How do you solve #x/2 + 2/3 = 5/6#?

2 Answers
May 23, 2016

Answer:

#x = 1/3#

Explanation:

#x/2 + 2/3 =5/6#

#x/2 =5/6 - 2/3#

The L.C.M of the denominators of the fractions of the R.H.S #= 6#

#x/2 =5/6 - (2 *2) / (3 *2)#

#x/2 =5/6 - 4/6#

#x/2 =1/6#

#x =(1/6) *2#

#x = 1/3#

May 23, 2016

Answer:

Alternative approach

#x=1/3#

Explanation:

Notice that all the denominators are factors of 6

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To change the way a number looks without changing its value multiply by 1 but where 1 is in another form. For example

Changing #x/2# into #6 "th"^("s")# multiply by 1 but in the form of #1=3/3" "-> x/2xx3/3=(x xx3)/(2xx3) = (3x)/6#

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Given:#" "x/2+2/3=5/6#

Write as:#" " (x/2xx3/3)+(2/3xx2/2)=5/6#

#=> (3x)/6+4/6=5/6#

As everything is divided by 6 the equation is also true if we totally ignored the 6. Alternatively if you are not 'happy' about doing that this will get you to the same point:

Multiply everything by 6 giving:

#3x+4=5#

Subtract 4 from both sides:

#3x=1#

Divide both sides by 3

#x=1/3#