Math Nightsmare--want to help?

[Welcome Back Apathy]

I'm trying to get the Maths Nightmare avatar (yeeeeah, this will take a while) and I have discovered that no, it will be impossible for me to get it on division potato counter. So I'm practicing division with brain tree difficulty.

 

Yeah, it's difficult. But I'm compiling a list of all the division mental math tricks I know to help me out--and boy, do I know some. But maybe you know more? Please add to my list if you know anything that will help.

 

1) Estimation. Round to the nearest ten--or nearest something that will help--and see what happens.

Example: 455/35 is kind of like 480/40 = 12. So it's somewhere around 12. Since you can try multiple numbers, start guessing numbers around 12.

 

2) Odd divided by an odd is odd. Even divided by an odd is even. This does help, I swear.

Example: 455/35 is near 12, but it has to be an odd number. So I try 11 (well, I don't, because I know from my 11s that it's not) and 13. It ends up being 13!

 

3) Treat it as a fraction and reduce.

Example: 455/35, I know 5 goes into both, so I divide 455/5 = 91 and 35/5 = 7. I know that 7 x 13 = 91, so the answer is 13.

 

4) Along the same lines: treat it as a fraction and UN-reduce. (What's the word for this?) This is AWESOME for multiples of 5.

Example: 455/35 = 910/70 = 91/7 = 13.

 

5) Other random tricks that are good to keep in mind:

*Dividing by multiples of 5: Is the smaller number (divisor) a multiple of 25? If not, is the bigger number (dividend) a multiple of 25? If so, your quotient (the answer) has to be a multiple of 5.

*Dividing by 25 or 50: multiply the dividend by 4, divide by 100 (take the two zeroes off.) Same thing for 50, but multiply by 2 and divide by 100.

 

EDIT: Also:

6) Think in 10s. (This goes along with estimating.) What's the nearest 10 that seems close? How many more is it?

Example: 455/35 is more than 10. 35 x 10 = 350. There is 105 left over, and 105/3 = 35.

 

Not all of these tricks is necessarily the best trick for this particular problem, but there are problems where they are really useful.

 

Anyone have anything else?

[RoboHissi]

The tips that you've brought up are good, but in order to go far, you're going to need to have most of the answers memorized. Once you can do that, you should have no problem getting the avatar score on the first of the month (and I got a nice silver trophy to go with it!).

 

On topic though, a number that ends in 5 divided by an odd number that isn't divisible by 5 is 15, and in rare cases, 35. I think the only one that has the answer of 35 is 805/23 = 35.