Adam wants to use a mental method to calculate 182 take away 97. He starts from 182. Here are some methods that Adam could use. Tick the methods that are correct. Add three and then subtract 90. Subtract 100 and then add three. Subtract seven and then subtract 90. Subtract three and then subtract 100.
In this question, we’re given four different methods that Adam could use to calculate 182 take away 97. We’re told that he starts from the number 182. So really what this question is asking us is which of these methods are the same as subtracting 97. Let’s go through them one by one to find out.
Part of the first method is to subtract 90. If this was all we did, it would take us to a position 90 less than 182. But the method suggests that we add three before we subtract 90. This takes us to a position 87 less than 182 because we added three before we took away 90. Adding three then subtracting 90 is the same as subtracting 87. So it’s not a method that Adam could use.
Method two again has two steps. First, take away 100. This is easy to do. But if Adam uses this method, he’s going to have taken away three too many. But then add three. This will take us to an answer 97 less than 182. Subtracting 100 and then adding three is the same as taking away 97. So we can tick the box for this method.
Method three is a little bit easier to think about because we’re using the same operation twice. First, subtract seven. This takes us to a number that would be seven less than 182. And then subtract another 90. Seven plus 90 equals 97. So the answer will be a number 97 less than 182. Taking away seven and then taking away 90 is the same as taking away 97. So we can tick the box for method three.
What about the final method? Is this the same as subtracting 97? This method tells us to subtract three, which would take us to a number three less than 182, but then to take away another 100. So we’ve taken away 103 in total. This is not the same as subtracting 97. So we don’t need to tick the final box.
This question is interesting because probably the two easier methods to think about are the two final ones, where we’re moving in the same direction each time. We’re using the same operation. We know that to subtract seven and then subtract 90 is the same as subtracting 97. So that’s correct. And we know that to subtract three and then 100 is the same as subtracting 103 altogether. And we know that that’s not correct. So we don’t need to tick that one.
Perhaps the two that are slightly more tricky are the ones where we use a combination of operations. We add but also we subtract. We need to think about these a little bit more carefully. Adding three and then subtracting 90 is the same as taking away 87. Subtracting 100 but then adding three is the same as taking away 97. With these first two in particular, sketching a number line can be really helpful.
So if Adam wants to use a mental method to calculate 182 take away 97, the methods that he could use are to subtract 100 and then add three and to subtract seven and then subtract 90.