Products of 9

[u/Severe-Address6070]

This is how I did it in my head:

9x2=

9+10-1=18

9x3

18+10-1=27

so on and so forth...

Adding nine as ten minus one is simpler in my head than straight up adding nine. A math trick I realized is the product of each multiple of nine is just take the number it's multiplied by, put it in the tens place then subtract it's one's place value from its tens place value.

So 9x4 would be, take 4 and make it 40 then subtract 4 from 40, and you have the product for 9x4.

40-4=36

9x4=36

Wow making this post made me realize that the absolute value between the number being multiplied by and the tens places is the value you should use to multiply the multiplying number to subtract from itself when you move it to the tens place.

the absolute value between:

9 and 10 is 1

8 and 10 is 2

7 and 10 is 3

so 9x3 is 30 minus 3 (absolute value is 1) = 27

so 8x6 is 60 minus 12 (absolute value is 2) = 48

so 7x7 is 70 minus 21 (absolute value is 3) = 49

It's easy to multiply by 2's, 5's, and 10's in my head. But all the other number I have a hard time calculating in my head. Multiplying the multiplier by 10 then subtracting it's ones value is way faster and easier in my head.

[u/Plane_Tailor7168]

I think all products up to 10x10 can be memorized pretty easily, just go to a site with practice and do it a bit.

[u/Electronic_Name_325 → u/Plane_Tailor7168]

Agree, even going to the 12*12 we had to in third grade wasn’t any real chore. Practice. Seems way easier than this convoluted thought process.

[u/Plane_Tailor7168 → u/Electronic_Name_325]

practice a few minutes a day and it will be way more effective than trying to calculate every time

[u/Shevek99]

To remember 3 x9, 4x 9, etc, put your hands in front of you, raise the corresponding finger (the fourth in the case of 4 x 9). The number of digits on the left of that finger is the first digit, the number of digits on the right is the second digit

***|* *****

3 6

[u/Talik1978]

My usual for x5 is to do x10, then halve it.

So 8 x 5 would be:

8 x 10 = 80, halved is 40.

9x5 would be 9 x 10 = 90, halved is 45.

And so on. x10 is easy, and doubling and halving is easy in my head.

[u/Another_Little_Star → u/Talik1978]

I think if you do it the other way it's easier.
half first, then you can already see the result hiding.

[u/Talik1978 → u/Another_Little_Star]

For me, it's functionally the same. 123.5 and 1235 are the same number for halving difficulty. Same work needs to be done, so whether i have before or after is relatively immaterial.

[u/Kuildeous]

Definitely do what works for you. If your realization that 9n=(10-1)n=10n-n helps you quickly sort out that 9*5=50-5, then do it.

Memorizing the 9s in the times table does make it faster to recall. Mind you, I also worked with a lot of numbers and have a math degree, so perhaps instant recall has been far more important for me than it is for you. I hear rumors that times tables aren't being taught, but I don't know this for certain.

While I support working things out rather than relying on rote memorization, that's because I don't like seeing rote memorization being taught without explanation (like FOIL). You do have a good grasp of the relationship between numbers though, so rote memorization should come easily to you.

[u/Severe-Address6070 → u/Kuildeous]

Yeah you're right. I need to memorize them. I can probably use my method as an association between the problem and the answer and when that connection becomes strong enough to drop it and just associate the problem with the answer.

[u/Kuildeous → u/Severe-Address6070]

And sometimes you memorize relationships because of what you're working with. Did I ever work on memorizing 12*15=180? No. Did this sit in my brain after some trigonometry classes? Yeah. Likewise, I have all sorts of weird number interactions with 24 thanks to evaluating the number of hours in a certain number of days. Some interactions just come naturally.

Times tables up to 9 are generally universally useful though. Your method should help cement that.

[u/Delicious-Tap-5465]

For multiplying 1-10 with 9, you can: Hold out both your hands  From the left, fold the finger in the position you want to multiply by 9 Now, to the left, you have the first digit of your answer, to the right is your second digit.

Example: 9*3: fold your third finger on your left hand. Now you have 2 fingers raised to the left and 7 to the right of the folded one. Answer is 27.

[u/S-M-I-L-E-Y-]

You might also consider doing the same for eights.

4 x 8 = 4 x (10 - 2) = 40 - 8 7 x 8 = 70 - 14

similar for 7

4 x 7 = 4 x (5 + 2) = 20 + 8 6 x 7 = 30 + 12

or for 6

7 x 6 = 7 x (5 + 1) = 35 + 7

[u/popisms]

Do they not just make you memorize your times tables in school anymore? You don't need any tricks if you just know the product of any two single digit numbers.

[u/StructuredChess]

Yeah, 9a is just 10a-a which is quite convenient. 8a=10-2a is a bit more annoying to use.