The correct answer is: " [tex]\frac{16}{21}[/tex] " .
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Step-by-step explanation:
" [tex]2\frac{2}{3}[/tex] ÷ [tex]3\frac{1}{2}[/tex] " =
" [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex] " ;
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" [tex]2\frac{2}{3} = \frac{[(3*2)+2]}{3} = \frac{(6+2)}{3} = \frac{8}{3}[/tex] " .
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" [tex]3\frac{1}{2} = \frac{[(2*3)+1]}{2} = \frac{(6+1)}{2} = \frac{7}{2}[/tex] " .
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→ " [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex] " ;
[tex]} = \frac{8}{3}[/tex] ÷ [tex]\frac{7}{2}[/tex] ;
Note that "dividing by a value" results in the same value as "multiplying by the reciprocal of that value" ;
The reciprocal of: " [tex]\frac{7}{2}[/tex] " ; is: " [tex]\frac{2}{7}[/tex] " ;
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[tex]= \frac{8}{3} *\frac{2}{7}= \frac{(8*2)}{(3*7)} = \frac{16}{21}[/tex] ; which cannot be further reduced as a fraction.
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The correct answer is: " [tex]\frac{16}{21}[/tex] " .
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Hope this is helpful!
Best wishes to you!
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