David G. answered • 02/19/18
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Analytics Professional, B.A. in Statistics, Flexible Tutor
First, remember the MDAS order of operations rule - Multiply, Divide, Add, Subtract. We do our multiplication operations before doing our addition operations.
Next, note that there are similarities between each of the four groups of numbers to be multiplied - all four groups of numbers start with 6 X 5 - all groups have a common factor. In other words...
6 X 5 X 15 + 6 X 5 X 85 + 6 X 5 X 35 + 6 X 5 X 165
...can be written as...
(6 X 5 X 15) + (6 X 5 X 85) + (6 X 5 X 35) + (6 X 5 X 165)
...which can be restated as...
(6 X 5) X (15 + 85 + 35 + 165)
...and if we solve for the equations inside the parentheses, we get...
(30) X (300)
...which is the same as...
9,000
...which is our final answer!
If you're using a calculator for this problem, use the following steps:
- Note that all four of the groups of multiplied numbers have a 6 X 5 term
- Enter 6 X 5 to get 30, and remember this term
- Clear your calculator, and add 15 + 85 + 35 + 165 to get 300
- Multiply 300 by 30 to get 9,000 - your final answer!
Hope this helps! Let me know if you have any questions.
Arthur D.
tutor
Hi David, sorry for the down arrow; going through your solution I hit the down button accidentally. Very nice explanation of the problem. I just answered the student's question on how fast to do the problem because he said he knew how to do it.
Arthur D.
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02/19/18
David G.
Hi Erer! No worries - I can clarify :) Let's remember our original equation...
6 X 5 X 15 + 6 X 5 X 85 + 6 X 5 X 35 + 6 X 5 X 165
...can be written as...
(6 X 5 X 15) + (6 X 5 X 85) + (6 X 5 X 35) + (6 X 5 X 165)
...can be written as...
(6 X 5 X 15) + (6 X 5 X 85) + (6 X 5 X 35) + (6 X 5 X 165)
...and can also be written as...
(15 X 6 X 5) + (85 X 6 X 5) + (35 X 6 X 5) + (165 X 6 X 5)
...if we move the 6 X 5 term to the end of each group, instead of putting it at the beginning.
Now, let's look at this equation a little more intuitively - using words instead of numbers:
(15 X 6 X 5) + (85 X 6 X 5) + (35 X 6 X 5) + (165 X 6 X 5)
...is the same as...
15 six-times-fives + 85 six-times-fives + 35 six-times-fives + 165 six-times-fives
...is the same as...
15 thirties + 85 thirties + 35 thirties + 165 thirties
...is the same as...
(15 + 85 + 35 + 165) thirties
...which, if we solve the addition problem, equals...
300 thirties
...which is equal to 300 X 30, or 9,000.
Hope this clarifies the concept a little bit more - feel free to let me know if you need me to explain anything else!
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02/19/18
Erer A.
oh Ok. I completely understand it now. Thanks!
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02/19/18
Erer A.
02/19/18