Question

Question #8d885

Answer 1

`4/9, 5/11, 3/5` (However, there are an infinite number of answers.)

Explanation:

`1/3 = bar .3`

`4/9 = bar .4`

`5/11 = bar .45`

`3/5 = .6`

`2/3 = bar .6`

Answer 2

Convert to equivalent fractions with bigger denominators.

Explanation:

The easiest way to find fractions between given fractions is to convert to equivalent fractions with much bigger denominators,
then you can write down any number of fractions by inspection.

We have `1/3 and 2/3` which are equal to `color(blue)(10/30 and 20/30)`

Fractions between these two have numerators from `11 " to " 19`

`color(blue)(10/30), 11/30, 12/30, 13/30 ....... 17/30, 18/30, 19/30, color(blue)(20/30)" "larr` (some simplify)

`1/3 and 2/3` are also equal to `color(blue)(15/45 and 30/45)`

Between these we have fractions with numerators from `16 " to " 29`

`color(blue)(15/45), 16/45, 17/45, 18/45 ..........27/45, 28/45, 29/45,color(blue)(30/45)`

The bigger you choose the denominator, the more choices you have:
`1/3 and 2/3` are equal to `color(blue)(100/300 and 200/300)`

Fractions between these two have numerators from `101 " to " 199`

`color(blue)(100/300),101/300, 102/300, 103/300............197/300, 198/300, 199/300,color(blue)(200/300)`

ad infinitum ....