To divide
[tex]2\frac{3}{5}\colon\frac{2}{7}[/tex]First we have to transform the dividend from a mixed number to an improper fraction. We can do that with a diagram. We need 2 units and 3/5 of another unit:
So we have that 2 3/5 is 5/5 plus 5/5 plus 3/5:
[tex]\frac{5}{5}+\frac{5}{5}+\frac{3}{5}=\frac{5+5+3}{5}=\frac{13}{5}[/tex]Now our division is:
[tex]\frac{13}{5}\colon\frac{2}{7}[/tex]To compute this division we'll use KCF rule:
• K,eep the dividend
,• C,hange division sign by multiplication sign
,• F,lip divisor
[tex]\frac{13}{5}\colon\frac{2}{7}=\frac{13}{5}\times\frac{7}{2}=\frac{13\times7}{5\times2}=\frac{91}{10}[/tex]This result cannot be simplified but it can be written as a mixed number. We can see that 90/10 plus 1/10 is 91/10. 90/10 can be simplified to 9. So:
[tex]\frac{91}{10}=\frac{90}{10}+\frac{1}{10}=9+\frac{1}{10}=9\frac{1}{10}[/tex]The correct answer is the first option
