SOLUTION: I am trying to help a student work a very simple world problem, but I do not know how to explain to her why she can't work as she wants to. Problem is: A smaller number plus 60,

Question 87040: I am trying to help a student work a very simple world problem, but I do not know how to explain to her why she can't work as she wants to. Problem is: A smaller number plus 60, when divided by the smaller number, the quotient is 4.
I set up as X + 60/X = 4 I told her it is easiest to solve this problem by getting rid of the fraction and that we should multiply the X + 60/X by X and the denominator X will be cancelled out, and the 4 by X (must do both sides of equation) Then we would be left with X + 60 = 4X, then we would solve for X. She doesn't understand why we just can't cancel the two X's out of the X + 60/X in the beginning and then be left with 60 = 4. What is the reason? I can't seem to explain it to her. Thanks for help!!!! P.S. No book, it was sent home homework problem.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Problem is: A smaller number plus 60, when divided by the smaller number, the quotient is 4.
---------------------
Let x be the smaller number.
EQUATION:
(x+60)/x = 4
x+60 = 4x
3x = 60
x 20
==============
I set up as X + 60/X = 4 I told her it is easiest to solve this problem by getting rid of the fraction and that we should multiply the X + 60/X by X and the denominator X will be cancelled out, and the 4 by X (must do both sides of equation) Then we would be left with X + 60 = 4X, then we would solve for X. She doesn't understand why we just can't cancel the two X's out of the X + 60/X in the beginning and then be left with 60 = 4. What is the reason?
--------
If you start with (x+60)/x = 4
You cannot cancel the x's because the x in x+60 is a term; it is not a factor
of the numerator.
You can only cancel factors.
For example, show your friend this:
(2+4)/2 according to her would be 4
But you know that (2+4)/2 = 6/2 = 3-
-------
Her way of doing it gives the wrong answer because 2 is not a factor of the
numerator; it is a term of the numerator.
-------------
What if the 2 was a factor?
Then you would have 2*4/2 = 4, which is correct.
-------------
General rule (a+b)/a is not b.
--------------
But ab/a is b
====================
Cheers,
Stan H.

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