Comparing Fractions

Key vocabulary:

 Numerator  – The number on the top of a fraction

 Denominator – The number on the bottom of a fraction

 Lowest Common Multiple – The smallest number that is in 2 sets of a given number’s multiplication tables.

E.g.

 Finding the LCM of 4 and 6

The multiples of 4 are:

 4,8,12,16,20…

The multiples of 6 are:

 6,12,18,20…

We can see that in both lists we have the number 12, this is the lowest common multiple that is in both lists.

Therefore 12 is the LCM

Equivalent – when something has the same value but might look different

Learning:

Comparing fractions is important because it shows you how much of the whole is being represented within each fraction.

Imagine you had a bag of sweets and you wanted to share them between your friends. You wouldn’t be happy if you for 3 and everyone else got 10 would you!? So we need to be able to compare fractions to make sure everyone would get an equal part.

Some fractions are easy to compare, for example:

We can clearly see that 3/4 has a greater value than 1/4 and therefore we would say that

3/4  > 1/4

This was super easy because our denominators (the amount our whole is cut into) were the same value, therefore we only needed to look at the numerator (the amount of parts we have) to see which fraction was bigger.

But what if our denominators are NOT the same? Let’s look at comparing these fractions:

When we look at these fractions with a bar model, it is clear that 4/5 has the greater value. But what would we do if we didn’t have the bar model?

Step 1 – Find a common denominator

Our first step is to find a common denominator which we can use to make ‘equivalent fractions’ To do this we can look for the LCM of the existing denominators

When we look at these multiples, we can see that there is a common multiple between these two sets. The number 20 is both a multiple of 5 and 4. It is also the lowest common number between both groups. Therefore, 20 is the LCM.

Step 2 – Re-write the fraction using the new LCM

We will now use this LCM as the new denominator for both of our fractions:

IMPORTANT: To keep our fractions equivalent, whatever we ‘do’ to the denominator we must also ‘do’ to the numerator. This will ensure that we are making an equivalent fraction and therefore keeping the value the same.

Let’s see what that looks like:

In the first fraction, to get from the 5 to the 20 we must multiply by 4

In the second fraction to get from the 4 to the 20 we must multiply by 5

Remember, what we do to the denominator we must do to the numerator. So, we must also multiply the numerator by the same amount. Like this:

Now we can see that our new equivalent fractions are: 16/20 vs 15/20.

Step 3 – Compare the numerators

Now that we have common denominators, we can simply look at the numerator to see which has the greater value. In this case we have 16/20 vs 15/20

16 parts of 20 are greater than 15, therefore:

Or to show in the original form:

Next Step:

Watch the video to see how this works with other examples and then download the question sheet, fill it in and check your answers.