# 6.1.7 True or False?

## True or False?

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

## Activity: True or False?

Read the following statements 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.

### Discussion

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

a.

True

b.

False

The correct answer is b.

### Answer

(a) 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.

### Discussion

What operation does a fraction bar represent?

a.

True

b.

False

The correct answer is a.

### Answer

(b) 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 **repeating decimals**. They
are accurately represented by placing a bar over the
repeating set, like this: .

An alternative representation for a repeating decimal is to place a dot over the first and last digit of the repeating set.

Often, these decimal numbers are rounded, so you might see rounded off to 0.29 or 0.286.

Keep in mind that rounded values, while useful for some purposes, are not the same as accurate representations.

(c) Fractions always have a value of less than one.

### Discussion

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

a.

True

b.

False

The correct answer is b.

### Answer

(c) 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.

### Brain Stretcher

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

### Discussion

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.

### Answer

(d) 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 repeating fractions: 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 proven that there are
some numbers, such as
**(pi)** and that cannot be written as fractions. These
are known as **irrational** numbers. In math, the word
*irrational *means it cannot be written as a
*ratio* of two integers.

6.1.6 Fractions of a Group