Before considering what an equivalent fraction is, let's recap our understanding of a fraction.
Definitions from a mathematical mouse
fraction: a part of a whole or part of a group which has been split into equal parts or equal groups
equivalent fractions: two or more fractions that have the same value - the same part of the whole or the same part of the group.
So that this is possible, the equivalent fractions will have different sizes of pieces/sections (denominators) but also will have a different number of those pieces (numerators).
I think it’s time for some classic MwaM diagrams to explain more clearly.
In each of the diagrams below, the whole group is made up of 18 squirrels - this is always the same even if the fraction is expressed in a different way.
Next, before we consider how to find lowest common denominators, let’s recap, our understanding of what a denominator is, and then, we need to learn how to find the lowest common multiples. Yes, you heard me correctly… Lowest common multiples!
If you want to practise finding common multiples, this manipulative from Mathsframe is perfect. You can view the multiples of a chosen number separately as you can see above or...wait for it...combine them to create diagrams like those below. I especially love how they use stripes for the common multiples!
This exact skill can be transferred to finding lowest common denominators, which is so important when adding and subtracting fractions.
ACTIVITY TIME
All aboard the Multiples and Factors train! Iin this activity, choo choo choose multiples rather than factors and then identify the lowest common multiple. Make sure you use my tips (see my guide above) to ensure that you find the lowest common multiple. Remember, if these were denominators, this skill would help you find the lowest common denominator. Simples!
The first thing you will notice when you enter Fraction Forest is that it feels a bit like being in a theme park due to the great music! The maths is great too. To find the equivalent frwctions, you need to make some changes to the fractions. If it seems unclear about what to do, you can have a look at the teacher's guide. I have added a helpful link below. Hope you don’t get lost in the forest!
Although Pyramid Math 2 from mathnook.com can be used for a range of maths skills, in my mousematical opinion, it is best for practising finding the lowest common multiple (LCM) which is a perfect skill when finding the lowest common denominator, and also for finding the greatest common factor (GCF) which is important when trying to simplify fractions.
Although the first two challenges in this great game from mathplayground.com relate to fractions on a number line, the third challenge involves finding equivalent fractions to the one indicated on the number line. Can you complete the whole chart? Why I do believe that you can! Don't forget to shout out Bin-Bing-Bingo! (unless you are playing on your own and that might be a bit strange!)
Hang the monkeys on the number line. How often do you get to say that? Well, that's exactly what you need to do in this great puzzle from digipuzzle.net With each level you manage to complete, the challenge increases until there are more and more and more monkeys!
Most tasks either ask for you to find the smallest or largest. Fickle Fractions can't make up its mind so you need to pay attention. Don't fall into its trap!
It's time for Tony to get a slice of the action in Tony Fraction's Pizza Shop. Read the instructions if you want to make the perfect pizza or you might be pointlessly clickly without success and won't be able to make these delicious pizzas from mrnussbaum.com