I need help with this problem. The question is : Find the exact value of the following expression. 6*22*5. Use any mental calculation technique you choose. Name the technique you use in each case. Here is what I have:

Question

60*(20+2)*5 but this is where I get stumped. Can someone explain this to me. Thanks.

Answer 1

I will show some examples and leave it to you to digest. If more explanations are needed, post again.

Multiply without carry
6*22*5
=(6*5)*22
=30*22
=10*(3*22)
=660

Double and half
6*22*5
=6*(22*5)
=6*(22/2)*(5*2)
=6*11*10
=660

Multiply simple numbers by 11
6*22*5
=(6*5)*2*11
=(30*2)*11
=60*11
=660

Answer 2

mathmate you are a really smart person

Answer 3

Isn't it amazing what brains, lots of hard work, and a good education can do for a person! :-)

Answer 4

Thank you both for the nice comments. I love mental arithmetic, and it's one of my soft spots.

Since it seems to arouse some interest, I will complete the explanation of the third one (multiplication by 11):

When we multiply by 11, we only have to add adjacent digits. It's easier if there is no carry, but it can be done too. I will give an example:
Pretend there is a imaginary zero before the first digit and after the last:
135*11
=(0)135(0)*11
=(0)+1 || 1+3 || 3+5 || 5+0
= 1 || 4 || 8 || 5
= 1485

With a little practice, you can do this without pen and paper.

Try
24513 * 11
= 269643