Today we’re talking equivalent fractions. This is where the numbers involved are different, but the actual value of the fraction is the same. For example, 1/2 and 2/4 are equivalent, or equal, to each other. We’ll learn about these through the medium of pizza and cake. If you’re hungry, you might want to get yourself a snack before you read this one.

Say you and me are having a night in, and we get a pizza*. There’s only the two of us, so we get a big one to share and cut it in half. We get two pieces, one each. This is 1/2 or one out of two parts. Then, if we were going to be fancy about it, we could cut it again into quarters. Now we have four pieces in total, two each. That’s 2/4 or two out of four parts.

We have the same amount of pizza each. it’s just in smaller pieces.

Now it’s after our pizza dinner and we decide to have some cake**. This time another friend has popped round for a cup of tea. We cut the cake into three, so that’s a 1/3 of the cake each.

That seems like a bit too much cake (as if such a thing existed) so then we cut each slice into two pieces. We now have six equal pieces of cake (3 x 2 = 6). We can have two slices each, one now and one for later. We’ve still got one third (1/3) of the cake each. So 1/3 is also equivalent or equal to 2/6.

Here are some more equivalent fractions:

What do you notice about the numerator and denominator? As the denominator gets larger, so does the numerator. Which makes sense if you think that you’re cutting your cake or pizza into smaller and smaller equal pieces, you’re definitely going to need more of them to make up the same amount. So in the case of the pizza, we cut it into two at first and then into four. We doubled the amount of pieces, so each person needed twice as many to get the same amount of pizza.

Learn more in equivalent fractions part 2.

If you have any request for Everyday Maths topics, please let me know in the comments, or email me at hello@everydaymaths.co.uk.

*Personally, I’m Coeliac, so the pizza is gluten free. Hope that’s OK. But this is the imaginary maths universe, so everything will taste delicious right?

**Also gluten-free. Also imaginary.

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