Video Transcript
Find all the missing numbers in
these related facts. Six times three equals what, three
times what equals 18, 18 divided by six equals what, and what divided by three
equals six.
In this question, we’re given four
number facts. And we’re told these aren’t just
any number facts. These are related. They’re part of a family. What’s the same and what’s
different about these facts? Well, firstly, as we’ve heard
already, each of the facts has a missing number. They’re all in different places,
though, so we need to think carefully about what numbers are missing. Two of the calculations are
multiplications, and two are divisions. And although these may seem like
different sorts of number sentences, they are related because we know that division
is the inverse or the opposite of multiplication.
You know, there’s one other
interesting thing about these number facts. Can you spot it? The same numbers keep cropping up
again and again. We can see the numbers six, three,
and also 18. These are the only numbers that are
being used in our number sentences. I wonder why this is. Well, the key to the whole thing
really is our first number fact. Six times three equals what. Let’s model this calculation using
counters. We can think of six times three as
being worth six lots of three. And this is the same as three, six,
nine, 12, 15, 18 altogether. Our missing number is the third of
our three numbers. Six times three equals 18.
Do you think maybe all of our
number facts have the same three numbers in them? Let’s have a look at the second
one. Three times what equals 18. Well, we know that we’ve got 18 in
this group, but 18 is worth three lots of what? To help us find the missing number,
we’re going to have to use some division, even though this is a multiplication
question. We’re going to need to start with
18 and split it into three equal groups. There are six counters in each
group. As though if we know six lots of
three are 18, we also know three lots of six equal 18, too. And of course, this is something we
know about multiplications, isn’t it? We can swap the numbers that we’re
multiplying around and they’ll still make the same product.
Our next fact is a division. And because the missing number is
the answer, the number that comes after the equal sign, we can just work out the
division. 18 divided by six equals what. Now, we could do one of two things
here. We could find out how many sixes
there are in 18, or we could split 18 into six equal groups and see how many there
are in each group. Let’s do the second one. One, two, three, four, five,
six. Now, I’m guessing you probably knew
what the answer was going to be before we started spitting up this number. If we know that six times three
equals 18, then we also know the inverse. 18 divided by six equals three.
And what number do we divide by
three to get six? The missing number in our last
division is 18. We know that multiplication and
division are inverse operations; they’re opposites. And so, with the number six times
three equals 18, we can find four related number facts. Six times three equals 18, three
times six equals 18, 18 divided by six equals three, and 18 divided by three equals
six. Our missing numbers are 18, six,
three, and 18 again.
