50 plus 36 divided by six equals what?
What do we notice about this calculation? Well, firstly, it’s a two-part calculation. And it contains two different operations that we need to work out to find the
answer. We need to add and we need to divide. The second interesting thing is that part of the calculation has been written inside
brackets. This division — 36 divided by six — has been written inside brackets for an important
reason, which we’ll come to in a minute.
Because the number sentence contains different symbols, we need to think carefully
about what we call the order of operations. What do we work out first? Do we work from left to right and work out 50 plus 36 and then divide the answer by
six or do we calculate the division first and then add it to 50?
Each different order gives a very different answer. So we need to be careful about which one is correct. If we need a reminder, this triangle is a good way of remembering the order of
operations. Firstly, anything in brackets takes priority; it’s most important. And we have to work out whatever is in brackets first.
Once we’ve done that, if there’s any multiplying or dividing to be done, we can
complete this part of the calculation. And finally, the operations that have lowest priority — unless of course they’re in
brackets — is addition and subtraction and we can complete those last.
Let’s use these order of operation rules to help us find the answer. Our calculation contains brackets. So we know this part takes priority over anything else and we have to complete it
first. We need to work out 36 divided by six before we do anything else.
How many sixes are in 36? Well, there are five sixes in 30. So there must be six sixes in 36. Because we’ve started out by working out the value of the division inside the
brackets, we can replace the brackets with the answer. This turns our calculation into 50 plus six. So having worked out the division, we now need to just add six to 50. 50 plus six equals 56.
How did we find our answer? Well, first, we noticed that we had two operations to do: we needed to add and we
needed to divide. But we also noticed that one of the operations was in brackets. So we knew we needed to complete this first. First, we worked out 36 divided by six to give us an answer of six and then we added
that number six to 50 to give us a final answer of 56. 50 plus 36 divided by six equal 56.
There is a fact about this number sentence that you might find interesting. Although the brackets do show us which part we need to work out first, if the
calculation had been written without any brackets at all, we’d still get the same
answer and we’d still have to work it out in the same order. This isn’t always the case. But it works with this number sentence. Can we see why?
Here’s what the number sentence looks like without any brackets at all. Which operation should we complete first? Well, if we look at our helpful order of operations triangle, we can see that
division is higher up or takes priority over addition. So even without any brackets, we’d still need to work out the division first. And then, we down the answer to 50 as before.
So we know why this question doesn’t really need the brackets. The answer is 56 with or without the brackets.