Remembering the Nines

"I know most of the multiplication tables. I'm just not good at the nines," a new student said to me recently.

"Then you are in luck!" I replied. "I know a couple of things that can help you."

The first method is pretty widely known among elementary teachers. It is the finger method. A student holds out their hands in front of them, imagining that each finger represents a number from 1 to 10; left to right. Whatever number is given to be multiplied by nine, that finger is bent down. Then count the number of fingers before the bent finger for the tens digit, and the number of fingers after it for the ones digit and you have the answer.

For example, if the student is trying to figure out 9 x 4 they bend down finger number four which is the index finger on the left hand. There are three fingers before it and six fingers after it so the answer they are looking for is 36.

The second method starts with a story that I tell. I learned this over twenty-five years ago when I did my student teaching in Milwaukee. My supervising teacher, Emma Beck told this story to her class, and I have told this story many times since.

Once upon a time there was a man who was looking for a job. He went from company to company and eventually found one that had an opening and wanted to hire him. The supervisor said, "There is just one thing. We have a test that we want you to take. It will only take a few minutes." The man was handed the test and it looked like this: (I have this written on the board ahead of time.)

1 x 9 =
2 x 9 =
3 x 9 =
4 x 9 =
5 x 9 =
6 x 9 =
7 x 9 =
8 x 9 =
9 x 9 =
10 x 9 =

The man took one look at the test and groaned. Now he was really wishing he had paid attention in math class and done the homework assignments he was supposed to do. He had no idea, but he wanted this job and he refused to give up. "Well," he said to himself, "I don't know how to do this, but I'm sure the answers will be numbers and I know the numbers, so I'll just count the problems." And going from top to bottom he started to write the numbers.

1 x 9 = 0
2 x 9 = 1
3 x 9 = 2
4 x 9 = 3
5 x 9 = 4
6 x 9 = 5
7 x 9 = 6
8 x 9 = 7
9 x 9 = 8
10 x 9 = 9


The man stopped and looked at what he had done so far. Surely that couldn't be right, so maybe he should do it again, but this time he would start at the bottom and go up.

1 x 9 = 09
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54
7 x 9 = 63
8 x 9 = 72
9 x 9 = 81
10 x 9 = 90

So I then conclude my story by asking: "Do you think the man got the job?"

This is a good time to ask students if they see a pattern. The sum of the digits in each product is nine. The number in the tens digit is one less than the number being multiplied by nine. So the number in the ones digit is what is added to the number in the tens digit to make a sum of nine. Middle school students can write this algebraically.

Number to be multiplied by nine: n
Tens digit of the product: n-1
Ones digit of the product: 9 - (n-1)

These methods really help students remember the nines table!