Sophia works out that 432 divided by 12 equals 36. And there are then three parts to the problem. Use Sophia’s working out to help you find 216 divided by 12. Use a similar approach to find 432 divided by 24. And then, finally, now use Sophia’s working out to help you calculate 864 divided by six.
So, in the three different parts to this problem, we’re asked to calculate three different divisions. But each time we’re told to use what we know already to help us find out the answer. We can see we’re told to use Sophia’s working out or use a similar approach. So, where is Sophia’s working out? What is the fact that we need to use to help us work out the answers to these divisions?
Well, we’re given the fact in the first sentence. Sophia works out that 432 divided by 12 equals 36. So, let’s go through each step carefully and use this fact that we already know to help us. Firstly, we’re asked to use Sophia’s working out to find the answer to 216 divided by 12. What’s the same and what’s different about these two calculations?
Well, in both calculations, the divisor, or the number that we divide by, is the same. We divide both numbers by 12. The difference is between the two dividends, that first number in each calculation. Let’s look carefully at these numbers. Can we see a link between 432 and 216? 216 is half of 432. If the dividend is halved, how will this affect the answer? Sometimes sketching a bar model can help us understand what happens to numbers when they change in a division.
In the first calculation, the dividend is 432. And if we divide that by 12, we’re told that each part is worth 36. So, what would we expect to see if we started off with a dividend that was half as large. We’re still dividing into 12 equal parts, but this time each part is half as large. We know that 36 divided by two equals 18. And so, we’ve use Sophia’s working out to find the answer to 216 divided by 12. If we have the first number in the division and everything else remains the same, then the answer is halved.
Let’s look at the second part of the problem. Again, we’re going to use Sophia’s working out the help us. This time we need to find the answer to 432 divided by 24. What’s the same and what’s different about the two calculations this time? This time the number that we’re dividing by, the dividend, stays the same in both divisions. So, if we try sketching a bar model again, we’re going to see that both bar models have a large bar worth 432.
The difference comes in the number that we’re dividing by. In Sophia’s calculation, we’re told that she divides by 12. But in the calculation, we need to work out, we need to divide by 24. What’s the link between 12 and 24? Well, 24 is double 12. What happens to the answer if we double the number that we’re dividing by?
Here’s what each part looks like if we divide by 12. But if we divide the number into twice as many parts, they become half as large. And so, they’re going to be worth half of 36, which we know is 18. So, if we double the number we divide by, or the divisor, in a division question but we keep the other number the same, the answer will half.
Finally, let’s use everything we’ve learnt so far to help calculate the last part of the problem, 864 divided by six. This time there is nothing the same about the calculations. But there are links between them. Let’s think about how each number will affect the answer. Let’s imagine that we were dividing by 12 and not by six. We can see that our starting number has doubled, 432 doubled equals 864. And so, if we divide double the amount by 12, we’d expect the answer to be double 36. And double 36 is 72.
But there’s one more change we need to make. We’re not dividing 864 by 12. We need to divide it by six. Six is half of 12. So, we’re splitting 864 into half as many parts. This means each part will be worth twice as much because there are less of them. Double 72 equals 144. And so, we found the answer to three different divisions using a number fact to help us. 432 divided by 24 also equals 18. And 864 divided by six equals 144.