Explain why this statement is true: when simplifying rational expressions, we must cancel factors only, and not terms. Give an example using just numbers.

Answer 1

e.g.

(12 + 6)/3
= 6(2+1)/3
= 2(3)
= 6

common error is to divide the 3 into the 12 to get
4 + 6 , that would be an example of canceling terms

Answer 2

( 12 * 48 ) /( 6 * 24 ) = ( 2 * 2 ) /( 1 * 1 ) = 4 / 1 = 4.

1. I divided 12 by 6 and 6 by 6.
2. I divided 48 by 24 and 24 by 24.
3. I multiplied 2 by 2 and 1 by 1.
4. Results = 4.

Now I'm going to change the multipli-
cation signs to plus signs:

( 6 + 24 ) / ( 12 + 48 ) =
30 / 60 = 2 / 4 = 1 / 2.
I had to get rid of the plus signs
by adding or combining the terms.
I can't legally divide 12 by 6 or 48 by 24.

Answer 3

10 divied by 16 =