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# 5.5 Fractions and Decimals

Part I: Examples 1-5
Part II: Examples 6-9

by

Tweet## Charles Gramatges

on 29 January 2013#### Transcript of 5.5 Fractions and Decimals

How to convert between the two types of numbers 5.5 - Fractions and Decimals POD: Review of Concepts Writing a Fraction as Decimal That is soooo irrational! When we convert fractions into decimals, we are building RATIONAL numbers - these numbers have either a TERMINATING or REPEATING decimal. Now YOU try it: Textbook p. 352 [ 17, 19, 31, 33) What do we do with the WHOLE NUMBER? When converting a MIXED NUMBER to a DECIMAL, think about the mixed number as having TWO parts: POD - Day 2 1. Explain the procedure used to write a fraction in decimal form.

2. Compare and contrast the two numbers 0.5 and 0.5

3. A student represented the repeating decimal 0.1333... as 0.1333. Is this correct? Why or why not?

4. Is 0.10100100010000... a repeating decimal? Why or why not? Complete the following WITH your partner and turn in ONE sheet together! Here is the basic method Sometimes a fraction creates a repeating decimal, meaning the decimal does not terminate (like having a remainder in the division problem). In this case, you will need to either

1. ROUND your decimal, or

2. Use an OVERBAR (also called a vinculum) .4444... = .4 4.5 1004.202 34.3 121 Some decimals do NOT come from fractions... Like pi - these decimals do NOT terminate (they never end!) nor do they show any sign of repeating. Directions:

1. In your spiral start your homework assignment and try these four problems WITH YOUR PARTNER.

2. Check each other's work (do NOT move to step 3, yet!)

3. Check your answers in the back of the book. Part I: Whole Number Part II: Fraction Step 1: Split the fraction from its whole number Step 2: Convert the fraction Your answer then includes the whole number and the converted fraction: 4.5 Example:

(you'll see it when you click 'next'). terminates terminates repeating! (these are Homework problems!) No need to turn them in...just keep going! This is the END of today's lesson!

Spend the rest of the period working on your HW! Pause!!!! (Don't game rage and throw the iPad, please) January 29, 2013 To Do Now: 1. Turn in CSR if you have not done so (on the round table).

2. Note: TEST THURSDAY!

3. Click past the GOOMBA for your POD

4. Complete the Prezi w/ your partner

5. Begin Homework

...how's that INDEPENDENT STUDY coming??? Concept Note: We will go over rational vs. irrational AGAIN...so this is just an introduction. repeating! Directions:

1. THINK about these problems for about 3 minutes (silently...write down your answers in your spiral).

2. PAIR up with your neighbor and compare your answers.

3. Later, we will SHARE your answers as a class. Problems involving Fractions AND Decimals When you have a problem that involves BOTH a fraction and a decimal... Now YOU Try It! The end... Determine which TYPE of number you wish to use to simplify. Textbook p. 353 [ 63, 73, 79] Directions:

1. In your spiral start your homework assignment and try these three problems WITH YOUR PARTNER.

2. Check each other's work (do NOT move to step 3, yet!)

3. Check your answers in the back of the book. (these are Homework problems!) No need to turn them in...just keep going! You've found the GOOMBA! Terminating 4.5 0.1 terminating repeating These two decimals are easily identifiable as repeating or terminating...but can you identify terminating vs. repeating when a number is in FRACTION form? vs. Repeating Discover the secret: A fraction's decimal equivalent will repeat if ...? ...if what? First turn these fractions into decimals : 1 4 = 3 8 = 2 9 = 2 7 = 5 6 = 4 11 = (you and your partner can split them up) What do you notice about the DENOMINATOR of the fractions that are repeating decimals? Now...which one(s) REPEAT? Hint #1: There are FOUR fractions from the examples that will have repeating decimal equivalents. Hint #2: A fraction will repeat based on certain characteristics of the denominator. Hint #3: A fraction will repeat if the prime factorization of the denominator contains only __________ numbers. You have discovered the secret and rescued the princess! A fraction will turn into a repeating decimal if the denominator's factors include any combination of 2's and/or 3's, or if the denominator is a prime numbers! Bowser cannot prevent you from starting tonight's homework!!! YOSHI

POWER UP!!

Full transcript2. Compare and contrast the two numbers 0.5 and 0.5

3. A student represented the repeating decimal 0.1333... as 0.1333. Is this correct? Why or why not?

4. Is 0.10100100010000... a repeating decimal? Why or why not? Complete the following WITH your partner and turn in ONE sheet together! Here is the basic method Sometimes a fraction creates a repeating decimal, meaning the decimal does not terminate (like having a remainder in the division problem). In this case, you will need to either

1. ROUND your decimal, or

2. Use an OVERBAR (also called a vinculum) .4444... = .4 4.5 1004.202 34.3 121 Some decimals do NOT come from fractions... Like pi - these decimals do NOT terminate (they never end!) nor do they show any sign of repeating. Directions:

1. In your spiral start your homework assignment and try these four problems WITH YOUR PARTNER.

2. Check each other's work (do NOT move to step 3, yet!)

3. Check your answers in the back of the book. Part I: Whole Number Part II: Fraction Step 1: Split the fraction from its whole number Step 2: Convert the fraction Your answer then includes the whole number and the converted fraction: 4.5 Example:

(you'll see it when you click 'next'). terminates terminates repeating! (these are Homework problems!) No need to turn them in...just keep going! This is the END of today's lesson!

Spend the rest of the period working on your HW! Pause!!!! (Don't game rage and throw the iPad, please) January 29, 2013 To Do Now: 1. Turn in CSR if you have not done so (on the round table).

2. Note: TEST THURSDAY!

3. Click past the GOOMBA for your POD

4. Complete the Prezi w/ your partner

5. Begin Homework

...how's that INDEPENDENT STUDY coming??? Concept Note: We will go over rational vs. irrational AGAIN...so this is just an introduction. repeating! Directions:

1. THINK about these problems for about 3 minutes (silently...write down your answers in your spiral).

2. PAIR up with your neighbor and compare your answers.

3. Later, we will SHARE your answers as a class. Problems involving Fractions AND Decimals When you have a problem that involves BOTH a fraction and a decimal... Now YOU Try It! The end... Determine which TYPE of number you wish to use to simplify. Textbook p. 353 [ 63, 73, 79] Directions:

1. In your spiral start your homework assignment and try these three problems WITH YOUR PARTNER.

2. Check each other's work (do NOT move to step 3, yet!)

3. Check your answers in the back of the book. (these are Homework problems!) No need to turn them in...just keep going! You've found the GOOMBA! Terminating 4.5 0.1 terminating repeating These two decimals are easily identifiable as repeating or terminating...but can you identify terminating vs. repeating when a number is in FRACTION form? vs. Repeating Discover the secret: A fraction's decimal equivalent will repeat if ...? ...if what? First turn these fractions into decimals : 1 4 = 3 8 = 2 9 = 2 7 = 5 6 = 4 11 = (you and your partner can split them up) What do you notice about the DENOMINATOR of the fractions that are repeating decimals? Now...which one(s) REPEAT? Hint #1: There are FOUR fractions from the examples that will have repeating decimal equivalents. Hint #2: A fraction will repeat based on certain characteristics of the denominator. Hint #3: A fraction will repeat if the prime factorization of the denominator contains only __________ numbers. You have discovered the secret and rescued the princess! A fraction will turn into a repeating decimal if the denominator's factors include any combination of 2's and/or 3's, or if the denominator is a prime numbers! Bowser cannot prevent you from starting tonight's homework!!! YOSHI

POWER UP!!