Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: Let’s have a look at subtracting with fractions.
Skip to 0 minutes and 11 seconds PAULA KELLY: OK. So we have here two fractions, common denominator. We have this whole one that’s been split into six sections. We’re going to say we have 5 of them. So we have 5/6.
Skip to 0 minutes and 28 seconds So from this, we’re going to subtract 3/6. So it’s been cut into 6 pieces. We have 3 of them.
Skip to 0 minutes and 39 seconds So looking at subtraction, we had 5/6 to begin. We took away 3 of them. We’re left with just 2 of them.
Skip to 0 minutes and 48 seconds MICHAEL ANDERSON: 2.
Skip to 0 minutes and 50 seconds PAULA KELLY: Another way to think about this is, what’s the difference between our 5/6 and 3/6.
Skip to 0 minutes and 58 seconds MICHAEL ANDERSON: If you look at the height almost, there’s two more in the 5/6 than there are in the 3/6. So again, the answer would be 2 out of 6.
Skip to 1 minute and 5 seconds PAULA KELLY: Fantastic. Good. OK. So I could write this as 2 out of 6.
Skip to 1 minute and 11 seconds MICHAEL ANDERSON: So is that it? Are we done?
Skip to 1 minute and 13 seconds PAULA KELLY: Well, we wouldn’t ever leave a fraction unsimplified.
Skip to 1 minute and 16 seconds MICHAEL ANDERSON: OK. Yep. So 2/6, we can look to simplify. They’re both even, so we can divide them both by 2. So I’m going to take the top number, and divide it by 2 to give me 1. I’m going to take 6, and do the exact same. Divide by 2 to give me 3. So that’ going to give me 1/3.
Skip to 1 minute and 33 seconds PAULA KELLY: We can see through my diagram as well if we had our equivalent fraction. We haven’t changed the size of our fraction, we just simplified it. Now if we come this way across, we can see here our whole one now is just in three pieces. And we have a full one of these, so one out of three.
Skip to 1 minute and 55 seconds MICHAEL ANDERSON: That makes sense, because we’ve got these two here, and then another two, and another two. So 2 out of 6 must be equal to 1/3.
Skip to 2 minutes and 3 seconds PAULA KELLY: Perfect.
Skip to 2 minutes and 5 seconds MICHAEL ANDERSON: So let’s have a look at an example where we’re subtracting two fractions with different denominators.
Skip to 2 minutes and 12 seconds PAULA KELLY: OK. If we look here, we have 5/6, subtract 1/4. So we know at the moment, looking at our diagrams, our parts of our whole are different sizes. So my whole has been cut into 6 equal parts, and I’m going to have 5 of them.
Skip to 2 minutes and 35 seconds MICHAEL ANDERSON: And for mine, the 1/4, it’s been split into 4 equal parts. And I’m just interested in one of them, 1/4.
Skip to 2 minutes and 46 seconds PAULA KELLY: OK. So before we can subtract them, we need to have our parts equally sized.
Skip to 2 minutes and 52 seconds MICHAEL ANDERSON: OK. Just like what we were doing with addition?
Skip to 2 minutes and 55 seconds PAULA KELLY: Exactly the same. Yeah, exactly. So again, same as with addition, looking for a common denominator. There are lots of numbers that are multiples of both 6 and 4.
Skip to 3 minutes and 5 seconds MICHAEL ANDERSON: 24, or 48, or something like that?
Skip to 3 minutes and 9 seconds PAULA KELLY: So ideally, we’d have our smallest or lowest common denominator. If we listed our 6 times table, our 4 times table, the first common number we’d come to would be 12.
Skip to 3 minutes and 19 seconds MICHAEL ANDERSON: OK. Yeah. Sounds good.
Skip to 3 minutes and 20 seconds PAULA KELLY: So let’s make this into a fraction out of 12. To get from a 6 to 12, I’m quite clear. I need to double it. So I’d double this as well, keep the same size. I’m going to have 10 out of 12.
Skip to 3 minutes and 35 seconds MICHAEL ANDERSON: OK. So you have converted your sixths into twelfths. I need to convert my quarters into twelfths as well. So to do that, I could think about splitting these up into three equal parts. And I’m going to multiply my 4 by 3 to give me that 12. I’m going to do the same to the 1, and times that by 3. 1 multiplied by 3 gives me 3/12.
Skip to 3 minutes and 59 seconds PAULA KELLY: Fantastic. OK. So now we can compare our two numbers, with our are wholes cut into the same size pieces. So again, I’m going to come straight across. Our areas are the same. I’m going to have 10 of these twelfths.
Skip to 4 minutes and 19 seconds MICHAEL ANDERSON: And 1/4 was equal to 3/12, so I’m going to fill in this bit, which thankfully is the exact same height as I started with.
Skip to 4 minutes and 29 seconds PAULA KELLY: Perfect. So if we’re doing a subtraction, if we’re starting with 10/12, and I’m subtracting 3 of these twelfths, I’m going to have 7/12 left.
Skip to 4 minutes and 41 seconds MICHAEL ANDERSON: So if you started here at 10, we dropped down 1, 2, 3, this area here would give us our solution? 7/12?
Skip to 4 minutes and 49 seconds PAULA KELLY: Yeah. In a very similar way, if we started here with our 10, if I came down 7 places, I’d end up with 3/12.
Skip to 4 minutes and 57 seconds MICHAEL ANDERSON: So the difference between 10/12 and 3/12 is 7/12. And the answer to our original question, 5/6 take away 1/4 quarter is 7/12.
Skip to 5 minutes and 7 seconds PAULA KELLY: Perfect.
The way questions are phrased and the use of language can support student understanding, particularly as students begin to notice the similarities between the way questions are constructed and the words and phrases used in questions.
When students first meet subtraction of whole numbers it is most often approached using the concept of ‘taking away’ one number from the other. For example questions like: if I have 6 counters and I take away 4 counters, how many counters do I have left?
This idea can be used when subtracting fractions. For example, if I have six tenths of a pizza and I take away four tenths of a pizza, how much pizza have I got left?
Another approach is to talk about ‘difference between’. Rather than say what is six tenths take away four tenths use the language ‘what is the difference between six tenths and four tenths’.
In this video Paula and Michael explore techniques to develop understanding when subtracting one fraction from another.
Now complete questions 7 and 8 from this week’s worksheet.
As a reminder, the worksheet can be found in the first step of this week.
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