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Video: Solving Word Problems Involving the Subtraction of Two Decimal Numbers

Tim Burnham

On a dive, some oceanographers saw a humpback whale which was 13.7 m long, and a killer whale which was 6.85 m long. How much longer was the humpback whale than the killer whale?

05:10

Video Transcript

On a dive, some oceanographers saw a humpback whale which was thirteen point seven metres long and a killer whale which was six point eight five metres long. How much longer was the humpback whale than the killer whale?

So the humpback whale was thirteen point seven metres long and the killer whale was only six point eight five metres long. And we’re trying to find the difference between these two. So we’re gonna do the calculation thirteen point seven take away six point eight five. And our answer is going to be in metres.

Now we’re gonna look at this in two different ways. So to start off with, let’s just do a straight column subtraction. So we can write that out like this: thirteen point seven take away six point eight five. Now I’m just gonna quickly write in the values of those digits in each of the different columns. So we got numbers in the tens column, the ones or units column, the tenths column, and the hundredths column. Nay, you normally wouldn’t bother writing those out. The only reason I’ve done that in this video is that I can refer to numbers and tell you what columns they’re coming from.

Now for our first number thirteen point seven, we’ve got nothing in the hundredths column; in other words, we’ve got zero hundredths. Now I’m gonna write a zero there so that when I do the subtraction calculation, it’s gonna be easier to see what’s going on. And likewise here with six point eight five, there’s nothing in the tens column. So I’m gonna write a zero there just to make our calculation a bit easier. Well, now we’ve got our two numbers written out in full. Let’s go starting from the right, from the column that’s got the smallest place value, and work our way left. So we’re doing zero take away five. Well we can’t do that, so I’m going to borrow one from the tenths column. So this seven, I’m borrowing one from there becomes six. And instead of seven-tenths, I’ve only got six-tenths. I’m gonna carry one of those over to the hundredths column. So that’s here and that’s got a value of ten hundredths. So ten take away five is five. And now six take away eight, well I’ve got another problem again six take away will give me a negative number. So I’m gonna have to borrow one from the ones column, which means that that three becomes a two and the one that I pulled across comes over here. And that one whole one is ten-tenths. So I’ve now got ten-tenths plus the six-tenths that I had originally, so that’s sixteen-tenths. So now I’m doing sixteen take away eight, which is eight.

Now moving on to the ones column: two take away six. Well, two take away six will be negative. So again I’m gonna have to borrow one from the next column, which means that this one lot of ten here is gonna become no lots of ten. And I’m gonna carry that over to this column here. So I’ve got ten lots of one plus the two lots of one that I already had in that column, which gives me twelve. So I’m now doing twelve take away six, which is six.

And then finally in the tens column, I’ve got zero take away zero, which is just nothing. And given that that is at the beginning of the number, I’m not going to write that leading zero. And my answer then is six point eight five metres longer. So the humpback whale is twice as long as the killer whale.

Now let’s look at a different way of doing this. The difference between thirteen point seven metres and six point eight five metres, well I’m gonna represent those on a number line. And the difference between the two is this journey from six point eight five up to thirteen point seven. So I’m gonna split that journey into three little sections. So first of all, I’m gonna go from six point eight five to seven point zero, and that’s a journey of zero point one five. I’m then gonna go all the way up to thirteen point zero and from seven all the way up to thirteen is a journey of positive six. And then I’ve gotta go from thirteen point zero to thirteen point seven, which is a journey of plus zero point seven. So this distance that we’re talking about is zero point one five plus six plus zero point seven. Now zero point one five plus zero point seven is zero point eight five and zero point eight five plus six is six point eight five.

So the second method took a bit of drawing out and a bit of thinking about, but it’s boiled down to just adding together three very simple numbers: six plus zero point one five plus zero point seven. I could do that in my head; that was a very easy calculation to do. With the other method, I did lots of borrowing and carrying and all that kind of stuff which made that calculation much more tricky. They both gave me the same answer; they’re both perfectly good ways of doing that question. You just have to choose which is your favourite method.