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The easiest way to handle mixed fractions is to convert them to improper fractions, do the processing and then convert any resulting improper fraction back to a mixed number:

19 1/4 × 9 1/2

= (19×4+1)/4 × (9×2+1)/2

= 77/4 × 19/2

= (77 × 19)/(4 × 2)

= 1463/8

= (182×8+7)/8

= 182 7/8

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Q: What is 19 1 4ths times 9 and a half?
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