# Introduction to Fraction Busting Equations with Rational Numbers/Cronnelly Lesson 6.2.3 P e s a e l The topic of todays lesson is fractions and decimals

Admit it You cant stand working with decimals. You despise fractions even more, dont you! Why cant we just learn about whole numbers. 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! Here are some real-world examples where exact mattered! 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 Dogs and Decimals? Maybe your interested in finding out about the worlds smallest dog. Meet a cute little Chihuahua named Brandy! n

a Br dy 6.1 inches nose to tail Weight 2 pounds Dogs and Fractions? Worlds tallest dog

Zenus The Great Dane 3 feet tall Ugliest dog This has nothing to do with decimals or fractions, but does anyone want to see this years UGLIEST dog winner? Are you sure you want to see this? Close your eyes if you want to. Its pretty ugly.

2015 1st Place Winner 2011 UGLIEST dog winner was actually kind of cute. Lets take a quick look before we get back to fractions and decimals. 2011 1st Place Winner Meet. YODA ! Longest Jump and

Fractions? Worlds 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. 4 in. Highest point on Earth?

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. Who is the Worlds 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 51.27 seconds in front of a licensed speech therapist. This works out to be an earhurting 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) Solve the simplified equation 4) Check your solution Steps 1 and 2 are not always 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. Well be doing problems like this: Well 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. Thats 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. 3 + =3 2 5 The LCM is the smallest number that both 2 and 5 divide into evenly. LCD of 2,5= Step 2: Multiply both sides of the equation by the LCD.

( Distribute and Simplify Click to Watch this Demo ! Its in slow motion ( 5 2 10 ( 10(3)

Your new equation without fractions! If your fractions dont completely cancel out Then you did something Solve the resulting equation like normal. Click to Watch Demo. 5 +6=30

6 6 5 5 24 5 24 4 4 5 5

Guided Practice #1 Step 1: Look at all of the denominators in the equation and find the LCD. 2 1 + = 5 3 Step 2: Multiply both sides

of the equation by the LCD. You Try #1 Step 1: at all of the Look denominators in the equation and find the LCD. 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 = 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 = 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. 3 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. 2 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. 4 3 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. 5 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 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 lets 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. ( . +. )= ( . ) ( . ) + ( . )=( . )New += = =

equation without decimals ! = 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 2 =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+5 =28.65 finall y Closer Lets close today by recapping the new procedures that we learned today I

k n i I th t i t o g !!! Clearing Fractions Step 1: Look at all of the denominators in the equation and

find the LCD. 3 + =3 2 5 The LCM is the smallest number that both 2 and 5 divide into evenly. LCD of 2,5= Step 2: Multiply both sides of the equation by the LCD.

( Watch the Recap ( 5 2 10 ( 10(3) If your fractions dont completely cancel

out Then you did something 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 lets 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.

( . +. )= ( . ) ( . ) + ( . )=( . )New += = = equation without decimals !

=

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