How do you solve #4\frac { 1} { 6} + a = 5\frac { 5} { 6}#?

1 Answer
Jim G.
Dec 29, 2016

#a=5/3#

Explanation:

The first step here is to change the #color(blue)"mixed numbers to improper fractions"#

#rArr4 1/6=25/6" and " 5 5/6=35/6#

The equation can now be written.

#25/6+a=35/6#

To ' eliminate' the fractions from the equation, multiply ALL terms on both sides by 6, the lowest common multiple (LCM) of both denominators.

#(cancel(6)^1xx25/cancel(6)^1)+(6xxa)=(cancel(6)^1xx35/cancel(6)^1)#

#rArr25+6a=35#

Leave 6a on the left side and collect numeric values on the right side.

subtract 25 from both sides.

#cancel(25)cancel(-25)+6a=35-25#

#rArr6a=10#

To solve for a, divide both sides by 6

#(cancel(6) a)/cancel(6)=10/6#

#rArra=10/6=cancel(10)^5/cancel(6)^3=5/3" in simplest form"#

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