How do you divide #6\frac { 7} { 15} \div 2\frac { 9} { 14}#?

1 Answer
smendyka
May 9, 2017

See a solution process below:

Explanation:

First, convert each mixed fraction to an improper fraction:

#6 7/15 -: 2 9/14 => ((15/15 xx 6) + 7/15) -: ((14/14 xx 2) + 9/14)#

#=> (90/15 + 7/15) -: (28/14 + 9/14) => 97/15 -: 37/14#

We can rewrite this as:

#(97/15)/(37/14)#

Now, we can use this rule for dividing fractions to complete the division:

#(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)(97)/color(blue)(15))/(color(green)(37)/color(purple)(14)) => (color(red)(97) xx color(purple)(14))/(color(blue)(15) xx color(green)(37)) => 1358/555 => (1110 + 248)/555 => 1110/555 + 248/555 =>#

#2 + 248/555 => 2 248/555#

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