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
