A ratio indicates the relative sizes of two or more quantities that
have the same kind of measurement, like length or weight. When you
write a ratio you use the symbol : between the numbers. For example
if you weigh 75 pounds and your parent weighs 150 pounds, the ratio
of your weights is 75:150. That seems a bit cumbersome, doesn't it?
Let's look at the numbers a little bit more. It's easy to see that
75 x 2 = 150, so 75 is half of 150. Your parent weighs twice as much
as you do. A better way to write the ratio is 1:2 which shows that
your parent weighs twice as much as you do. In fact, ratios are often
written so that the first number is 1. This way the ratio gives you
a quick idea of how the two items are related.
Sometimes the numbers in the ratio aren't exact but still give you
a reasonably accurate idea of the relationship between the two things
being compared. What if you weighed 72 pounds and your parent weighed
156 pounds? It's still accurate to say that the ratio of your weights
Another way to simplify a ratio is to divide the numbers by 10, 100
or 1,000. For example if the numbers to compare were 6,467 and 8,953,
you could say that the ratio was 6:9 (8,953 was rounded up to 9,000).
This can be simplified as 2:3. Do you see how this was done? Three
is the highest common factor between 6 and 9. Isn't the ratio 2:3
easier to comprehend than 6,467:8,953?
When the ratio was 1:2 you understood right away that one person
weighed half as much as the other. You can write half as the fraction
1/2. In a fraction the first number is the numerator and the second
number is the denominator. The denominator (the number after the /)
shows how many parts into which the item is divided. The numerator
(the number before the /) shows how many parts are in the fraction.
What happens when you look at the example where the ratio turned
out to be 2:3? Can you say that the first number is two-thirds of
the second? Let's do the arithmetic.
8,953 x 2/3 = 17906/3 = 5968.66
You see, a ratio is designed to give us a general idea of
how two values are related but it's not always exact. The ratio and
the fraction made from the ratio don't always give the same result.
It's okay to say the ratio is 1:2 because everyone knows ratios indicate
the general relationship between two items. But if you wanted to use
the fraction, you would have to say that item one is approximately
2/3 of item two because fractions are meant to be exact numbers.
Let's look at another example. Pretend that you have 10 beach balls,
4 red and 6 yellow. What is the ratio of red balls to yellow balls?
That would be 4:6 which would simplify to 2:3, the same as our last
example. If you convert the ratio to a fraction, you get 2/3. But
what does 2/3 mean?
While the numbers come out okay, that 2/3 x 6 = 4, you can't say
that 2/3 of the yellow balls are red, can you? Let's try something
else. There are 10 balls and 2/3 of the balls are yellow. Does that
work? Do the arithmetic:
10 x 2/3 = 20/3 = 6.666
There's no such thing as 0.666 of a ball, is there?
By now you should be convinced that a ratio and a fraction are not
the same thing.