# Some Simple Mistakes Children Make With Fractions

I have read that when adding fractions some children make the mistake of adding both the top and the bottom, for example $frac{1}{6} + frac{1}{6} = frac{2}{12}$

Now it may be that these children were not taught very well.

Or maybe they have not had enough practice with adding fractions.

Probably the most useful piece of advice with maths is to think of a physical example.

I like to think of cake.

If a cake is cut into 6 parts and you eat 1 part and then another part how many have you eaten?

Most children can get that right, although they might think the answer is so obvious that you’re a bit silly for asking.

A slightly different questions is

If a cake is cut into 6 parts and you eat 1 part and then another part how many parts of the whole cake have you eaten?

2 parts of the 6 parts that made up the cake.

When your children are learning fractions (or any part of maths) encourage them to think of physical examples for the questions they have to answer.

When talking about fractions explain that we start with a whole of something (cake) then split it into parts.  When we add fractions we are counting the number of parts, but we need to remember how many parts the whole was split into. So when we say

one sixth and one sixth

this is short hand for

one sixth part of the whole and one sixth part of the whole

it should be more obvious that the answer is two sixth parts of the whole.

To make it more obvious why not get a real cake and cut it up!

Once your children understand what is meant they should find it easier to understand $frac{1}{6} + frac{1}{6} = frac{2}{6}$

is just a short hand way of writing this down.  The number on the bottom is the number of equal parts the whole (e.g cake) was divided into, the number on the top is the number of these parts.

In English there are two sets of names for numbers,  Cardinals and Ordinals. Cardinals are just ordinary numbers.  Ordinals are the names we use for the position of something, say in a race.  Most of these names come from Anglo Saxon but a few from Latin.

Cardinal Ordinal Fraction
one first
two second half
three third third
four fourth quarter
five fifth fifth
six sixth sixth

The first few numbers are a bit irregular but from 6 onwards there is a pattern

• The cardinal is just the ordinal with “th” at the end.
• The fraction is the same as the cardinal.

Second and quarter come from Latin, the rest from Anglo Saxon.  Half was special even in Anglo-Saxon.

It is not hard to imagine that fraction started out as something like

One equal part of six

which over time changed to

One part of six, or one sixth part

and finally was abbreviated to just

One sixth

Even if this was not how the names of fractions developed it is a story, and stories are great ways to convey ideas.  The idea we want to  convey is that fractions are about parts of a whole.  When we add fractions we just count the number of parts, the size of the parts never changes.

Maths, at least at school level, is a means of calculating answers by manipulating symbols rather than stuff.  The rules have been designed to give the same answer as you would get if you actually did manipulate stuff.  It’s worth explaining this to your children so they understand it’s not a collection of squiggles but a description of what would happen in the real world.  For example, cutting a piece of cake into 6 equally sized pieces and then taking two of them.

This entry was posted in Fractions. Bookmark the permalink.