Comparing Fractions

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Fractions Units

Comparing fractions is not as straight forward as comparing common numbers. In a fraction the numbers may appear to be larger but in fraction form their real value could be smaller. For example, 13/20 may appear bigger than 3/4 but in acutal fact it is smaller.

Numerator

Denominator

A fraction always refers to part of a whole thing. So, a fraction like 3/4 means three quarters of a thing. It could mean three quarters of a glass of water or three quarters of the population or three quarters of a footy match.

When comparing fractions we must first make sure that they parts of the same number the whole thing was divided into. This means to compare fractions, they must first have the same denominator. Comparing

Examples

Which is bigger:

Changing these to equivalent fractions with a common denominator, we can see that:

and

So, we see that

is the same thing as:

Hence,

is bigger than

Hints

In this example we can't compare these fractions as the number of parts of the whole (denominator) in two fractions is different.

We need to look for equivalent fractions of 3/4 and 4/5 that have the same numbers as denominator.

and

We can see that and

Here, we see that 16 parts out of 20 is greater than 15 parts out of 20.

Have a Go

Problem 1

Compare these to find which is greater:

or

Problem 2

Compare these:

and

Practice Questions

Question 1

Which is larger

Question 2

Which is bigger

Question 3

Which is smaller

Question 4

Which is larger

Question 5

Which is bigger

Question 6

Which is bigger

Solution 1

or

In this problem is the same as

So now we have

or

17 parts out of 21 is a greater fraction than 12 parts out of 21.

Hints

Here when we see equivalent fractions of we find that it has an equivalent fraction with 21 as a denominator. So we won't need to change for comparing them.

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Solution 2

Comparing and

First we need to change into a simple fraction

are equal fractions.

Hints
This is a bit tricky problem because the second fraction is a compound fraction and needs to be simplified first.

Note that when you divide a fraction by another number or fraction, the terms can be re-written using a multiply function:

= =

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