Chloe is learning about different
strategies to multiply. She drew this to help her calculate
nine times four. What expression is missing in four
times nine equals what take away four times one? What is four times nine?
There are lots of different methods
or strategies that we can use to multiply numbers together. And in this question, Chloe is
using one of them. We’re told that she wants to find
the answer to nine times four. And we can see that she’s drawn a
rectangle on squared paper to help her. Now, before we move on and start to
answer the questions, let’s take a moment to look at this rectangle and understand
what Chloe is doing here to try and work out the answer to this multiplication.
The first thing that we can notice
is that Chloe’s drawn one large rectangle and then split it up into smaller
parts. So, it seems like she started off
drawing a rectangle that’s four squares tall and 10 squares wide. But wait a moment. If we do a four-by-10 rectangle or
an array like this, we’d expect it to show the multiplication four times 10 or 10
times four, not nine times four. Why would Chloe use a rectangle
like this to help work out the answer to nine times four? Well, Chloe knows two things that
can help her.
Firstly, she knows what 10 times
four is. She can remember it really
quickly. But importantly, she knows how to
use this to help. She knows that 10 times four is
only one lot of four more than nine times four. And that’s why her diagram shows
this big area nine times four here, this is the answer she’s trying to find, and
then one lot of four at the end here that she doesn’t need any more. In other words, she knows that nine
times four is four less than 10 times four. Let’s cross out four counters to
show these on our array too.
Now that we can see what Chloe is
doing in breaking up 10 times four into different parts, let’s complete the first
part of our question. What expression is missing in four
times nine equals what take away four times one? Well, as we’ve just said, to find
the answer to nine times four or four times nine as it’s written here, Chloe’s first
going to use her knowledge of the 10 times table to help. Because nine, of course, is very
close to 10. She’s going to find the answer to
four times 10 and then take away four times one. The missing expression is four
In the final part of the question,
we’ve just got to do what Chloe was doing. We need to use her method to find
the answer. What is four times nine? We know that four times 10 is equal
to 40. And we need to take away four times
one which, of course, is four. And 40 subtract four is 36.
This question’s being really
interesting to answer because although we know we often can split a much harder
multiplication into two easier multiplications and add those two multiplications
together, in this question, what we’ve done is start with an easier fact that we
know already and split it up so that we have to take away to find the answer that
we’re looking for. It’s still a very good example of
what we call the distributive property of multiplication where we can partition a
multiplication fact to help us.
To find the answer to nine times
four or four times nine, Chloe realized she could use the answer to four times 10 to
help her. She just needed to work out 10 lots
of four take away one lot of four or, in other words, four times 10 take away four
times one. The expression that was missing in
that first sentence was four times 10. So, four times nine is the same as
40 take away four, which equals 36.