So far we’ve talked about using pizza fractions to create an equivalent fractions table, and to learn to add and subtract fractions. Today we will move on to multiplying and dividing fractions! Here is the set we purchased and that you’ll see in the pictures below:
There is no reason you can’t just make your own pizza fractions either – just color some circles and cut them in the right number of pieces! It is important that you are accurate in creating equal size pieces for the fractions, so they can be exchanged for other equivalent fractions through size comparisons alone.
Pizza fractions are a great way to give hands on practice adding and subtracting fractions. Students often find fraction work confusing at first; changing it to a visual exercise helps it make sense when they move to working on paper. Here’s how to do it:
Multiplying by integers:
This one is pretty straightforward! You will need enough pizza slices for your problem. So, to multiply 2/3 x 2 – you will need 4 1/3 pieces. Put together 2 sets of 2 1/3 pieces to create 2 2/3 pieces. Explain that multiplying is just repeated addition, and show how you put 2 2/3 pieces together to multiply it by 2.
We haven’t yet discussed writing fractions greater than one. It’s pretty clear in the pizzas when you reach a whole pizza, so this should make sense right away to your students. In the above example, when we put together the 2 x 2/3 pieces we have one whole pizza and a 1/3 piece left over. So, this would be written 1 1/3.
Multiplying by simple fractions:
By simple fractions – I mean 1/a number. I think pizza fractions work well for simple fractions but are probably not the best method once you get into more advanced calculations!
To multiple by a simple fraction, first explain that since 1/2 equals 1 out of 2 equal pieces, when we multiply something by 1/2 we want to figure out which 2 equal pieces it will separate into and that is the answer. Then, pull out a 1/3 pizza piece and ask the student to figure out which pieces would be needed to divide it into 2 equal pieces. Once they figure out that they need 2 1/6 pieces – tell them great job! and then go over the problem again – 1/3 x 1/2 = 1/6.
Dividing by integers:
This is basically the same process as above. If we are dividing by 2 we want to divide what we have into 2 equal groups or pieces. So, to divide 1/3 by 2 we need to find two equal pieces which equal 1/3 when combined. Once we have them, we divide by separating the two pieces, and the answer will be that 1/3 divided into 2 pieces or groups = 2 1/6 pieces, or an answer of 1/6.
If your student hasn’t already noticed this – show them that multiplying by 1/2 and dividing by 2 give the same answer by doing both problems again. So, if they feel intimidated by multiplying by a fraction – they can instead divide by the same fraction “upside down” – so multiplying by 1/3 becomes dividing by 3/1 or 3.