Question #05bea

For the first one and the third one, use the same concept of being able to flip the denominator if it was a fraction and change the question to multiplication.

For the second one, what you do is multiply #1/6# by #2# to get #1/3#

#1/6 xx 2 = 2/6=1/3#

Using the shortcut method

Part 1: #->1-:2/6#

So that you fully understand what is going on write 1 as #1/1#

#1/1-:2/6# turn the #2/6# upside down and multiply

#1/1xx6/2 " "=" "(1xx6)/(1xx2) =6/2#

#6/2=(6-:2)/(2-:2) =3/1=3#
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Part 2:#->" how many sixths make "1/3#

Let the unknown number be #x#

#x/6=1/3#

Multiply by 1 and you do not change the value. However, 1 comes in many forms so you can change the way a value looks without changing 'what it is worth'.

#color(green)(x/6=1/3color(red)(xx1))#

#color(green)(x/6=1/3color(red)(xx2/2))#

#x/6=(1xx2)/(3xx2) = 2/6#

So it takes two sixths to make #1/3#
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Part 3:#->"What is "1/3 -: 1/6#

Using the shortcut method of turning upside down and multiplying

#1/3-:1/6# gives the same answer as #1/3xx6/1#

#(1xx6)/(3xx1) = (6-:3)/(3-:3) = 2/1=2#