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)`
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)`
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)`
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)
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)`
This material is intended as a summary. Use your textbook for detail explanation.
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