Subtraction by breaking apart

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 200,

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 53.

minus 30.

Does that make sense?

Well, let's think about it.

What they're doing,

is they're subtracting out first the 200,

so that 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

and then subtracting 30.

53 plus 30 is 83.

Now, you might be wondering

why would they even do it this way?

What is 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.

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.