Addition and subtraction are inverse operations to each other. By re-expressing a calculation, you can check your answer with the inverse operation.
Inverse operation
To be an inverse operation means to undo what the operation did. If you add five, this can always be undone by subtracting five. Hence the inverse operation of addition is subtraction. Similarly, if you subtract two, you can always undo this by adding two. Therefore addition is the inverse operation of subtraction.
Example 1
Some number plus six equals fourteen. What is the number?
First express this as a mathematical equation. Since you don't yet know the number, call it x. So:
x+6=14
To find x, find the inverse of what has been applied to x, and apply it to 14. The inverse of adding 6 is subtracting 6. Hence the following is also true:
x=14−6
This gives 8, so
x=8.
Checking answers
Beyond being used to solve problems like the example above, inverse operations are helpful when checking answers.
Example 2
Calculate 74−49.
−67421495
So 74−49=25. Now you can check this is correct using the inverse operation. Initially, you subtracted 49 from 74 to find 25. The inverse is to add 49 to 25. You can now check if this does give 74:
+2147594
As expected, you get 74, so you can be confident that 74−49=25.
See that by inverting the process, you have returned to 119, hence you can be more confident that 119+15=134.
Note:You need not stick to just the column method, or just the number line method. Use whichever you prefer, unless it is stated to use one particular method.