What is the number that, when divided by five, gives nine?
In this problem, we’re looking for a number that gives the answer nine when we divide it into five. We can write the problem as something divided by five equals nine. What is the something? And how can we find it?
If we remember, the opposite, or the inverse, of division is multiplication. So, we can read this number sentence backwards and think of it as a multiplication fact instead. Nine multiplied by five equals something. So, if we can find the answer to nine lots of five, we’ll have found the number that when divided by five gives us nine. So, how can we work out what nine fives are?
We could skip count in fives nine times, five, 10, 15, and so on. We could sketch an array where there are nine lots of five. Or perhaps you already know the multiplication fact for nine times five already. All of these methods will get you the correct answer. Let’s use a different method though. Let’s use a fact that we already know to help us.
Nine lots of five is very close to a multiplication fact that is quite easy to remember, 10 lots of five. And if we know what 10 times five is, we can use this to help us find nine times five. 10 multiplied by five equals 50. Nine multiplied by five is one less five than this. If ten fives is a 50, then nine fives must be 45 because 50 take away five equals 45.
Remember that multiplication is the opposite, or the inverse, of division. And so, we know that the mystery number is 45. 45 divided by five gives us nine. 45 split into five equal groups gives nine in each group. The number that gives nine when divided by five is 45.