Download Introduction to Fraction Busting

Introduction to Fraction Busting
Lesson 2.2.3
Admit it…
Sometimes in life
an “ESTIMATE” is
just not good
enough.
Fractions and
decimals give us a
way of measuring
things to an
“EXACT”!
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”
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
Weight
2 pounds
World’s tallest dog…
Zenus
The
Great Dane
𝟐
𝟑
3 feet tall
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
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
Meet…. YODA !
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.
Mt. Everest in China
29,028.75 feet
If you want to the highest point
on earth you have to know
exactly how tall something is.
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 51.27 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 12.5
syllables per second.
Ricky Brown
aka “No Clue”
Prior…

In the last lesson, you were introduced to
solving equations.

You learned that to solve an equation you:
1) Distribute to remove any parentheses
2) Combine the like terms
3) Move the variables to one side and the
constants to the other
4) Solve the simplified equation
Steps 1 and 2 are not always necessary!
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
+ =3
2 5

We’ll also solve equations with decimals.
Section 1: Equations with Fractions
Section 2: Equations with Decimals
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!
Steps
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
𝑥 3
+ =3
2 5
The LCM is the smallest
number that both 2 and 5
divide into evenly.
LCD of 2,5 = 𝟏𝟎
Step 2:
Multiply both sides of
the equation by the
LCD.
10 (
𝑥
2
+
3
)
5
= 3 (10)
Distribute and Simplify
Click to Watch this Demo !
It’s in slow motion…
10 (
5
𝑥
2
𝑥
2
2
+
3
5
) = 10(3)
3
5
10 ( ) + 10 ( ) = 10(3)
𝟓𝒙 + 𝟔 = 𝟑𝟎
Your new equation
without fractions!
If your fractions don’t completely cancel out…
Then you did something wrong!
Solve the resulting equation like normal.
Click to Watch Demo.
5x
+6
=
−6
30
−6
5𝑥 = 24
5
5
𝑥 =
24
4
𝑜𝑟 4
5
5
Guided Practice #1
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
2
1
𝑥 +
= −
5
3
Step 2:
Multiply both sides of
the equation by the
LCD.
You Try #1
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
2
1
𝑥+ = −
3
21
Step 2:
Multiply both sides of
the equation by the
LCD.
Guided Practice #2
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
3
6
− 𝑥=−
4
7
Step 2:
Multiply both sides of
the equation by the
LCD.
You Try #2
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
2
6
− 𝑥 =−
5
7
Step 2:
Multiply both sides of
the equation by the
LCD.
Guided Practice #3
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
3𝑎
13
7
−
=−
4
20
10
Step 2:
Multiply both sides of
the equation by the
LCD.
You Try #3
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
2𝑥
5
1
− =−
3
2
2
Step 2:
Multiply both sides of
the equation by the
LCD.
Guided Practice #4
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
4𝑥
3𝑥
17
+
=
3
2
6
Step 2:
Multiply both sides of
the equation by the
LCD.
You Try #4
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
𝑥
5𝑥
1
−
=
2
6
9
Step 2:
Multiply both sides of
the equation by the
LCD.
Section 1: Equations with Fractions
Section 2: Equations with Decimals
Decimal Busting - Review
Step 1:
Step 2:
Look for the decimal
with the most digits.
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.
1)
Multiply both sides by 100
Multiply both sides by 10
Multiply both sides by 1000
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)
𝟐𝟓𝒙 + 𝟔𝟎 = 𝟏𝟎
− 𝟔𝟎
−𝟔𝟎
New
equation
without
decimals!
𝟐𝟓𝒙 = −𝟓𝟎
𝟐𝟓𝒙
−𝟓𝟎
=
𝟐𝟓
𝟐𝟓
𝒙 = −𝟐
Guided Practice #5
Step 1:
Step 2:
Look for the decimal
with the most digits.
Multiply both sides of
the equation by that
power of 10.
1.3 − 2𝑑 = 2.7
You Try #5
Step 1:
Step 2:
Look for the decimal
with the most digits.
Multiply both sides of
the equation by that
power of 10.
24.2 + 5𝑝 = 28.65
finally
Closer
Let’s close today
by recapping the new
procedures that we learned
today…
Clearing Fractions
Step 1:
Look at all of the
denominators in the
equation and find the
LCD.
𝑥 3
+ =3
2 5
The LCM is the smallest
number that both 2 and 5
divide into evenly.
LCD of 2,5 = 𝟏𝟎
Step 2:
Multiply both sides of
the equation by the
LCD.
10 (
𝑥
2
+
3
)
5
= 3 (10)
Watch the Recap
10 (
5
𝑥
2
𝑥
2
2
+
3
5
) = 10(3)
3
5
10 ( ) + 10 ( ) = 10(3)
𝟓𝒙 + 𝟔 = 𝟑𝟎
If your fractions don’t completely cancel out…
Then you did something wrong!
Clearing Decimals
Step 1:
Step 2:
Look for the decimal
with the most digits.
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.
1)
Multiply both sides by 100
Multiply both sides by 10
Multiply both sides by 1000
Watch the Recap
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)
𝟐𝟓𝒙 + 𝟔𝟎 = 𝟏𝟎
− 𝟔𝟎
−𝟔𝟎
New
equation
without
decimals!
𝟐𝟓𝒙 = −𝟓𝟎
𝟐𝟓𝒙
−𝟓𝟎
=
𝟐𝟓
𝟐𝟓
𝒙 = −𝟐