Nodehill Maths

Simple fractions - How to recognise them.

Children tend not to like the topic of fractions, as the groans I get from classes when I say that we will be doing some fraction work testify. However as long as children can count they should be able to recognise simple fractions.

Fractions basically have a bottom number (denominator) which explains into how many equal pieces the object or shape is divided into, and a top number (numerator) which says how many lots of those pieces you have.

If you look at the fractions here, each one has been divided into ten equal pieces, and you have 3 lots of these pieces shaded, so each fraction is 3/10.

A common mistake that children would make would be to say that each of these is actually 3/7. This is because they count the number of shaded pieces first (3), and than merely count how many are left unshaded (7) and make this the denominator.

Because examiners know that in order to recognise fractions all children really have to be able to do is  count, they try to make it more difficult by sometimes not drawing in all the dividing lines. If this is the case all the children have to do is draw the dividing lines onto the shape, before counting.

I have included a worksheet, which can be downloaded below, on which the children can practise recognising fractions where the dividing lines have been put in, and some where they have been omitted. I have also put in a blank sheet, which you can colour in, in order to give your child extra practise.

Download microsoft_word_fractions.pdf

Equivalent Fractions

Once children can recognise basic fractions, they must then be able to say which fractions are the same size as each other i.e. equivalent. e.g. 1/2 is the same size as 2/4 or 3/6 or 12/24 etc.

The basic trick, which childen need to grasp, in order to find equivalent fractions, is that if they multiply the numerator and denominator by the same number, the new fraction will be equivalent to the old one. e.g. if you have 3/4 and multiply the numerator by 3 and the denominator by 3 you will end up with 9/12. This is because:- 3 x 3 = 9, 4 x 3 = 12 so 3/4 and 9/12 are equivalent.

Therefore finding equivalent fractions is really just practising children's table knowledge, for all they are really doing is multiplying the top and bottom of the fraction by the same number, which is why I often use it as a mental warm up. I will ask, "What fraction is the same size as 3/8?" They will then multiply the numerator and denominator by the same figure and get 6/16, 9/24, 15/40, 30/80 etc. They can thus easily practise this at home, for all you have to do is ask, "Can you give me three fractions the same size as 4/5?" or 5/6, or 5/9 etc.

I have included a worksheet which you can print off which deals with equivalent fractions, and as usual it includes a blank, which can also be printed if they require more help.

Download microsoft_word_equivalents.pdf

Fractions of Numbers

Children are often asked in tests to find fractions of numbers, such as, what is 3/8 of 24? 5/6 of 42? etc. It is a topic which they seem to struggle with, as they find it hard to visualise the problem, but if a child can visualise a problem they are much more likely to be able to solve it.

I thus explain to children that fractions of numbers has a lot to do with either cake, or chocolate bars (two of my favoutire things). If you wanted to find 3/8 of a chocolate bar the first thing that you would have to do is break up the chocolate bar, or divide it, into 8 equal pieces. You would then take 3 lots of these pieces. Similarly if you wanted to find 5/6 of a cake you would cut, or divide, the cake into 6 pieces and then take 5 lots of the pieces. 

Therefore if you wanted to find 3/8 of 24 you would do exactly the same. You would firstly divide the number 24 into 8 equal pieces (each piece being worth 3 because 24 divided by 8 is 3) and then take 3 lots of these pieces (3 x 3 = 9) so 3/8 of 24 is 9.

Similarly to find 5/6 of 42 you would divide 42 into 6 equal pieces (each piece being worth 7) and then take 5 lots of these pieces (5 x 7 = 35). Thus 5/6 of 42 = 35.

I find it a lot easier if the children draw diagrams to help them visualise what is happening, although after a lot of practice and examples they should notice the pattern that they are always dividing the number by the denominator (bottom number) and multiplying the answer to this division sum by the numerator (top number). Hence the mantra DBMAT - Divide by the Bottom and Multiply the Answer by the Top.

Below I have put two worksheets which may be downloaded in order to practise finding fractions of numbers. The first download gives visual clues, whereas the second relies on the children being able to calculate them. As always both sheets have one page with questions completed followed by a blank on which different numbers can be added, so that your child can have plenty of practise. Although the lines on the first document look odd, they do seem to print out fine.

Download microsoft_word_visual_fractions_of_numbers.pdf

Download microsoft_word_calculating_fractions_of_numbers..pdf