1. Find `3 1/2 / 1 3/4`
Solution:
`=3 (1)/(2) -: 1 (3)/(4)`
Converting mixed number to improper fraction
`=(3xx2+1)/(2) -: (1xx4+3)/(4)`
`=(7)/(2) -: (7)/(4)`
`=(7)/(2) xx (4)/(7)`
`=(7xx4)/(2xx7)`
`=(7xx2*2)/(2xx7)` (Find factors)
`=(cancel{(7)}xxcancel{(2)}*2)/(cancel{(2)}xxcancel{(7)})` (Remove common factors)
`=2`
2. Find `2 3/4 / 1 5/6`
Solution:
`=2 (3)/(4) -: 1 (5)/(6)`
Converting mixed number to improper fraction
`=(2xx4+3)/(4) -: (1xx6+5)/(6)`
`=(11)/(4) -: (11)/(6)`
`=(11)/(4) xx (6)/(11)`
`=(11xx6)/(4xx11)`
`=(11xx2*3)/(2*2xx11)` (Find factors)
`=(cancel{(11)}xxcancel{(2)}*3)/(cancel{(2)}*2xxcancel{(11)})` (Remove common factors)
`=(3)/(2)`
`=1 1/2` (Converting improper fraction to mixed number)
3. Find `2 3/4 / 1 1/4`
Solution:
`=2 (3)/(4) -: 1 (1)/(4)`
Converting mixed number to improper fraction
`=(2xx4+3)/(4) -: (1xx4+1)/(4)`
`=(11)/(4) -: (5)/(4)`
`=(11)/(4) xx (4)/(5)`
`=(11xx4)/(4xx5)`
`=(11xx2*2)/(2*2xx5)` (Find factors)
`=(11xxcancel{(2)}*cancel{(2)})/(cancel{(2)}*cancel{(2)}xx5)` (Remove common factors)
`=(11)/(5)`
`=2 1/5` (Converting improper fraction to mixed number)
4. Find `2 1/4 / 34`
Solution:
`=2 (1)/(4) -: 34`
Converting mixed number to improper fraction
`=(2xx4+1)/(4) -: 34`
`=(9)/(4) -: 34`
`=(9)/(4) xx (1)/(34)`
`=(9xx1)/(4xx34)`
`=(9)/(136)`
This material is intended as a summary. Use your textbook for detail explanation.
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