Algebraic fractions for year 8 (Australian curriculum).

1. Algebraic Fractions Worked Solutions
Example 1:
Example 1b:
1
2
+ x = 2 Same principle applies. Bring the x to be by itself.
x = 2 -
1
2
As the
1
2
is a positive number, you minus it from both sides.
x =1
1
2
Method 2 Gets the exact same answer...
1
2
- 2 = -x We had to minus the x and then minus the 2 from either
side to get the numbers on one side and the letters (pronumerals)
on the other.
-1
1
2
= -x Now, we get rid of the negative, by dividing it by -1
-11
2
-1
=1 because negative x is the same as -1x
x =1
1
2
Now the x is on it's own, we have the answer. So it doesn't
matter which side you take to which side as you get the same answer.
Method 1
1
2
+ x = 2
x = 2 -
1
2
x =1
1
2
Method 2 Gets the exact same answer...
1
2
- 2 = -x
-1
1
2
= -x
-11
2
-1
=1
x =1
1
2
Just the Math

2. Algebraic Fractions Worked Solutions
Example 2:
Example 3 – Done 2 different ways (Both are correct):
Use the same principles now with the harder questions.
An explanation of the problem to the right.
x
2
= 6 This is the same as saying x ¸2 = 6
x
2
´2 = 6´2 Doing this will get the x on its own,
x =12 which is what we need to do.
The Maths without
the words..
x
2
= 6
x
2
´ 2 = 6´2
x =12
x
3
+ 2 = 8 1. You need to get the x on its own. As these problems
get harder we add another skill to the mix.
2. We leave the bit with the x in it to last.
x
3
+ 2 -2 = 8- 2
x
3
= 6 Now we do the x bit.
x
3
´3= 6´3
x =18 This is the answer as x is on its own.
Method 2:
x
3
+ 2 = 8
You can treat this as a fraction and just add it
once you have the same denominator.
x
3
+
6
3
= 8 or
x + 6
3
= 8
x + 6 = 8´3
x + 6 = 24
x = 24- 6
x =18
You notice that you get the same answer.