Skip to 0 minutes and 7 secondsMICHAEL ANDERSON: So let's take a look at our original question, where we were comparing 2/5 and 3/7.

Skip to 0 minutes and 13 secondsPAULA KELLY: OK, so I have my chocolate bar. Same size as your chocolate bar. I'm going to have 2/5. So whole thing has been cut into 5 equal slices. I'm going to have 2.

Skip to 0 minutes and 31 secondsMICHAEL ANDERSON: OK, so with the 3/7, this same size chocolate bar-- same width, same length-- has been split into 7 equal parts, and we're looking at just 3 of them.

Skip to 0 minutes and 47 secondsSo with these diagrams, it's still quite hard to compare them. It's difficult to see which one's larger, which one's smaller just by looking at these two pictures.

Skip to 0 minutes and 59 secondsPAULA KELLY: Because my slices are a different size to yours, so just looking at these, it is really difficult to tell who's had the most.

Skip to 1 minute and 6 secondsMICHAEL ANDERSON: Yeah. So what can we do to maybe help us clarify which one's larger and which one's smaller?

Skip to 1 minute and 11 secondsPAULA KELLY: Well, there's a number of different methods. We can compare, for this example, if we had a look at making our equivalent numerators. So to do that, we need a number that's a multiple of 2 and a multiple of 3.

Skip to 1 minute and 25 secondsMICHAEL ANDERSON: So a number that's in the 2 times tables and that's in the 3 times tables. Well, the smallest one is 6.

Skip to 1 minute and 30 secondsPAULA KELLY: OK, let's have that one. So I'm going to have six pieces.

Skip to 1 minute and 36 secondsMICHAEL ANDERSON: And I'm going to try and convert this to 6 as well.

Skip to 1 minute and 39 secondsPAULA KELLY: OK, so I notice, with mine, to go from 2 to 6, I multiply by 3. And that makes sense, because each of my one pieces has been cut, here, into three pieces.

Skip to 1 minute and 52 secondsMICHAEL ANDERSON: OK, yeah.

Skip to 1 minute and 53 secondsPAULA KELLY: OK.

Skip to 1 minute and 56 secondsAnd then because we have equivalent fractions, it's still the same chocolate bar-- if I multiply this by 3, let's do the same with this.

Skip to 2 minutes and 3 secondsMICHAEL ANDERSON: Right, I see.

Skip to 2 minutes and 4 secondsPAULA KELLY: So I multiply this by 3 to get 15. I should have 15 pieces here. So just to check-- so I have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

Skip to 2 minutes and 20 secondsMICHAEL ANDERSON: OK. So for 3 over 7, I'm going to do the same thing and change that into an equivalent fraction that has 6 as the numerator. So just like you were saying, I'm thinking about what I did to 3 to get to 6. Well, I'm going to multiply by 2. And that's the same when we look at the diagram. We're splitting all of these three sections into halves. So I'll have 2 here, 2 here, and 2 here. So I'll have six pieces in this new diagram. But I'm going to have to do the exact same thing to the denominator as I did to the numerator. So I'm going to multiply the 7 by 2 as well, to get 14.

Skip to 3 minutes and 1 secondPAULA KELLY: OK, so now we have the same number of slices. So I can shade in mine-- six of my slices. So I have 1, 2, 3, 4, 5, 6. And it's quite easy to see, with mine, it's the same height, same area. I'm still eating the same amount. I have six smaller pieces.

Skip to 3 minutes and 20 secondsMICHAEL ANDERSON: OK, so I'll shade in 6 of my 14 this time. So I've got 1, 2, 3, 4, 5, 6.

Skip to 3 minutes and 34 secondsShade in those bits. So how does this help?

Skip to 3 minutes and 38 secondsPAULA KELLY: So slightly easier. I can see yours is slightly higher than mine. So it does look like, actually, you're having slightly more than me.

Skip to 3 minutes and 47 secondsMICHAEL ANDERSON: So 3/7 is greater than 2/5.

Skip to 3 minutes and 49 secondsPAULA KELLY: Absolutely. Also, we could have a look at-- actually, if your chocolate bar's been split into 14 pieces, mine's been split into 15. Your slice is slightly larger than mine.

Skip to 4 minutes and 1 secondMICHAEL ANDERSON: Because we're having the same amount-- same number of slices. So you're having six pieces. I'm having six pieces. But mine are worth slightly more, each, than yours, because we've divided this one by 14 and this one by 15.

Skip to 4 minutes and 14 secondsPAULA KELLY: Absolutely. You're having six larger pieces than my six smaller pieces.

Skip to 4 minutes and 19 secondsMICHAEL ANDERSON: So 6/14 is greater than 6/15.

Equivalent fractions: comparing numerators

In this video we return to our problem of which fraction is the larger: two fifths or three sevenths?

In the previous two steps, we showed ways of creating equivalent fractions. To solve our problem, we use the method of finding equivalent fractions to find two fractions which both have the same numerators. One will need to be equivalent to two fifths, the other equivalent to three sevenths.

We see how our understanding of fractions helps decide which fraction is larger using a numerical method, rather than using a diagram.

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre