How do you divide #\frac { 4} { 245} -: \frac { 8} { 343} #?

2 Answers
Mar 8, 2018

#7/10#

Explanation:

Notes:
#color(white)("XXX")245=7xx7xx5#
#color(white)("XXX")343=7xx7xx7#
#color(white)("XXX")#To divide by a fraction, invert the fraction and multiply.

#4/245div 8/343#
#color(white)("XXX")=4/245 xx 343/8#

#color(white)("XXX")=4/(7xx7xx5) xx(7xx7xx7)/8#

#color(white)("XXX")=4/(cancel(7)xxcancel(7)xx5) xx(cancel(7)xxcancel(7)xx7)/8#

#color(white)("XXX")=4/5 xx7/8#

#color(white)("XXX")=cancel(4)/5 xx7/cancel(8)_2#

#color(white)("XXX")=7/10#

Mar 8, 2018

#4/245-:8/343=7/10#

Explanation:

Dividing a fraction #a/b# by another fraction #c/d# means multiplying former by the reciprocal or multiplicative inverse of latter i.e. #c/d#.

Reciprocal or multiplicative inverse of #c/d# is obtained by reversing the numerator and denominator. Hence reciprocal or multiplicative inverse of #c/d# is #d/c# and #a/b-:c/d=a/bxxd/c#.

Hence #4/245-:8/343=4/245xx343/8#

As #4# and #8# are divisible by #2# and #245# and#343# are divisible by #7#, this become

#(cancel4^1)/(cancel245^35)xx(cancel343^49)/(cancel8^2)#

= #1/35xx49/2# and as #35# and #49# are again divisible by #7#,

this becomes #1/(cancel35^5)xx(cancel49^7)/2#

= #7/(5xx2)#

= #7/10#