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

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

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

`=(3)/(8)`

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

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

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

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

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

`=(5)/(8)`

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

Solution:
`=(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 * 5/6`

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

`=(3xx2xx5)/(4xx3xx6)`

`=(3xx2xx5)/(2*2xx3xx2*3)` (Find factors)

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

`=(5)/(12)`

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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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