How do you evaluate #4\frac{3}{4}\div 28\frac{1}{2}#?

1 Answer
smendyka
Sep 16, 2017

See a solution process below:

Explanation:

First, convert the mixed numbers to improper fractions:

#4 3/4 -: 28 1/2 =>#

#(4 + 3/4) -: (28 + 1/2) =>#

#([4/4 xx 4] + 3/4) -: ([2/2 xx 28] + 1/2) =>#

#(16/4 + 3/4) -: (56/2 + 1/2) =>#

#(16 + 3)/4 -: (56 + 1)/2 =>#

#19/4 -: 57/2#

Next, rewrite the expression as:

#(19/4)/(57/2)#

Now, use this rule for dividing fractions:

#(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))#

#(color(red)(19)/color(blue)(4))/(color(green)(57)/color(purple)(2)) => (color(red)(19) xx color(purple)(2))/(color(blue)(4) xx color(green)(57)) => (cancel(color(red)(19)) xx cancel(color(purple)(2)))/(cancel(color(blue)(4))2 xx cancel(color(green)(57))3) => 1/6#

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