Question

Question #05bea

Answer 1

`1/(2/6)=1 xx 6/2=3`

`2` sixths make a third

`(1/3)/(1/6) =2`

Explanation:

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`

Answer 2

`1-:2/6 = 3`

It takes two sixths to make `1/3`

`1/3 -: 1/6=2`

Explanation:

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`