1. Find `1/2 / 3/4`

Solution:
`=(1)/(2) -: (3)/(4)`

`=(1)/(2) xx (4)/(3)`

`=(1xx4)/(2xx3)`

`=(1xx2*2)/(2xx3)` (Find factors)

`=(1xxcancel{(2)}*2)/(cancel{(2)}xx3)` (Remove common factors)

`=(2)/(3)`

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2. Find `3/4 / 5/6`

Solution:
`=(3)/(4) -: (5)/(6)`

`=(3)/(4) xx (6)/(5)`

`=(3xx6)/(4xx5)`

`=(3xx2*3)/(2*2xx5)` (Find factors)

`=(3xxcancel{(2)}*3)/(cancel{(2)}*2xx5)` (Remove common factors)

`=(9)/(10)`

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3. Find `3/4 / 3/2`

Solution:
`=(3)/(4) -: (3)/(2)`

`=(3)/(4) xx (2)/(3)`

`=(3xx2)/(4xx3)`

`=(3xx2)/(2*2xx3)` (Find factors)

`=(cancel{(3)}xxcancel{(2)})/(cancel{(2)}*2xxcancel{(3)})` (Remove common factors)

`=(1)/(2)`

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4. Find `3/4 / 2/3`

Solution:
`=(3)/(4) -: (2)/(3)`

`=(3)/(4) xx (3)/(2)`

`=(3xx3)/(4xx2)`

`=(9)/(8)`

`=1 (1)/(8)` (Converting improper fraction to mixed number)

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5. Find `1/2 * 3/4 / 5/6`

Solution:
`=(1)/(2) xx (3)/(4) -: (5)/(6)`

`=(1)/(2) xx (3)/(4) xx (6)/(5)`

`=(1xx3xx6)/(2xx4xx5)`

`=(1xx3xx2*3)/(2xx2*2xx5)` (Find factors)

`=(1xx3xxcancel{(2)}*3)/(cancel{(2)}xx2*2xx5)` (Remove common factors)

`=(9)/(20)`

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