Substitute Numbers

To check the answer to a calculation, we use substitute numbers instead of the original numbers we were working with. A substitute on a football team or a basketball team is somebody who takes another person’s place on the team. If somebody gets injured, or tired, they take that person off and bring on a substitute player. A substitute teacher fills in when your regular teacher is unable to teach you. We can use substitute numbers in place of the original numbers to check our work. Th e substitute numbers are always low
and easy to work with. Let me show you how it works. Let us say we have just calculated 12 × 14 and come to an answer of 168. We want to check this answer.

12 × 14 = 168

The first number in our problem is 12. We add its digits together to
get the substitute:
1 + 2 = 3

Three is our substitute for 12. I write 3 in pencil either above or
below the 12, wherever there is room.

The next number we are working with is 14. We add its digits:
1 + 4 = 5

Five is our substitute for 14.

We now do the same calculation (multiplication) using the substitute numbers instead of the original numbers:
3 × 5 = 15

Fifteen is a two-digit number, so we add its digits together to get our check answer:
1 + 5 = 6
Six is our check answer.

We add the digits of the original answer, 168:
1 + 6 + 8 = 15

Fifteen is a two-digit number, so we add its digits together to get a one-digit answer:
1 + 5 = 6

Six is our substitute answer. Th is is the same as our check answer, so our original answer is correct.