### Video Transcript

Look at these cards: two times
nine, zero times nine, eight times nine, and nine times four. Which expression has the smallest
product? Which expression has the largest
product?

In this question, we’re given four
cards to look at. And on each one, there’s a
multiplication expression. Now, we’re asked two very similar
questions. We need to look at the expressions
on the cards and decide which one has the smallest product and which one has the
largest product. Remember that the word product is
what we get when we multiply numbers together. It’s the answer to a
multiplication. So really, our questions are asking
us which multiplication has the smallest value or the smallest answer and which one
has the largest.

Now, there are two ways we could
solve this problem. Firstly, we could go through each
card, multiply the numbers together, and then just compare all the answers. This would definitely be a way to
solve the problem. But is there a quicker way to find
the answer? If we look really carefully at
these number cards, do you notice anything? Two times nine, zero times nine,
eight times nine, nine times four. The number nine keeps cropping up a
lot, doesn’t it? In fact, the number nine is a
factor in each of the multiplications. They’ve all got it in. In fact, the first three
multiplications are very easy to compare because the number nine is in the same
position in each of them.

We can see straightaway which is
the smallest out of two times nine, zero times nine, and eight times nine. But if we look at our last
multiplication, the number nine is at the start. Does this make any difference to
us? Not at all, because we know it
doesn’t matter which order we multiply two numbers together. They give the same answer or the
same product. So we know that nine times four is
exactly the same as four times nine. And if it helps us, we could think
of this last card as showing four times nine.

Now, all our cards show something
times nine. So which has the smallest
product? Two times nine, zero times nine,
eight times nine, or four times nine. Because we’re multiplying by nine
each time, we simply need to look for the smallest number that we’re multiplying by
nine. And that’s zero. And the opposite is true. If we want to find the expression
with the largest product, we need to find the one that has the largest number that
we’re multiplying by nine. And that’s eight times nine.

Although we could’ve compared these
multiplication expressions by working each one out individually and comparing all
the answers, we noticed that they had something in common. And we used the fact that they were
all to do with multiplying by nine to help us solve the problem without working out
any of the answers. The expression that has the
smallest product is zero times nine, and the expression that has the largest product
is eight times nine.