Question 170722
For ANY number of the form {{{a/b}}}, the multiplicative inverse is {{{b/a}}}. In other words, to find the find the multiplicative inverse of any fraction, simply flip the fraction.



Note: if you multiply the number {{{a/b}}} by the the multiplicative inverse {{{b/a}}} you will get 1 since {{{(a/b)(b/a)=(a*b)/(b*a)=(cross(a)*cross(b))/(cross(b)*cross(a))=1}}}



So the multiplicative inverse of {{{3/7}}} is {{{7/3}}}



The multiplicative inverse of {{{-4/11}}} is {{{-11/4}}}



I'll let you do the rest of the problems involving a simple fraction

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To find the multiplicative inverse of {{{6&1/3}}}, we need to convert this mixed fraction into an improper fraction.


To do that, multiply the denominator 3 by the whole number 6 to get 18. Now add 18 to the numerator 1 to get 19. So {{{6&1/3=(6*3+1)/3=(18+1)/3=19/3}}}



So the multiplicative inverse of {{{19/3}}} is {{{3/19}}}



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Here's another example:



{{{4&1/9=(4*9+1)/9=(36+1)/9=37/9}}}



So the multiplicative inverse of {{{37/9}}} is {{{9/37}}}




I'll let you do the rest of the problems involving a mixed fraction