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.
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
mathmate you are a really smart person
Isn't it amazing what brains, lots of hard work, and a good education can do for a person! :-)
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
Sure! I can help explain how to solve this problem using mental calculation techniques.
To find the exact value of the expression 6*22*5, we can break it down into smaller calculations using the distributive property.
Starting with what you've already done:
60*(20+2)*5
First, we can simplify the expression inside the parentheses, which is 20+2.
20+2 = 22
Next, we replace the expression in the original expression:
60*(22)*5
Now, we can use the technique of multiplying numbers in any order. In this case, we can rearrange the order of multiplication to make it easier.
Let's multiply 60 and 5 first:
60 * 5 = 300
Now, we multiply the result by 22:
300 * 22
To find the product of 300 and 22, we can use the technique of multiplying by 2 and then multiplying by 10.
First, multiply 300 by 2:
300 * 2 = 600
Next, multiply 600 by 10:
600 * 10 = 6000
So, the exact value of the expression 6*22*5 is 6000.
In summary, the mental calculation techniques used in this problem are simplifying the expression inside the parentheses, rearranging the order of multiplication, and multiplying by 2 and then by 10.