Samantha measured #40 1/2# inches. Over the next #5 1/2# years, she grew to a height of 57 inches. During the #5 1/2# years, what was the average yearly change in Samantha's height?

1 Answer
Apr 8, 2017

Explained the principle behind cancelling out.

Average (mean) change in height is 3 inches per year

Explanation:

The total change is final height - initial height

#57-40 1/2=16 1/2# inches#->33/2#inches

This difference is spread over #5 1/2 ->11/2# years

So the average (mean) change for each year is:

#33/2 -:11/2#

#color(blue)("First principle method")#

#color(brown)("What follows is the principle behind cancelling out")#

This is the same as: #33/2xx2/11" "->" "33/11xx2/2#

But #2/2=1# so we have #color(brown)(larr" the cancelling out bit")#

#33/11xx1->33/11=3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Shortcut method and jumping steps")#

#33/2 -:11/2" " =" " 33/(cancel(2))xx(cancel(2))/11" "=" "3#