3.1 Thinking more about fractions
The next activity is different from the numerical activities you’ve seen so far: it asks you to consider some general statements about fractions and decide whether they are true or false. This will give you the chance to think more about what a fraction is.
Activity 3 True or false?
Read the following statements carefully and decide whether they are true or false.
(a) ‘Only a fraction of the group were on time’ always means that less than half the people were on time.
Hint: can you think of a fraction that is larger than one half?
Comment
False. The fraction could be or
, which are both bigger than one half. Be careful! The use of the word ‘only’ may suggest to you that it is a small fraction, perhaps less than one half, but this could be a wrong interpretation.
(b) You can write any fraction in a decimal form.
Hint: what operation does a fraction bar represent?
Comment
True. A fraction can be thought of as a division problem. For example, is the same as
. However, some decimal fractions do not stop; instead they have a repeating set of digits, such as
These are known as recurring decimals. They are accurately represented by placing a dot over the first and last numbers of the repeating set, like this:
.
Often, these decimal numbers are rounded, so you might see rounded to 0.29 or 0.286. Keep in mind that rounded values, while useful for some purposes, are not the same accurate representations as fractions.
(c) Fractions always have a value of less than one.
Hint: could the numerator (top number) of a fraction be larger than its denominator?
Comment
False. But don’t worry if you said true! This is something new, and is a bit tricky. We can have fractions that are equal to one (e.g. is equal to 1) or even bigger than one (e.g.
(seven-thirds) has a value greater than 1 because it means
, which is greater than 2. You will look more at fractions like this later this week.
Now, back to working with specific numbers, rather than general rules! In the next section you are going to look at mixed numbers – these consist of both a fraction and a whole number.
OpenLearn - Succeed with Maths – Part 1
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