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Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: So let’s look at another way of comparing two fractions. So we’ve got our 2/5 and our 3/7 again, and we’d like to know which one’s larger. Is there another way of doing this?

Skip to 0 minutes and 17 seconds PAULA KELLY: Yeah, there’s lots of methods. So this time, rather than compare numerators, we’re going to have a look and make equal denominators. OK, so let’s start again, same chocolate bar, same as yours. I’m going to have 2/5.

Skip to 0 minutes and 35 seconds MICHAEL ANDERSON: And I’ll shade in three of the sevens here.

Skip to 0 minutes and 46 seconds PAULA KELLY: OK, so if we’re going to compare these two fractions, we could do with a common denominator. So we’re thinking of a number, the lowest common denominator. So what number do 5 and 7 go into?

Skip to 1 minute and 1 second MICHAEL ANDERSON: So if we think of the 5 times tables or the 7 times tables, which number’s in both? Well, I’m going up in 5’s– 5, 10, 15, 20, 25, 30. 35 seems to be the first one, because that’s also in the 7 times tables. So should we go for that?

Skip to 1 minute and 16 seconds PAULA KELLY: Let’s do that. And if you weren’t sure, what we could do is, list our 5’s, list our 7’s, and look for the first number to appear in both lists. OK, so we want to have a fraction of 35. So for my 2/5, if I notice that I have multiplied this by 7, to keep our equivalent fraction, the amount I’m eating is mostly the same. Or also times this by 7. So I should have of an equivalent fraction, 40/35.

Skip to 1 minute and 46 seconds MICHAEL ANDERSON: So what you’ve done there is taken each fifth and you divided it into seven equal parts. And then we’ve got five lots of seven, which gives us our 35. And these two powers have been split, again, into sevenths. And that gives us 14 smaller parts out of 35.

Skip to 2 minutes and 4 seconds PAULA KELLY: Perfect.

Skip to 2 minutes and 5 seconds MICHAEL ANDERSON: OK, so I’m going to have to try and do something similar with my 3 over 7. And I noticed that you are multiplying your 5 by 7 to get 35. And I’m going to kind of use that information, because I know that, if I multiply 7 by 5, I’m going to get 35 as well. So whatever I do to the bottom number, I also have to do to the top number. So if I multiply 7 by 5, I’m also going to multiply this 3 by 5 as well. So three lots of five or five lots of three would give us 15. So the equivalent fraction of 3 over 7 is 15 over 35. And we can compare them.

Skip to 2 minutes and 48 seconds PAULA KELLY: So yeah, we can compare. We’ve got the same denominator. Visually, we can see we have the same chocolate bar. It’s still the same size, still the same width. But each one of these has both been cut into 35 pieces.

Skip to 3 minutes and 1 second MICHAEL ANDERSON: OK, so all the pieces here are exactly the same size as the pieces here.

Skip to 3 minutes and 6 seconds PAULA KELLY: Perfect. I’m going to have 14 of them. You’re going to have 15 of them.

Skip to 3 minutes and 11 seconds MICHAEL ANDERSON: So I think this one, 3 over 7, is going to be larger than 2 over 5.

Skip to 3 minutes and 15 seconds PAULA KELLY: I think, yes, you’ve done a lot of this. So if we put in our 14, so we’ve got 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. I can see it’s still the same height. So this is how much I’m going to have.

Skip to 3 minutes and 34 seconds Let’s compare that to yours.

Skip to 3 minutes and 35 seconds MICHAEL ANDERSON: So I’ve got to shade in 15. So I’m just going to go across one more, and then shade in all of this part.

Skip to 3 minutes and 46 seconds And still, the height of the shaded bar is going to be the same as the height of this shaded bar, as well.

Skip to 3 minutes and 52 seconds PAULA KELLY: But it’s so much easier to compare. Whereas, this we had different size pieces. Now have an equivalent fraction, an equivalent amount of chocolate. But this time, we can see that all of our pieces are exactly the same size. That’s really helpful because I can see. Although with these numbers, I can see you have an extra piece compared to me, it just really helps show us visually to see you have one extra piece, which is exactly the same size as all of my pieces.

Skip to 4 minutes and 19 seconds MICHAEL ANDERSON: So this method’s possibly more useful than the previous method. Because if we’ve got common denominators, we can compare them very easily. But I can also see that, actually, when I look at 3/7 versus 2/5, 3/7 is larger. And it’s larger by 1/35, 1 out of 35.

Skip to 4 minutes and 37 seconds PAULA KELLY: Perfect.

Equivalent fractions: comparing denominators

In this video we consider a slightly different method to compare the fractions two fifths and three sevenths.

We use the method of finding equivalent fractions, this time by making the denominators equivalent and comparing the numerators.

Michael and Paula discuss why this method has a possible advantage over the previous method.

Problem worksheet

Now complete questions 5 to 11 from this week’s worksheet.

The problem worksheet is available from the Downloads at the bottom of step 1.1.

Teaching resources

A series of simple videos covering the topics we’ve looked at over the last few steps can be found on the STEM Learning website.

  • What is a fraction?
  • Equivalent fractions
  • Writing a fraction in its simplest form
  • Comparing the size of fractions
  • Calculating a fraction of an amount

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre