How do you evaluate #(\frac { 5a } { 3b } ) \div ( \frac { 15c } { 9a ^ { 2} } )#?

2 Answers
Nov 18, 2017

See a solution process belowL

Explanation:

First, rewrite the expression as:

#((5a)/(3b))/((15c)/(9a^2))#

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)(5a)/color(blue)(3b))/(color(green)(15c)/color(purple)(9a^2)) =>#

#(color(red)(5a) xx color(purple)(9a^2))/(color(blue)(3b) xx color(green)(15c)) =>#

#(color(red)(color(black)(cancel(color(red)(5)))a) xx color(purple)(color(black)(cancel(color(purple)(9)))3a^2))/(color(blue)(color(black)(cancel(color(blue)(3)))b) xx color(green)(color(black)(cancel(color(green)(15)))3c)) =>#

#(3a^3)/(3bc) =>#

#(color(red)(cancel(color(black)(3)))a^3)/(color(red)(cancel(color(black)(3)))bc) =>#

#a^3/(bc)#

Nov 18, 2017

# a^3/(bc)#

Explanation:

Lets split this into two parts. Numbers and letters (variables)

#color(blue)("Dealing with the numbers.")#

#5/3-:15/9# It gives the wrong answer if you cancel out at this stage.

Write as

#5/3xx9/15 larr" Now you can cancel"#

I am swapping things round to make the cancelling more obvious

#5/15xx9/3 #

# 1/3xx3/1=1#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Dealing with the variable.")#

#a/b-:c/a^2#

#a/bxxa^2/c = a^3/(bc)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together.")#

#1xxa^3/(bc) = a^3/(bc)#