocolates for every 4 toffees in
the box. So we have to work out how many times we could take out
3 chocolates and 4 toffees until the box was empty. The really,
really easy way to do this is add the two numbers in the ratio ‘3:4’
(3+4=7) and divide the total number of sweets by this amount.
Total number of sweets = 35
Divided by 7 (Ratio was 3:4, so 3+4.)
35 7 = 5
Now we multiply each number in the ratio by 5 and this should give
us the number of chocolates and toffees in the box.
Ratio = 3:4
3 x 5 = 15
4 x 5 = 20
There are 15 chocolates and 20 toffees in the box of sweets.
Always remember to check to see if your answer is reasonable.
You have said there are 15 chocolates and 20 toffees. Does this
add up to the number of sweets you were told were in the box
altogether?
15 + 20 = 35
Is that a
reasonable
answer?