How do you evaluate #4\frac { 3} { 4} \div \frac { 7} { 8}#?

1 Answer
smendyka
Dec 5, 2017

See a solution process below:

Explanation:

First, rewrite the mixed number as an improper fraction:

#4 3/4 = 4 + 3/4 = (4 xx 4/4) + 3/4 = 16/4 + 3/4 = (16 + 3)/4 = 19/4#

Now we can rewrite the expression as:

#4 3/4 -: 7/8 = 19/4 -: 7/8 => (19/4)/(7/8)#

Now, use this rule 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))#

#(color(red)(19)/color(blue)(4))/(color(green)(7)/color(purple)(8)) = (color(red)(19) xx color(purple)(8))/(color(blue)(4) xx color(green)(7)) = (color(red)(19) xx color(blue)(cancel(color(purple)(8)))color(purple)(2))/(color(purple)(cancel(color(blue)(4))) xx color(green)(7)) = 38/7#

If necessary, we can convert this into a mixed number:

#38/7 = (35 + 3)/7 = 35/7 + 3/7 = 5 + 3/7 = 5 3/7#

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