Do I convert to a mixed number first

[Nicola]

3 2\5 x 2 1\2

Do I need to convert to improper fractions first?

17\5 x 5\2 = 85\10
or
3 x 2=6 2x1=2
5x2=10
=6 2\10

Thank you.

 

[lookagain]

3 2\5 x 2 1\2

Do I need to convert to improper fractions first?

17\5 x 5\2 = 85\10
or
3 x 2=6 2x1=2
5x2=10
=6 2\10

Thank you.

No, you don't *need* to convert to improper fractions first,
but it is recommended.

If you're going to change them to improper fractions as you did,
then try to cancel numerators with denominators as much as
possible to not have to do reducing in the product.


$\displaystyle \frac{17}{5} \times \frac{5}{2} = \frac{17}{1} \times \frac{1}{2} = \frac{17}{2} = 8\frac{1}{2}$


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$\displaystyle Otherwise, \ you \ might \ interpret \ it \ to \ be:$

$\displaystyle 3\frac{2}{5} \times 2\frac{1}{2} =$

$\displaystyle (3 + \frac{2}{5})(2 + \frac{1}{2}) =$

$\displaystyle 3(2) + 3(\frac{1}{2}) + \frac{2}{5}(2) + \frac{2}{5}(\frac{1}{2}) =$

$\displaystyle 6 + \frac{3}{2} + \frac{4}{5} + \frac{1}{5} =$

$\displaystyle 6 + 1\frac{1}{2} + \frac{5}{5} =$

$\displaystyle 6 + 1\frac{1}{2} + 1 =$

$\displaystyle 8\frac{1}{2}$