# Solving for variables

Q: Solve for the following variables:

(1) a + 2/3 = 1/3

(2) (1/2)x =3/4

(3) g-4/5 = 3/5

A:

(1):  a + 2/3 = 1/3

To solve for a, we have to get it by itself.  This means, we have to subtract 2/3 from each side:

a + 2/3 – 2/3 = 1/3 – 2/3

[notice that the 2/3 on the left side will cancel out!  Good news]

a = 1/3 – 2/3

a = (1-2)/3

a = -1/3

(2) (1/2)x =3/4

Again, we need to get x by itself, right?  The best way to “get rid of” a fraction is to multiply by its reciprocal (which is just the fraction flipped over).  For example, the reciprocal of 3/7 is 7/3.  The reciprocal of 3 is 1/3.  Make sense? So, to “get rid of” the 1/2, we can multiply by 2/1… Remember, whatever you do to one side of an equation, you must do to the other side:

(2/1)*(1/2)x =(3/4)*(2/1)

[Remember, when multiply fractions: just multiply across the top and multiply across the bottom]

(2/2)x = (6/4)

Since 2/2 = 1, we just end up with 1x (or just x) on the left:

x = 6/4 = 3/2

(3) g-4/5 = 3/5

We gotta get g by itself.  There is a -4/5 on the left side with the g, so, let’s add 4/5 to both sides:

g-4/5 + 4/5 = 3/5 + 4/5 [notice that the numbers on the left side will cancel out!]

g = (3+4)/5 = 7/5