# 3.1 Thinking more about fractions

Before you continue by looking at different types of fractions, you’re going to think about some general statements about fractions and decide whether they are always true. This will give you the chance to think more about what is a fraction.

This activity is different from the numerical activities you’ve seen so far: it asks you to consider some general statements about fractions.

## Activity 4 True or false?

Read the following statements carefully and decide whether they are true or false. Remember to click on 'Reveal comment' if you need a hint.

(a) ‘Only a fraction of the group were on time’ always means that less than half the people were on time.

### Comment

Can you think of a fraction that is larger than one half?

a.

True

b.

False

The correct answer is b.

### 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.

### Comment

What operation does a fraction bar represent?

a.

True

b.

False

The correct answer is a.

### 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.

### Comment

Could the numerator (top number) of a fraction be larger than its denominator?

a.

True

b.

False

The correct answer is b.

### Comment

False. A positive fraction in which the numerator is greater than the denominator has a value greater than 1. For example, (seven-thirds) has a value greater than 1 because it means , which is greater than 2.

(d) A number can always be written as a fraction.

### Comment

Can you write a whole number as a fraction? Can you write a decimal number such as 0.375 as a fraction?

a.

True

b.

False

The correct answer is b.

### Comment

False. Some numbers, but not all, can be written as fractions. Whole numbers, such as 8, can be written with a denominator of 1, like this:

So, if you have a finite number that stops after a certain number of decimal places, then it can be written as a fraction; for example:

These are not approximations or recurring decimals: 0.375 is exactly equal to: .

Even decimals that have a repeating sequence can be written as fractions; for example:

and .

However, it can be shown that there are some numbers, such as π (**pi**) and (square root of two) that cannot be written as fractions. These are known as **irrational** numbers. In maths, the word *irrational *means a number cannot be written as a **ratio** of two whole numbers – that is, a fraction.

If you are interested you can search the internet to find out to how many decimal places pi has been calculated.

Now, back to working with numbers! In the next section you are going to look at mixed numbers – these consist of both a fraction and a whole number.