any way to simplify multiplying big numbers in your head?

[nckoliss]

is their any way to simplify multiplying big numbers in your head like 167x782? just curiouse cuz i am on the number sense team at school and i wanna try to make it easier. number sense is when you do math in your head with no scratch paper.

 

[mmm4444bot]

No scratch paper? Yikes.

One could approach your example like the following.

167 * 782 = (100 + 60 + 7) * (700 + 80 + 2)

I do this sort of multiplication mentally, from time to time, but always with much smaller numbers.

Now use the distributive property.

Multiplying 700, 80, and 2 by 100 is easy to do mentally. Being able to remember the intermediate results is not something that I'm very good at.

70000 + 8000 + 200 = 78200

Multiplying 700, 80 and 2 by 60 isn't too difficult, either.

42000 + 4800 + 120 = 46800 + 120 = 46920

Multiplying 700, 80, and 2 by 7 is easy.

4900 + 560 + 14 = 5460 + 14 = 5474

I did these steps mentally without issue, but I don't have the ability to remember the results! Even if I were able to retrieve them from the scary chambers of my mind, trying to subsequently sum them mentally would make my head spin.

167 * 782 = 78200 + 46920 + 5474 = 130594

I'm sure there are lots of "tricks" for this type of mental calculation. I only know a few that work with smaller numbers.

Two examples for "smallish" multiples of 11:

11 * 27

Add the digits 2 and 7; then put the result between them.

2 + 7 = 9

11 * 27 = 297

How about 11 * 43?

4 + 3 = 7.

11 * 43 = 473

Your post looks like a job for Denis, to me.

 

[Deleted member 4993]

is their any way to simplify multiplying big numbers in your head like 167x782? just curiouse cuz i am on the number sense team at school and i wanna try to make it easier. number sense is when you do math in your head with no scratch paper.

If you have multiplication like:

31 * 29 = 30[sup:1zlrene9]2[/sup:1zlrene9] - 1 = 899......and so on....