What is the simplified value of #7 8/9 - 5 3/5 #?

2 Answers
Jul 11, 2016

#color(green)(103/45)# or #color(green)(2 13/45)# as a mixed number.

Explanation:

Make both mixed fractions improper fractions.

1.) Multiply the whole number by the denominator
2.) Add that to the numerator
3.) Put the whole thing over the original denominator

Example:

#a b/c = ((atimesc)+b)/c#

So, we end up getting:

#71/9 - 28/5#

We don't have common denominators. Multiply the fraction on the left by #5/5# and multiply the fraction on the right by #9/9# to get a common denominator of #45#.

#(71times5)/(9times5) - (28times9)/(5times9)#

#355/45# - #243/45#

Now we can subtract.

#(355-252)/45#

#=color(green)(103/45)#

That is your final solution!

Jul 12, 2016

#2 13/45#

Explanation:

Split the values into 2 parts. Whole numbers and fractions

#color(brown)("As "8/9" is bigger than "3/5" we can use 7-5")#

#color(blue)("Consider the whole numbers part")#

#" "color(green)(7-5=2)#

;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Consider the fraction part")#

#" "8/9-3/5#

A fraction is split up into 2 parts.

#" "("The count")/("The size indicator")->("numerator")/("denominator")#

#color(brown)("You can not directly add or subtract the 'counts' unless the size")##color(brown)("indicators are the same.")#

#color(brown)("Multiply "8/9" by 1 but in the form of "1=5/5" giving:")#

#" "8/9xx5/5 = (8xx5)/(9xx5) = 40/45#

#color(brown)("Multiply "3/5" by 1 but in the form of "1=9/9" giving:")#

#" "3/5xx9/9 = (3xx9)/(5xx9) = 27/45#

#color(brown)("Putting all it together")#

#color(green)(" "8/9-3/5" " =" " 40/45-27/45" " =" " 13/45)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#" "bar(ul(|color(white)(2^2/2^2)7 8/9 - 5 3/5" " =" " 2 13/45color(white)(2/2)|))#