1. Solving
Multi-Step Equations
Containing Fractions
Title

2. Let's look at fraction equations.
Ex. 1
The easiest way to solve a fraction equation is to first get rid of the fraction !!!
HOW???
Multiply each term by the common denominator!!
Like this...
This will cancel the denominator, leaving just numerators!!
Watch...
h has a denominator of one, so just multiply 14 times h.
Now reduce
Now Solve like before!!

3. You try it!! Now solve!! ... and reduce!! Ex. 2
First, multiply each term by the common denominator!!
This will cancel the denominator, leaving just numerators!!
m has a denominator of one, so just multiply 8 times m.
Now solve!!
... and reduce!!

4. Ex. 3
Even though the problem looks different, follow the same steps.
First, multiply each term by the common denominator!!
-2 and 8 have a denominator of one, so just multiply (-2)(9) and (8)(9).
Now solve!!

5. You try it!!
Ex. 4
First, multiply each term by the common denominator!!
-2 and 4 have a denominator of one, so just multiply (-2)(5) and (4)(5).
Now solve!!

6. Ex. 5
The problem looks different again but still follow the same steps.
First, multiply each term by the common denominator!! What is it?
NOW, divide 3 into 12. This will cancel the 3.
This will give you 4. Now multiply 4(-2).
Now solve!!

7. You try it again!! Now solve!! Ex. 6
First, multiply each term by the common denominator!! What is it?
3 will go into 12, 4 times. (4)(-1) =
2 will go into 12, 6 times. (6)(1) =
Now solve!!

8. What about one like this?
Ex. 7
Separate the double fraction then use same steps as before!!
The x – 8 becomes
x + -8 when we separate the fractions.
Now multiply by LCD.
Fix your signs back.
Now solve for “x”

9. You try it!!
Ex. 8
Separate the double fraction AND fix your double sign.

10. Ex. 9
With this type of problem you will FIRST distribute, THEN separate.
Get rid of the LCD. What is it?
5(11) = 55

11. You try it!! Ex. 10 USE THESE STEPS First Distribute Separate
Multiply by LCD
Solve

12. Try this one False Ex. 11 No Solution USE THESE STEPS Separate
Multiply by LCD
Solve
What happened to the variables?
The variables cancelled each other out. The statement left says 1 = 20. IS THAT TRUE OR FALSE?
False
No Solution
If the statement had been TRUE, the answer would have been ALL REAL NUMBERS