Simplify each using positive exponents Using LCD method. (Please show solution)

Question

a) 42x⁴/y²/24x³/y^{6          b)} 35a^4/22b¹¹/49a⁶/55b¹⁵

Answer 1

DO them backwards.....

Remember when dividing fractions, KFC: Keep, flip, change

 

y^2/1 divided by 24x^3/y^6 =

 

y^2/1 * y^6/24x^3 = y^8/24x^3

 

42x^4/y^2 divided by y^8/24x^3 =

 

42x^4/y^2 * 24x^3/y^8 =

 

1008x^7/y^8

 

(b)  Same pattern. I will leave it for you to verify...

 

   (25a^4 * 49a^6) /  (22b^11 * 55b^15)=

 

 1225a^10/1210b^26

 

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It is very tempting to want to cancel them. But as written, YOU CANNOT!!!

I will now change the problems so that they will cancel. Notice the difference

in the order of the fractions compared to the original problem.

 

(a)

 

42x^4/y^2/y^6/24x^3  <--- again, going backwards using KFC

 

 

(42x^4)(y^6)

---------------- 

y^2(24x^3)

 

 =   7xy^4/4 <--- 42/24 = 7/4 by dividing by factor of 6/6

 

 

(b)     (35A^4)/22b^11/55b^15/49a^6

 

         (35a^4)(55b^15)

       -----------------------

          (22b^11)(49a^6) 

 

   (5/2)(5/7)(b^4/a^2) =  <----  35 and 49 reduce by factor of 7; 55 and 22 reduce by factor of 11

 

   25b^4

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

   14a^2

 

 

 

Finally consider the model:

 

A divided by B divided by C divided by D =

 

A/1 divided by B/1 divided by C/1 divided by D/1 

 

The C and the D gets flippled twice because 

there are two divisions being done.

So if it is on the bottom, it will stay on the bottom

after two flips. If it is on the top it will stay on the

top after two flips