How do you solve #\frac{m}{m + 5} = \frac{6}{8}#?

2 Answers
Tony B
Sep 16, 2016

Explained using first principles showing every step.
Much faster to use the shortcuts.

#m=15#

Explanation:

#color(blue)("Principle for add, subtract, multiply and divide:")#

To move to the other side of the = reverse the process. So for multiply you divide, for add you subtract and so on.

#color(brown)("What you do to one side you do to the other.")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Given:#" "m/(m+5)=6/8#

Multiply both sides by #(m+5) larr" gets rid of the LHS "1/(m+5)#

#(m+5)/(m+5)xxm=6/8xx(m+5)#

But #(m+5)/(m+5)=1#

#1xxm=6/8xx(m+5)#

#m=6/8(m+5)#

Multiply both sides by 8 #larr" gets rid of the RHS "1/8#

#8m=8/8xx6(m+5)#

But #8/8=1#

#8m=6(m+5)#

Multiply out the bracket

#8m=6m+30#

Subtract 6m from both sides #larr" gets rid of the RHS "6m#

#2m=30#

Divide both sides by 2 #larr" gets rid of the RHS 2 from "2m#

#m=15#

Atika Khan
Sep 16, 2016

#8m=6(m+5)#
#8m=6m+30#
#8m-6m=30#
#2m=30#
#m=30/2#
#m=15#

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