# Comparing fractions (part 2)

How do you compare fractions with different denominators? Comparing fractions is a nightmare for pupils and teachers.
This is a very difficult subject to teach and probably an even worse topic to
learn. Put this on an examination paper and you will separate the wheat from
the chaff, and mostly it will be chaff. How can we be more successful and not
have to teach it year after year to the same pupils.

Comparing fractions - how many segments? |

Possibly the root of the problem is fractions are hard to
understand. Read the quote below does it ring any bells?

“It has been said that
‘fractions’ have been responsible for putting more people off mathematics than
any other single topic. In fact the very
word

*fraction*has been known to make strong men wince!”
(Nuffield Maths 3
Teachers’ Handbook: Longman 1991)

### Starting the journey

Here is one way that I have adopted which has proved
successful, it involves using a graphical method. The pupils draw the fractions
in equal size grids, then compare. You have to guide them with the size of the
fractions.

It does of course rely on them being able to employ the
strategy outlined in my previous blog which has the gripping title Comparing fractions (part 1).

So for example they are asked to compare 4/5 with 2/3. Which
of these two fractions is bigger? Give them two grids like those below which
are 3 x 5.

If they have been given enough practice and help with the
previous work they should be able to produce grids which look like this.

They should be able to spot that 4/5 is bigger than 2/3
simply by counting the squares. I suggest you do a number of questions like
this. This practice is vital and will form the basis of further discussion.

### Moving forward

Of course it my not be possible to draw grids every time. We
may want to use a numerical method but we can now link the two, graphical and
numerical. Using the example above point out we have used grids that are 3x5
and surprise, surprise that matches the values of the two denominators.

Chose another example you have given them, say compare 3/5 and
4/7, the grids they used to compare these should have been 5x7, and point out
that the dimensions match the denominators. After several examples they should
get the idea.

### Destination

Inform the pupils that this is no coincidence. The
denominators have to be the same just like the grids were the same. Using the
first question you can now demonstrate that the denominators can match the
dimensions of the grid. So

__4 x 3__=

__12__

__2 x 5__=

__10__

5 x 3 15
3 x 5 15

The link between the grid fractions shown diagrammatically
and how we compare fractions numerically is made. The visual is really
important for lot of kids, they cannot jump straight to the numbers, this
approach also establishes the only way we can compare fractions, by using
equivalent denominators.

*Does anyone else have another way of comparing fractions? If so we not leave a comment.*

*Follow me on Twitter*@ croftsr1.