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Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: When dealing with fractions, it’s really important to consider the whole amount that we’re taking a fraction from. For example, with a fifth, we can think of pizzas. Now the whole amount is the whole pizza. And we can divide this into five equal slices. So 1/5 is one slice of pizza. Now this changes slightly when the whole isn’t just one. It could be a bag of sweets. So if we had a bag of sweets that had 10 sweets in it, the whole are the 10 sweets in total. If we would take 1/5 of the bag of sweets, that would be 2 sweets, because we can divide the 10 into five, equal sections each worth 2 sweets.

Skip to 0 minutes and 46 seconds PAULA KELLY: So we established earlier that 3/7 is larger than 2/5. Would that always be the case?

Skip to 0 minutes and 52 seconds MICHAEL ANDERSON: It depends on the examples that we’re looking at. And it’s always important to go back to that whole idea. So with 2/5, we could have, like we had previously, 10 sweets. So 2/5 of 10 sweets– if I divide my 10 by 5, and then I have 2 lots of them, that’s going to give me 4 sweets. And then similarly, if we had 3/7, let’s say we had a bigger bag of maybe 21 sweets, well, I can divide my 21, the whole, into 7 equal parts. So each part is going to be worth 3. And if I have three 7’s, I’ll have three lots of 3, and that will give me 9.

Skip to 1 minute and 30 seconds So it really just depends on the whole when we’re considering the fractions of different quantities.

Skip to 1 minute and 41 seconds So it’s important to consider our starting amount that we’re taking a fraction of. We’re going to look at one example that could be slightly more surprising. So if we look at 2/5 of 35, I can split my 35 into five equal groups, each worth 7, and then multiply those by 2. So two lots of 7 is 14. So here, 2/5 of something represents 14. We can then have a look at 3/7, a larger fraction, as we’ve seen from the diagrams. But if I take 3/7 of, say, 28, then I could take my 28, divide that into seven equal parts to give me 4 for each part. Times that by 3, so three lots of 4 gives me 12.

Skip to 2 minutes and 27 seconds So in this case, the larger fraction actually has a smaller amount, because the wholes which we’re talking about are different. In this one we have 35, and in this one we have 28. And if I’m really clever, I could try and think of fractions of different amounts where these answers might actually be the same. So we have 2/5 and 3/7, and we’re going to do 2/5 of 15. Now 5 into 15 is 3, so divide that 15 into five equal parts, I get 3. Two lots of 3 gives me 6. And then equally, if I do 3/7 of 14, 14 divided into seven equal parts is 2. And then 3 times 2 gives me 6.

Skip to 3 minutes and 12 seconds So it really depends on the question that we’ve been asked and the whole which we are working with. It turns out that I start a question it was a little bit ambiguous really it wasn’t the best of questions, because depending on what we’re looking at and the circumstances, 2/5 could be larger than 3/7, 3/7 could be larger than 2/5, or they could be the same.

Skip to 3 minutes and 33 seconds PAULA KELLY: So that can be quite ambiguous. And it’s really important, the fraction of this whole amount we’re looking at. So as a challenge, could you think of your own examples where 2/5 could be larger, where 3/7 could be larger, and as we’ve seen here, where they’re both worth the same?

A fraction of many

When we talk about fractions we often assume that the ‘whole’ is one whole one.

For example, some text books will represent two fifths by showing a pizza which has been split into five equal amounts with two slices representing two-fifths.

In this video we consider cases where the whole amount is not ONE, but MANY as in the case of a bag of sweets which contains ten sweets, the whole therefore being ten sweets. We highlight the need when referring to fractions to state not only the fraction but be clear about what the ‘whole’ is that the fraction refers to.

Problem worksheet

Now complete questions three and four from this week’s worksheet.

If you haven’t downloaded the worksheet, please go to the bottom of step 1.1.

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Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre