1. Equations with Fractions

2. YUCK!

3. What to do? What to do? Let’s get rid of the dang fractions!
Remember the miracle of multiplying fractions:
CANCELLATION!

4. If you multiply by 2, you get
Cancellation
If you multiply by 2, you get

5. If you multiply by 6, you get
Cancellation
If you multiply by 6, you get

6. Getting rid of 2 denominators
We have to get rid of both a 2 and a 6.
What number can we multiply by that will cancel both of them?
The Least Common Denominator!

7. LCD
Unless someone flat out asks you what the least common denominator is, you can really use any common denominator in most fraction problems. They just like to use the smallest one to keep the numbers in the problem small.

8. LCD and Least Common Multiple
If thinking of the LCD makes your eyes cross, go for the least common multiple instead!
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 6: 6, 12, 18, 24, 30

9. Smallest number on both lists: Multiples of 2: 2, 4, 6, 8, 10, 12
Least Common Multiple
Smallest number on both lists:
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 6: 6, 12, 18, 24, 30

10. Notice that there are other numbers on both lists:
Common Multiples
Notice that there are other numbers on both lists:
Multiples of 2: 2, 4, 6, 8, 10, 12,…,18
Multiples of 6: 6, 12, 18, 24, 30
You could use any of these to get rid of the fractions in your equation.

11. Let’s Multiply by 6!

12. Let’s Multiply by 6!

13. Wrap-up
3x + x + 2 = 42
4x + 2 = 42
4x = 42 – 2
4x = 40
X = 10

14. Check

15. Minus Signs Between Fractions
Cancel the fractions!
Distribute the -1

16. Dreaded Fractions Any time you have an equal sign and fractions:
Determine a common denominator
Multiply each term by it.
If all your fractions don’t cancel, you picked the wrong number!.