introduction to fraction busting lesson 2.2.3
TRANSCRIPT
Introduction to Fraction Busting
Lesson 2.2.3
Please
The topic of todayβslesson isβ¦
fractions and decimals
Admit itβ¦ You canβt stand working with decimals.
You despise fractions even more, donβt you!
Why canβt we justlearn about whole numbers.
Sometimes in life an βESTIMATEβ is just not good enough.
Well, becauseβ¦
Fractions and decimals give us a way of measuring things to an βEXACTβ!
Here are some real-world examples where βexactβ 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
βFamous Maroon Bandβ
Band Director
Maybe your interested in finding out about the worldβs smallest dog.
Meet a cute little Chihuahua named Brandy!
Bran
dy
6.1 inches nose to tail Weight 2 pounds
Dogs and Decimals?
Worldβs tallest dogβ¦
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. Itβs pretty uglyβ¦.
This has nothing to do with decimals or fractions,but does anyone want to see this yearβs UGLIEST dog winner?
2015 1st Place Winner
Ugliest dogβ¦
Meetβ¦. YODA !
2011 1st Place Winner
2011 UGLIEST dog winner was actually kind of cute. Letβs take a quick look before we get back to fractions and decimals.
Worldβs 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. 4ΒΌ 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 βNo Clueβ) 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 βNo Clueβ
Who is the Worldβs Fastest Rapper?
Priorβ¦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!
Todayβ¦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.
Weβll be doing problems like this:
Weβll also solve equations with decimals.
Section 1: Equations with Fractions
Section 2: Equations with Decimals
Fraction Busting Fractions in an equation can get very messyβ¦
especially the ones you will see in Algebra 1 and Algebra II.
Thatβs 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 βclearing the fractionβ instead if fraction busting.
In this process, the fractions are eliminated first so that you are left with a simpler equation to solveβ¦.
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.
( π₯2
+35=3
LCD of 2,5=ππ
The LCM is the smallest number that both 2 and 5 divide into evenly.
Distribute and Simplify
(
10 ( 10(3)5 2
π π
If your fractions donβt completely cancel outβ¦ Then you did something
wrong!
Click to Watch this Demo ! Itβs in slow motionβ¦
ΒΏππYour new equation without fractions!
Solve the resulting equation like normal.
Click to Watch Demo.
β6 β6
5 π₯ΒΏ245 5
π₯ΒΏ245ππ 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.
π₯+25=β
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.
β34π₯=β
67
You Try #2
β25π₯=β
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.
3π4β1320
=β710
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.
2π₯3β52=β
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 π₯3
+3 π₯2
=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.
π₯2β5 π₯6
=19
Section 1: Equations with Fractions
Section 2: Equations with Decimals
Decimal Busting - Review
We are not going to solve these equations, but letβs just look at what you would multiply each side by to βclearβ 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.
πππ (π .πππ+π .π )=πππ (π .π )πππ (π .πππ )+πππ (π .π )=πππ (π .π)
πππ+ππ=ππ
πππ=βπππππππ
=βππππ π=βπ
New equation without decimals!
Guided Practice #5
1.3β2π=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+5π=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.
CloserLetβs close today
by recapping the new procedures that we
learned todayβ¦
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.
( π₯2
+35=3
LCD of 2,5=ππ
The LCM is the smallest number that both 2 and 5 divide into evenly.
Clearing Fractions
Watch the Recap
(
10 ( 10(3)5 2
π π
If your fractions donβt completely cancel outβ¦ Then you did something
wrong!
ΒΏππ
Clearing Decimals
We are not going to solve these equations, but letβs just look at what you would multiply each side by to βclearβ 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.
πππ (π .πππ+π .π )=πππ (π .π )πππ (π .πππ )+πππ (π .π )=πππ (π .π)
πππ+ππ=ππ
πππ=βπππππππ
=βππππ π=βπ
New equation without decimals!
