their basic parts.
How do you add 8 plus 5? You could add 5 plus 10 and subtract 2. Or you could add 8 plus 2 to make
10, then add another 3 (to make up the 5) to give the same answer of 13.
How do you add 7 + 6? Six is 3 + 3. Seven plus 3 is 10, plus the second 3 is 13.
Note to parents and teachers
Often children are just told, ‘You simply have to memorise the answers to 8 plus 5 or 8 plus 4.’ And with practice they will be
memorised, but give them a strategy to calculate the answer in the mean time.Checking addition by casting out nines
Just as we cast out nines to check our answers for multiplication, so we can use the strategy for
checking our addition and subtraction.
Here is an example:
We add the numbers to get our total of 143,835.
Is our answer correct? Let’s check by casting out nines, or working with our substitute numbers.Our substitutes are 6, 3, 2 and 4. The first 6 and 3 cancel to leave us with just 2 and 4 to add.
2 + 4 = 6
Six is our check or substitute answer.
The real answer should add to 6. Let’s see.
After casting nines, we have:Our answer is correct.
But there is a further shortcut when you are casting nines to check a calculation in addition. You can
cast out (cross out) any digits anywhere in the addition that add to 9. You can’t, of course, cross out
digits in the answer with digits you are adding. So, you could have cast out the 6 in the fourth number
with the 3 in the third, the 7 in the third number with the 2 in the fourth. You could have cast out every
digit in the top two numbers as each digit in the top number combines with a digit in the second to equal