How do you evaluate #9\frac { 2} { 6} \div 6\frac { 1} { 2}#?

1 Answer
smendyka
Sep 25, 2017

See a solution process below:

Explanation:

First, rewrite the expression by converting both mixed numbers to improper fractions:

#(9 + 2/6) -: (6 + 1/2) =>#

#(9 + 1/3) -: (6 + 1/2) =>#

#([3/3 xx 9] + 1/3) -: ([2/2 xx 6] + 1/2) =>#

#(27/3 + 1/3) -: (12/2 + 1/2) =>#

#28/3 -: 13/2#

Next, use this formula for dividing fractions to evaluate the expression:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

#28/3 -: 13/2 => (color(red)(28)/color(blue)(3))/(color(green)(13)/color(purple)(2)) => (color(red)(28) xx color(purple)(2))/(color(blue)(3) xx color(green)(13)) => 56/39#

Now, if necessary, we can convert this improper fraction to a mixed number:

#56/39 => (39 + 17)/39 => 39/39 + 17/39 => 1 + 17/39 => 1 17/39#

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