Subtraction by breaking apart | Khan Academy

We're told that Linde isn't sure how to

subtract 853, we are told Linde isn't

sure how to subtract 853 minus 283.

Help Linde by choosing an expression that

is the same as 853 minus 283.

So pause this video and see if you can

answer it on your own before we work

through it together. Alright, now that we

look at all the choices, they all start

with 853. Now, this first choice they

subtract out 200.

That makes sense because we

have 2 hundreds right over there.

Then they subtract out 50 and then they

subtract out 3,

so the 200 and the 3 make sense.

You can view 853 minus 283 as 853 minus

200s minus 80, 8 tens right here, minus 3.

But that's not what they wrote over here.

Instead of putting 80 here, they put a 50.

So we can rule that out.

Here we have 853 minus 20 minus 800 minus

3. Well this is a little bit strange

because we don't have 2 tens, we have 2

hundreds and we don't have 8 hundreds. We

have 8 tens, so this is also incorrect.

Now it's probably going to be this one,

but let's just make sure we feel

comfortable with this.

So this one has 853 minus 200 minus 50

minus 30. Does that make sense?

Well let's think about it. What they're

doing, they're subtracting out first the

200s, this part right over here, so that

makes sense. They're subtracting out first

that. And then they're subtracting out 53

and then subtracting out 30. Well, that is

the same thing as subtracting out 83

because subtracting out 83 is the same

thing as subtracting out 53 and

subtracting 30. 53 plus 30 is 83. Now, you

might be wondering why would they even do

it this way? Well, it's easier to do in

your head. 853 minus 200 is 653.

You take away

53 from that, so you take away 53 from

that and you're going to be left with 600.

And then 600 minus 30, you might recognize

that you could do 60 tens minus 3 tens,

it's going to be 57 tens or you might be

able to do it in your head, 600 minus 30

is 570. So that's why they broke out, they

broke up the 83. Instead of just breaking

it up into 80 and 3, they broke it up into

53 and 30 to match this 53 over here, so

it's easier to work out the result.

Let's do another example. So here we're

asked to fill in the blank. They say 143

minus 79 is the same as blank minus 80.

So pause this video and see if you can

figure this out.

So the key here is to realize is when

you have a difference here, as long as you

add or subtract the same amount to both of

these, the difference will be the same.

So it looks like they tried to turn 79

into, it looks like they turned the 79

into an 80 by adding 1 and so if we want

the difference to be the same, we would

add 1 to the 143 as well. So 143 plus 1 is

144. If we add one to both of these

numbers the difference would be the same.

And we're done. So it's 144 minus 80.