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Common fractions:

Learners should by now know the basics of fractions. We are going to start with comparing fractions.

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Prior knowledge learners should have:

• Know which number of the fraction is the numerator 
• Know which number of the fraction is the denominator
• LCM (Lowest common multiple)
• Equivalent fractions
• Simplifying fractions 

Comparing fractions:

Ask your learners, just by looking at these 2 fractions, if they can say which fraction is bigger and which one is smaller.

Learners will tell you that is bigger because the denominator is 5. They will say that 5 is bigger than 3. 

As a teacher you must remind them that, when working with fractions, the bigger the denominator, the smaller the fraction part will be.

Let's take an example:

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On the fraction wall, learners can see that the bigger the denominator is, the smaller the fraction part will be.

Learners will also be able to see on this fraction wall, if you add two halves, it will be equal to 1, as it will be for the rest.  If you take thirds, 3 thirds will be 1 whole. 4 Quarters added together will be equal to 1 whole etc.

If learners start comparing fractions, it will be wise to use the fraction wall at first.

Ask your learners to use their ruler to see which other fractions will be equal to

Learners can take their ruler, and do the following:

• On the fraction wall they will put their ruler on the line of a

• Place the ruler vertically on
• Go vertically down with the ruler until the line of the crosses with any other line.
• The first line it will cross here, is the fraction part of
• Count how many of these fraction parts there are in front of the ruler.
• Learners will count that there are 2 parts of 6.
• This means that is equal to .
• Ask your learners if there are more equivalent fractions on this fraction wall.

Comparing fractions without using the fraction wall

We don't always have time in class to use the fraction wall, so getting an easier way to compare fractions, we will do the following:

• The easiest and only way to compare fractions, is when the denominators are equal.
• To get the denominators equal to each other, we have to get the LCM of the denominators.
• LCM = Lowest common multiple.
• We have to get the multiples of the denominators and see which of those numbers are the lowest at both.

Comparing the following 2 fractions:

Fill in > , < or = 

The denominators are 5 and 3.

Multiples of 5 = 5 ; 10 ; 15 ; 20 ; 25 ; 30 ....

Multiples of 3 = 3 ; 6 ; 9 ; 12 ; 15 ; 18 ; 21 ; 24 ; 27 ; 30.....

Learners will see that multiples will carry on, they can give the first 5 multiples of each number to get the LCM, if there are no common multiple, they have to carry on with the multiples until there's a common number at both of the denominators.

In the example given, there are 2 numbers circled. The first common multiple is 15.  The second common multiple is 30.  Learners have to use the first common multiple of 15, because this will be the lowest common multiple.

Now that we have the LCM we can put the sum as follow:

• We've calculated the LCM as 15.  
• Learners can now put both fractions on 15 as the denominator.
• Go back to the fraction given, and see what did you do with 5 to get 15 and what did you do with 3 to get 15?

• The first fraction of , we mutliply 5 with 3 to get 15.  If we multiply with 5 at the bottom, we have to multiply with 5 at the top too.
• The second fraction , we multiply 3 with 5 to get 15.  Again, if you multiply with 3 at the bottom, you have to do the same at the top.
• Now that we have the numbers to multiply with, we can calculate the numerators too.

Learners can now see that both my denominators are the same, and they can see the different parts of the fraction.

 will be smaller than .

Writing it in mathematical language will be: