Chapter 18
FRACTIONS MADE EASY
When I was in primary school I noticed that many of my teachers had problems when they had to
explain fractions. But fractions are easy.
Working with fractions
We work with fractions all the time. If you tell the time, chances are you are using fractions (half past, a
quarter to, a quarter past, etc.). When you eat half an apple, this is a fraction. When you talk about
football or basketball (half-time, second half, three-quarter time, etc.), you are talking about fractions.
We even add and subtract fractions, often without realising it or thinking about it. We know that two
quarters make a half.
Half-time during a game is at the end of the second quarter. Two quarters make one half.
If you know that half of 10 is 5, you have done a calculation involving fractions. You have half of
your 10 fingers on each hand.
So what is a fraction?
A fraction is a number such as ½. The top number — in this case 1 — is called the numerator, and the
bottom number — in this case 2 — is called the denominator.
The bottom number, the denominator, tells you how many parts something is divided into. A football
game is divided into four parts, or quarters.
The top number, the numerator, tells you how many of these parts we are working with — three-
quarters of a cake, or of a game.
Writing ½ is another way of saying 1 divided by 2. Any division problem can be expressed as a
fraction: 6/3 means 6 divided by 3; 15/5 means 15 divided by 5. Even 5,217 divided by 61 can be
written as 5,217/61. We can say that any fraction is a problem of division. Two-thirds (2/3) means 2
divided by 3.
We often have to add, subtract, multiply or divide parts of things. That is another way of saying we
often have to add, subtract, multiply or divide fractions.
I am going to give you some hints to make your work with fractions easier. (If you want to read and
learn more about fractions you can read my book Speed Mathematics.)
Here is how we add and subtract fractions.
Adding fractions
If we are adding quarters the calculation is easy. One-quarter plus one-quarter makes two-quarters, or a
half. If you add another quarter you have three-quarters. If the denominators are the same, you simply
add the numerators. For instance, if you wanted to add one-eighth plus two-eighths, you would have an
answer of three-eighths. Three-eighths plus three-eighths gives an answer of six-eighths.
How would you add one-quarter plus one-eighth?
If you change the quarter to 2/8 then you have an easy calculation of 2/8 + 1/8.