Carlos B. answered • 03/19/15
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(2/9) ÷ (w/3) = [ (2/9) / (w/3) ] because 1 ÷ a = (1/a)
but a fraction in the denominator equals that reverse fraction in the numerator.
There is a fraction (2/9) in the numerator and one in the denominator, i.e. the SECOND factor, i.e. the DIVISOR (w/3). The ORDER of dividend and divisors is CRITICAL in division (UNLIKE multiplication. See: 2 x 4 = 4 x 2 = 8, but 2÷4=(1/2) while 4÷2=2.
Therefore:
[ (2/9) / (w/3) ] = (2/9)(w/3) = (2/9) X (w/3)
because the division of 2 fractions equals the multiplication of the first fraction times the reverse of the second. Therefore the first step is to invert the second fraction and to change ÷ for X, thus converting what WAS ONCE a division of fractions into a MULTIPLICATIOB of fractions. Now the order of the 2 fractions do no longer matter.
How do you multiply factors. You multiply the 2 numerators and you multiply the 2 denominators. You could just leave it at that or, for the sake of style, simplify if possible:
(2/9)(3/w) = (3/w)(2/9) = (3 X 2) / (9 X w) = (6 / 9w)
Division is now done. Now let us simplify. You can see also that simplification could have been performed before or during the division. You just need to have all factors in prime number form (i.e. factored out). You cannot factor 2 or 3 or w any further. You can factor 9, because 9 = 3 X 3) and you can factor 6 ( 6 = 3 X 2).
Simplification:
(6/9w) = [ (2 X 3) / (3 X 3 X w)) ]
Factors that REPEAT in both the numerator and the denominator cancel one another because (a/a) = 1, so all repeated factors equal 1, which does not change the value because 1 X a = a.
[ (2 X 3) / (3 X 3 X w)) ] =
[ (2) / (3 X w)) ] X (1) = (2/3w), final answer
Michael J.
03/19/15