Tutor HuntResources Maths Resources

Mathematical Secrets: The Patterns Of The 9s

Things you`ve won`t have been taught (unless you`ve studied with me)

Date : 21/06/2019

Author Information

Julia

Uploaded by : Julia
Uploaded on : 21/06/2019
Subject : Maths

This is my first `mathematical secrets` post. These will be about aspects that I think are under-discussed. Often they`ll be patterns that were not pointed out to me by a teacher but that I noticed on my own as a student. These little discoveries always seemed magical and I want to share them.

I grew up thinking everyone had spotted what I had seen in the 9s but the conversations that tutoring allows has made it clear that this is not the case.

"Why have I not been shown this before?" demanded one student (and a parent!).

Let`s right some wrongs and make sure everyone knows about the patterns of the nine times tables. You`ll find some questions below for you to consider, with answers or hints, depending on how helpful I`m feeling, in the footnotes.

Part 1

1 x 9 = 09

2 x 9 = 18

3 x 9 = 27

4 x 9 = 36

5 x 9 = 45

Look at the underlined numbers, what do you notice? 1


Example: 5 x 9.

5 - 1 = 4 (the answer is 40-something).


Part 2

9, 18, 27, 36, 45, 54, 63, 72 ...

Pick one of these numbers, add the digits together and keep adding them together until you have a one digit answer. What do you find? 2

In fact, any number in the 9 times tables fits this pattern and any number that fits this pattern can be "divided by 9". 3

Continuing the example: 5 x 9.

5 -1 = 4 (the answer is 40-something).

9 - 4 = 5.

The answer is 45.

Challenge: Do these patterns ever stop showing up? Do other patterns appear later on?

Why does this happen? For that, algebra is our friend and there will be another post about this just as soon as I have written it. If you scroll to the bottom and sign up to receive notifications of new blog posts, you won`t risk missing it.

1. The difference between the number on the left and the one on the right is always 1.

2. That final digit is ..?

3. This oversimplification is a mild bugbear of mine. Any number can be divided by any lt;/strong>number (let`s not talk about zero for a moment as it adds complications), you just might not get an integer i.e. a whole number. Similarly, any number can be subtracted from any other, you just might not get a positive answer. This is not a problem if you know what to do with your answer. You should expect to know what to do with your answer& that`s one of the differences between performing a routine and understanding maths. If you don`t know, ASK.

4. Don`t look at me, I asked you! Feel free to comment below or message me your thoughts.

This resource was uploaded by: Julia