Complete: four multiplied by what multiplied by nine equals 20 multiplied by
In this problem, we have two calculations either side of an equal sign. The first calculation shows two multiplications, four multiplied by something
multiplied by nine. And the second multiplication shows 20 multiplied by nine. The first thing that we can say about these calculations is that both of them are
worth the same. We know this because there’s an equal sign in between them. Both sides of the equal sign have the same value. So we need to use what we know about 20 multiplied by nine to help us work out what
the missing number is in the longer multiplication.
Now, one way we could try to work out the answer here is to calculate 20 multiplied
by nine and then work backwards from whatever the answer is to try to find what the
missing number is. But there’s a much much quicker or more efficient way to find the answer. So let’s go through that. To solve the problem, let’s look at both calculations either side of the number line
and see what’s the same about them. They both show an amount being multiplied by nine. In the first calculation, the amount that we’re multiplying by nine is four
multiplied by something. And on the right-hand side of the equal sign, the value that we’re multiplying by
nine is 20.
Now remember, both expressions are worth exactly the same. And so we know that both parts that are being multiplied by nine must be worth the
same. Four times something and also 20 must be equal. So now we just need to think what do we multiply four by to get the value of 20. Four multiplied by five equals 20. If we make the missing number five and work through this expression, four multiplied
by five makes 20. And then we would multiply 20 by nine. And on the right-hand side of the equal sign, we have 20 multiplied by nine. So both sides, both expressions, are exactly the same.
We didn’t even need to work out the value of each expression. 20 multiplied by nine is actually 180. But we didn’t need to work that out. We just needed to think about what the equal sign meant and notice the similarities
in the expressions between both sides. We know that four multiplied by five equals 20. And so if we multiplied both these expressions by nine, we’re going to get the same
result. Four multiplied by five multiplied by nine equals 20 multiplied by nine.