645 divided by 43 equals what?
How do we know that this is a
division question? There isn’t a division symbol. Well, when we set a calculation out
like this using these two lines, it shows us that what we’re doing is splitting 645
into 43. We need to ask ourselves how many
of this number fit into this number.
We start by looking at the number
645 digit by digit. We know there are no 43s in the
number six because it’s too small. So let’s look at the first two
digits instead. How many 43s are in 64?
Well, we know that there’s
definitely one lot of 43. But two lots of 43 is going to be
80 something, so it’s going to be too large. There’s only one lot of 43 in
64. So we can write the number one at
the top. One lot of 43 equals 43. So if we write this underneath 64,
we can subtract the two numbers to find out what’s left. What’s the reminder? 64 take away 43 leaves us with
Let’s keep dividing. How many 43s are in 21? Well, 21 is too small. Let’s bring down the five ones from
our original number and include those. How many 43s are in 215? If we think of the number 43 as
being around 40, then we can say that two lots of 43 is about 80 something. And four lots of 43 would be double
that, so it would be around 160. 160 is getting closer to 215. So we can estimate our answer might
be five 43s, possibly six 43s.
We don’t know what five 43s
are. But we do know what 10 43s are. We can use this to help. Multiplying by 10 is always quite
quick to do. 43 multiplied by 10 equals 430. Half of 10 is five. So the answer to 43 times five will
be half of the answer to 43 times 10.
What is half of 430? Half of 400 is 200, and half of 30
is 15. So half of 430 is 215. And that’s exactly the number that
we wanted to divide by 43. There are five lots of 43 in
215. So let’s write the digit five at
the top as part of our answer. Five 43s are 215 exactly. But just to check there’s no
remainder, we can subtract 215 from 215 to show that there’s nothing left over.
How did we find the answer of
15? We couldn’t divide six by 43. So we looked at the first two
digits. We found there’s one lot of 43 in
64. But there were some left over. So we subtracted 43 from 64 to give
us 21. We knew there were no 43s in 21
because it was too small. So we included the five ones from
the first number and we brought down the digit five to make 215.
We estimated that there was
probably going to be about five or six lots of 43 in 215. So to find out what five 43s were,
we used known facts to help. First, we calculated 10 lots of 43
and then we divided that answer by two. We wrote the answer at the top. And then we subtracted just to
check that there was nothing left over. 645 divided by 43 equals 15.