1. Introduction to Fraction Busting
Lesson 2.2.3
Please

2. fractions and decimals
The topic of today’s
lesson is…
fractions and decimals

3. Admit it…
You can’t stand working with decimals.

4. You despise fractions even more, don’t you!

5. Why can’t we just
learn about whole numbers.

6. Well, because…
Sometimes in life an “ESTIMATE” is just not good enough.
Fractions and decimals give us a way of measuring things to an “EXACT”!

7. Here are some real-world examples where “exact” mattered!

8. Band Director
Elva Lance
A marching band has 6.5 minutes to perform at a football game during halftime. If they go over 6.5 minutes their team could be penalized!
“Famous Maroon Band”

9. Dogs and Decimals? Brandy nose to tail 6.1 inches Weight 2 pounds
Maybe your interested in finding out about the world’s smallest dog.
Meet a cute little Chihuahua named Brandy!
6.1 inches
nose to tail
Brandy
Weight
2 pounds

10. Dogs and Fractions? Zenus 3 𝟐 𝟑 feet tall World’s tallest dog… The
Great Dane
3 𝟐 𝟑 feet tall

11. Ugliest dog… 2015 1st Place Winner
This has nothing to do with decimals or fractions,
but does anyone want to see this year’s UGLIEST dog winner?
Are you sure you want to see this? Close your eyes if you want to. It’s pretty ugly….
2015
1st Place Winner

12. Meet…. YODA ! 2011 1st Place Winner
2011 UGLIEST dog winner was actually kind of cute. Let’s take a quick look before we get back to fractions and decimals.
2011
1st Place Winner
Yoda's short clusters of hair, protruding tongue, and long, seemingly hairless legs were enough to earn it the World's Ugliest Dog title. The 14-year-old Chinese crested and Chihuahua mix won the honor in 2011’s Ugliest Dog Contest.
Meet…. YODA !

13. Longest Jump and Fractions?
World’s longest jump belongs to this man, Mike Powell from the United States. He broke the record in the 1991 World Championship in Tokyo.
Guess how far he jumped!
29 ft. 4¼ in.

14. Highest point on Earth? 29,028.75 feet Mt. Everest in China
If you want to the highest point on earth you have to know exactly how tall something is.

15. Who is the World’s Fastest Rapper?
Seconds mattered back in 2005 when a Seattle rapper named
Ricky Brown (aka “No Clue”) made the Guinness Book of Records by rapping 723 syllables in seconds in front of a licensed speech therapist. This works out to be an ear-hurting 14.1 syllables per second ! This beat out 7 year record holder Rebel XD who only belted out syllables per second.
Ricky Brown
aka “No Clue”

16. Prior… In the last lesson, you were introduced to solving equations.
You learned that to solve an equation you:
Distribute to remove any parentheses
Combine the like terms
Move the variables to one side and the constants to the other
Solve the simplified equation
Steps 1 and 2 are not always necessary!

17. Today…
We are going to continue to solve equations, but the equations are going to be
rational equations.
Rational equations are equations where one or more of the terms are fractional.
We’ll be doing problems like this:
𝑥 =3
We’ll also solve equations with decimals.

18. Section 1: Equations with Fractions Section 2: Equations with Decimals

19. Fraction Busting
Fractions in an equation can get very messy… especially the ones you will see in Algebra 1 and Algebra II.
That’s why it is very important that you learn a process called Fraction Busting. You are going to need this skill for your upper level math classes.
A lot of people like to call the process “clearing the fraction” instead if fraction busting.
In this process, the fractions are eliminated first so that you are left with a simpler equation to solve….
One that does not have any fractions!

20. Steps 𝑥 2 + 3 5 =3 10 ( 𝑥 2 + 3 5 )=3 (10) LCD of 2,5 =𝟏𝟎 Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
𝑥 =3
10 ( 𝑥 )=3 (10)
The LCM is the smallest number that both 2 and 5 divide into evenly.
LCD of 2,5 =𝟏𝟎

21. Distribute and Simplify
Click to Watch this Demo ! It’s in slow motion…
10 ( 𝑥 )=10(3) 5 2
10 ( 𝑥 2 ) ( ) = 10(3)
+ 𝟔
Your new equation without fractions! 𝟓𝒙
= 𝟑𝟎
If your fractions don’t completely cancel out…
Then you did something wrong!

22. Solve the resulting equation like normal.
Click to Watch Demo.
5x =
− 6
− 6 5𝑥 24 = 5 5 𝑥 = 𝑜𝑟

23. Guided Practice #1 𝑥 + 2 5 = − 1 3 Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
𝑥 = − 1 3
Work on board. Have students work along with you in their notes.
Answer: − 11 15

24. You Try #1
Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
𝑥 = − 1 21
Have students try this one on their own. Then review.
Answer: − 15 21

25. Guided Practice #2 − 3 4 𝑥=− 6 7 Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
− 3 4 𝑥=− 6 7
Answer:

26. You Try #2
Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
− 2 5 𝑥 =− 6 7
Answer:

27. Guided Practice #3 3𝑎 4 − 13 20 =− 7 10 Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
3𝑎 4 − =− 7 10
Answer: − 1 15

28. You Try #3
Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
2𝑥 3 − =− 1 2
Answer: 3

29. Guided Practice #4 4𝑥 3 + 3𝑥 2 = 17 6 Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
4𝑥 𝑥 2 = 17 6
Answer: 1

30. You Try #4
Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
𝑥 2 − 5𝑥 6 = 1 9
Answer: − 1 3

31. Section 1: Equations with Fractions Section 2: Equations with Decimals

32. Decimal Busting - Review
Step 1:
Look for the decimal with the most digits.
Step 2:
Multiply both sides of the equation by that power of 10.
We are not going to solve these equations, but let’s just look at what you would multiply each side by to “clear” the decimals.
Multiply both sides by 100
Multiply both sides by 10
Multiply both sides by 1000

33. Example
Here is a problem that I found on the internet where the person cleared their decimals first.
Decimal with the most digits.
𝟎.𝟐𝟓𝒙+𝟎.𝟔=𝟎.𝟏
𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙+𝟎.𝟔 =𝟏𝟎𝟎 𝟎.𝟏
𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙 +𝟏𝟎𝟎 𝟎.𝟔 =𝟏𝟎𝟎(𝟎.𝟏)
New equation without decimals!
𝟐𝟓𝒙+𝟔𝟎 = 𝟏𝟎
Teachers, just skip this slide if you prefer your students to solve decimal problems the normal way (instead of clearing the decimal).
− 𝟔𝟎 −𝟔𝟎
𝟐𝟓𝒙=−𝟓𝟎
𝟐𝟓𝒙 𝟐𝟓 = −𝟓𝟎 𝟐𝟓
𝒙 = −𝟐

34. Guided Practice #5 1.3−2𝑑=2.7 Step 1:
Look for the decimal with the most digits.
Step 2:
Multiply both sides of the equation by that power of 10.
1.3−2𝑑=2.7
Answer: −0.7

35. You Try #5
Step 1:
Look for the decimal with the most digits.
Step 2:
Multiply both sides of the equation by that power of 10.
𝑝=28.65
Answer: − 15 21

36. finally
Closer
Let’s close today by recapping the new procedures that we learned today…
I think I got it
!!!

37. Clearing Fractions 𝑥 2 + 3 5 =3 10 ( 𝑥 2 + 3 5 )=3 (10) LCD of 2,5 =𝟏𝟎
Step 1:
Look at all of the denominators in the equation and find the LCD.
Step 2:
Multiply both sides of the equation by the LCD.
𝑥 =3
10 ( 𝑥 )=3 (10)
The LCM is the smallest number that both 2 and 5 divide into evenly.
LCD of 2,5 =𝟏𝟎

38. Then you did something wrong!
Watch the Recap
10 ( 𝑥 )=10(3) 5 2
10 ( 𝑥 2 ) ( ) = 10(3) 𝟓𝒙
+ 𝟔
= 𝟑𝟎
If your fractions don’t completely cancel out…
Then you did something wrong!

39. Clearing Decimals
Step 1:
Look for the decimal with the most digits.
Step 2:
Multiply both sides of the equation by that power of 10.
We are not going to solve these equations, but let’s just look at what you would multiply each side by to “clear” the decimals.
Multiply both sides by 100
Multiply both sides by 10
Multiply both sides by 1000

40. Watch the Recap 𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙+𝟎.𝟔 =𝟏𝟎𝟎 𝟎.𝟏 𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙 +𝟏𝟎𝟎 𝟎.𝟔 =𝟏𝟎𝟎(𝟎.𝟏)
Decimal with the most digits.
𝟎.𝟐𝟓𝒙+𝟎.𝟔=𝟎.𝟏
𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙+𝟎.𝟔 =𝟏𝟎𝟎 𝟎.𝟏
𝟏𝟎𝟎 𝟎.𝟐𝟓𝒙 +𝟏𝟎𝟎 𝟎.𝟔 =𝟏𝟎𝟎(𝟎.𝟏)
New equation without decimals!
𝟐𝟓𝒙+𝟔𝟎 = 𝟏𝟎
− 𝟔𝟎 −𝟔𝟎
Teachers, just skip this slide if you prefer your students to solve decimal problems the normal way (instead of clearing the decimal).
𝟐𝟓𝒙=−𝟓𝟎
𝟐𝟓𝒙 𝟐𝟓 = −𝟓𝟎 𝟐𝟓
𝒙 = −𝟐