introduction to fraction busting lesson 2.2.3

Introduction to Fraction Busting

Lesson 2.2.3

Please

The topic of today’slesson is…

fractions and decimals

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

You despise fractions even more, don’t you!

Why can’t we justlearn about whole numbers.

Sometimes in life an “ESTIMATE” is just not good enough.

Well, because…

Fractions and decimals give us a way of measuring things to an “EXACT”!

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

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!

Elva Lance

“Famous Maroon Band”

Band Director

Maybe your interested in finding out about the world’s smallest dog.

Meet a cute little Chihuahua named Brandy!

Bran

dy

6.1 inches nose to tail Weight 2 pounds

Dogs and Decimals?

World’s tallest dog…

Zenus The Great Dane 3 feet

tall

Dogs and Fractions?

Are you sure you want to see this? Close your eyes if you want to. It’s pretty ugly….

This has nothing to do with decimals or fractions,but does anyone want to see this year’s UGLIEST dog winner?

2015 1st Place Winner

Ugliest dog…

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.

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.

Longest Jump and Fractions?

Highest point on Earth?

Mt. Everest in China29,028.75 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”

Who is the World’s Fastest Rapper?

Prior…In the last lesson, you were introduced to

solving equations.

You learned that to solve an equation you:1) Distribute to remove any parentheses2) Combine the like terms3) Move the variables to one side and the

constants to the other4) 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 berational equations.

Rational equations are equations where one or more of the terms are fractional.

We’ll be doing problems like this:

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!

StepsStep 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.

( 𝑥2

+35=3

LCD of 2,5=𝟏𝟎

The LCM is the smallest number that both 2 and 5 divide into evenly.

Distribute and Simplify

(

10 ( 10(3)5 2

𝟓 𝒙

If your fractions don’t completely cancel out… Then you did something

wrong!

Click to Watch this Demo ! It’s in slow motion…

¿𝟑𝟎Your new equation without fractions!

Solve the resulting equation like normal.

Click to Watch Demo.

−6 −6

5 𝑥¿245 5

𝑥¿245𝑜𝑟 4

45

5x + 6 = 30

Guided Practice #1Step 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+25=−

13

You Try #1Step 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.

Guided Practice #2Step 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.

−34𝑥=−

67

You Try #2

−25𝑥=−

67

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.

Guided Practice #3Step 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.

3𝑎4−1320

=−710

You Try #3Step 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.

2𝑥3−52=−

12

Guided Practice #4Step 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.

4 𝑥3

+3 𝑥2

=176

You Try #4Step 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.

𝑥2−5 𝑥6

=19

Section 1: Equations with Fractions

Section 2: Equations with Decimals

Decimal Busting - Review

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)

Step 1:

Look for the decimal with the most digits.

Step 2:

Multiply both sides of the equation by that power of 10.

Multiply both sides by 100

Multiply both sides by 10

Multiply both sides by 1000

ExampleHere is a problem that I found on the internet where the person cleared their decimals first.

Decimal with the most digits.

𝟏𝟎𝟎 (𝟎 .𝟐𝟓𝒙+𝟎 .𝟔 )=𝟏𝟎𝟎 (𝟎 .𝟏 )𝟏𝟎𝟎 (𝟎 .𝟐𝟓𝒙 )+𝟏𝟎𝟎 (𝟎 .𝟔 )=𝟏𝟎𝟎 (𝟎 .𝟏)

𝟐𝟓𝒙+𝟔𝟎=𝟏𝟎

𝟐𝟓𝒙=−𝟓𝟎𝟐𝟓𝒙𝟐𝟓

=−𝟓𝟎𝟐𝟓 𝒙=−𝟐

New equation without decimals!

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.

You Try #5

24.2+5𝑝=28.65

Step 1:

Look for the decimal with the most digits.

Step 2:

Multiply both sides of the equation by that power of 10.

CloserLet’s close today

by recapping the new procedures that we

learned today…

I think I

got it

!!!

finally

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.

( 𝑥2

+35=3

LCD of 2,5=𝟏𝟎

The LCM is the smallest number that both 2 and 5 divide into evenly.

Clearing Fractions

Watch the Recap

(

10 ( 10(3)5 2

𝟓 𝒙

If your fractions don’t completely cancel out… Then you did something

wrong!

¿𝟑𝟎

Clearing Decimals

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)

Step 1:

Look for the decimal with the most digits.

Step 2:

Multiply both sides of the equation by that power of 10.

Multiply both sides by 100

Multiply both sides by 10

Multiply both sides by 1000

Watch the RecapDecimal with the most digits.

𝟏𝟎𝟎 (𝟎 .𝟐𝟓𝒙+𝟎 .𝟔 )=𝟏𝟎𝟎 (𝟎 .𝟏 )𝟏𝟎𝟎 (𝟎 .𝟐𝟓𝒙 )+𝟏𝟎𝟎 (𝟎 .𝟔 )=𝟏𝟎𝟎 (𝟎 .𝟏)

𝟐𝟓𝒙+𝟔𝟎=𝟏𝟎

𝟐𝟓𝒙=−𝟓𝟎𝟐𝟓𝒙𝟐𝟓

=−𝟓𝟎𝟐𝟓 𝒙=−𝟐

New equation without decimals!