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Word Problems/Muliplication

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Question
Hello:

Why are 100 and 40 the only amounts subtracted from the calculation below?  Why not subtract the two 4's as well? The two products (400 & 160# can be subtracted and get the 240 as well.

100 X 4 = 400
-40 X 4 = 160
-------------
60 X 4 = 240

The above is a confusing way to indicate #100 - 40) X 4 = 240.

I thank you for your follow-up reply.

Answer
What they are trying to show is that (100-40) x 4 is the same as 100*4 - 40*4.
See, on the left side, they too 100 - 40 and got 60, then multiplied by 4 and got 240.

On the right side, they multiplied by 4 first.
They took 100 * 4 and got 400, then -40*4 and got -160.
It can then be seen that 400 - 160 is 240.

Just think of
100
-40
-----
60, and that is the basic problem they are showing.

----------------------------------------------------------------------------------------------

If we multiplied each term (100, -40, and 60) by 2,
we'd get 100*2 = 200, -40*2 = -80, and 60*2 =120.

This would give
200
-80
-----
120, and that can be seen to be correct.

----------------------------------------------------------------------------------------------

If we multiplied each term (100, -40, and 60) by 7,
we' get 100*7 = 700, -40*7 = -280, and 60*7 = 420.
This would give
700
-280
------
420, and that can be seen to be correct as well.

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