Posted by **B.B.** on Tuesday, June 9, 2009 at 4:13pm.

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:

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

- Math -
**MathMate**, Tuesday, June 9, 2009 at 4:55pm
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

- Math -
**angelica**, Tuesday, June 9, 2009 at 6:14pm
mathmate you are a really smart person

- Math -
**Ms. Sue**, Tuesday, June 9, 2009 at 6:25pm
Isn't it amazing what brains, lots of hard work, and a good education can do for a person! :-)

- Math -
**MathMate**, Tuesday, June 9, 2009 at 9:00pm
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

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