Question

Can u show me common core way this problem how to do 5/9 ×3 1/2

Answer 1

1.) you want to make 3 1/2 an improper fraction. so multiply 3 times 2 (your denominator) then add 1 (numerator). 
3x2= 6  6+1=7, then put 7 over your denominator which would be 7/2.
2.) multiply 5/9 times 7/2
5 times 7 is 35
9 times 2 is 18
your answer is 35/18
3.) make it a proper fraction
18 times 2 is 36 so that would't work to have two!
so you only can put 18 into 32 once so subtract 32-18 so you know what is left over after you take a whole out. 32-18=14. 14 is now the numerator and so put your whole number first then put your numerator over your denominator: 1 14/18
4.) simplify
1 14/18=  1 7/9, I divided 14 and 18 by 2 to simplify


The answer is 1 7/9

Answer 2

First off, we change the mixed fraction to an "improper" fraction, and then multiply like we would any other fractions, so let's do so,

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies\cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{5}{9}\times 3\frac{1}{2}\implies \cfrac{5}{9}\times\cfrac{7}{2}\implies \cfrac{5\times 7}{9\times 2}\implies \cfrac{35}{18}\implies 1\frac{17}{18} \\\\\\ \textit{keep in mind that }1\frac{17}{18}\implies \cfrac{1\cdot 18+17}{18}\implies \cfrac{35}{18}$