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Skip to 0 minutes and 7 seconds PAULA KELLY: OK, so we’ll look at now comparing our two fractions. There’s three different possible methods we could use. So our first one, if we want to have our equal numerators– so you want to have a number that 4 and 6 can both go into, a multiple of 4 and 6.

Skip to 0 minutes and 23 seconds MICHAEL ANDERSON: OK, so we could have 24, but 12 is also in the four times tables and in the six times tables, so should we use the smaller one?

Skip to 0 minutes and 31 seconds PAULA KELLY: Let’s have 12. Yeah, small one’s better. So we’re going to have our same numerators. We’re going to make them both into fractions with 12 as numerator. So if that’s been multiplied by 3, we know same with this one multiplied by 3. And then that’s been doubled, so also double this.

Skip to 0 minutes and 51 seconds MICHAEL ANDERSON: So how does that help us, then?

Skip to 0 minutes and 53 seconds PAULA KELLY: So we saw how we had our different ways of splitting our wholes. If something’s been split into 22 pieces, those pieces are going to be smaller than our objects with 21 pieces. So we can get the same numerator. We know these are smallest pieces. These are larger pieces. This is our large fraction.

Skip to 1 minute and 12 seconds MICHAEL ANDERSON: So 12/21 is bigger than 12/22, so 4/7 is bigger than 6/11.

Skip to 1 minute and 18 seconds PAULA KELLY: Perfect, so rather than have equal numerators, we could also have equal denominators. So we’re going to need a denominator for 7 and 11. What are they both factors of?

Skip to 1 minute and 32 seconds MICHAEL ANDERSON: Well, 7 times 11 is 77, so that would be a good one.

Skip to 1 minute and 35 seconds PAULA KELLY: Yep, and often, that’s quite a nice way of doing it, if you just multiply them together. Doesn’t always give you the smallest, OK? So with that, we’ve just done 7s into 77. We know it’s 11, so we times this by 11. We have 44.

Skip to 1 minute and 52 seconds 11s into 77, we know is 7, so six 7s are 42.

Skip to 2 minutes and 1 second So with this method, we have the same denominator. We have 42/77. We have less than 44.

Skip to 2 minutes and 9 seconds MICHAEL ANDERSON: OK, so we’ve split it into 77 parts. On this side, we’ve got 44, this side, 42. So thankfully, we get the same answer that this side is bigger than this side.

Skip to 2 minutes and 18 seconds PAULA KELLY: Yeah, it should always be the same, very good point.

Skip to 2 minutes and 21 seconds MICHAEL ANDERSON: Cool.

Skip to 2 minutes and 21 seconds PAULA KELLY: So our third and final method, we could use our division. As we know, a fraction is just a division. So 4/7– now, I would say use the calculator for this. It’ll give you a long, recurring decimal. So our 4/7 is going to be 0.5714.

Skip to 2 minutes and 40 seconds MICHAEL ANDERSON: OK, and that goes on forever?

Skip to 2 minutes and 42 seconds PAULA KELLY: It will go on forever, so I’ll do some dot, dot, dots. Such a nice pattern with those. [INAUDIBLE] Again, with our 11s, is a really nice pattern. So we know we’re going to have 0.54, also reoccurring. The five and the four will reoccur.

Skip to 2 minutes and 57 seconds MICHAEL ANDERSON: And that’s just using the calculator, 6 divided by 11?

Skip to 3 minutes and 0 seconds PAULA KELLY: Very much, yeah. So similar to how we saw our comparing decimals with our place value, we’ve got zero units, same so far. Tenths, again, are the same. Our hundreds, however, we have– so seven hundredths, four hundredths here. So thankfully, again, this is our largest number.

Skip to 3 minutes and 22 seconds MICHAEL ANDERSON: Excellent.

Skip to 3 minutes and 24 seconds PAULA KELLY: So three different methods–

Skip to 3 minutes and 26 seconds MICHAEL ANDERSON: Yeah, which one would you recommend, then?

Skip to 3 minutes and 28 seconds PAULA KELLY: Entirely depends where you have some quite small numbers to have your quite low numerators. However, you probably wouldn’t use your calculator method for these numbers. They’re quite tricky numbers. It really depends on personal preference and what numbers you have.

Skip to 3 minutes and 42 seconds MICHAEL ANDERSON: And if you’ve got a calculator to hand.

Skip to 3 minutes and 43 seconds PAULA KELLY: Yes, very much, yes, yeah.

Skip to 3 minutes and 45 seconds MICHAEL ANDERSON: Excellent.

Comparisons: fractions

When comparing fractions it is useful to have a number of strategies to call on. The strategy chosen may depend upon whether the fractions being compared or whether you are able to use a calculator.

In Week 1 we looked at comparing fractions by making the denominator the same, or making the numerator the same. To work out what value denominator or numerator to use, we find the lowest common multiple.

In this step, Paula and Michael consider three methods which build upon skills covered earlier in the course: finding equivalent fractions (making denominators or numerators the same) and converting a fraction to a decimal. Watch the video and consider each of the three methods.


In the comments below, share the advantages and disadvantages of using each of the methods:

  • Making denominators the same.
  • Making numerators the same.
  • Converting fractions to decimals

Are there any observations you can make about how you might need to plan to teach the skills needed for each approach?

Problem worksheet

Now complete question 4 from this week’s worksheet.

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre