M9 U3 Notes 2017.notebook

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November 30, 2016

Oct 9­9:04 AM

Math 9

Unit 3: Rational Numbers

Oct 9­9:07 AM

3.1 What is a Rational Number?

Any number that can be written in the form mn

,where m and n are integers and n = 0.

In other words, any number that can be written as a

fraction without 0 on the bottom.

This includes decimals that can be written as fractions.

ex. 0.5 = 5

1012

=

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November 30, 2016

Oct 14­9:12 AM

5 2 1 4 . 3 7 8 9Place Value

Oct 10­9:15 AM

Converting from decimals (non-repeating) to fractions:

Step 1: Take the number after the decimal and put it on

top of the fraction.

Step 2: Put a 1 on the bottom of the fraction, followed

by as many 0s as there are spots after the decimal.

Step 3: Simplify.

ex. 0.75

ex. 0.081

ex. 2.15

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November 30, 2016

Oct 24­10:08 AM

2 It goes into all EVEN numbers

1 It goes into everything!!!

3 Add all the digits in the number up and if that is

divisible by 3 then the original number is divisible by 3

Divisibility Rules Refresher:

Oct 24­10:09 AM

5 All numbers that end in 0 or 5 are divisible by 5

6 Any number divisible by BOTH 2 and 3 are divisible by 6

4 Look at the last two digits of a number. If they are divisible

by 4, then the whole number is divisible by 4

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November 30, 2016

Oct 24­10:09 AM

7 No rule. :'(

8 Look at the last three digits of a number. If they are

divisible by 8, then the whole number is divisible by 8

9 Add all the digits in the number up and if that is divisible

by 9 then the original number is divisible by 9

10 All numbers that end in 0 are divisible by 10

11 It's complicated...

Oct 10­9:28 AM

Converting from decimals (repeating) to fractions:

Step 1: Take the repeating number after the decimal and

put it on top of the fraction.

Step 2: Put as many 9s on the bottom as there are spots

after the decimal.

Step 3: Simplify.

ex. 0.47

ex. 0.3

ex. 1.023

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November 30, 2016

Oct 14­8:58 AM

Rounding:

4 54.54.25 4.75

ex. Is 4.8 closer to 4 or 5?

ex. Round 4.8 to the nearest whole number.

Oct 14­9:09 AM

ex. Round 8.7 to the nearest whole number.

ex. Round 8.78 to the nearest tenth.

When rounding, 0.5 to 0.9 rounds ________ and everything under 0.4 rounds _________.

ex. Round 8.2 to the nearest whole number.

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November 30, 2016

Oct 14­9:20 AM

ex. Round 2.8473 to the nearest hundredth.

ex. Round 4.75243 to the nearest tenth.

ex. Round 9.95 to the nearest tenth.

ex. Round 4.749 to the nearest tenth.

Oct 9­9:18 AM

Converting from fractions to decimals:

Step 1: Divide numerator by denominator.

24

ex.

ex. 79

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November 30, 2016

Oct 25­10:28 AM

Oct 14­9:38 AM

If a fraction is negative, where do I put the sign?

ex. Which one is correct?

- 25

-25

2-5

-2-5

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November 30, 2016

Oct 17­9:23 AM

less than

greater than

less than or equal to

greater than or equal to

equal to

Oct 20­8:57 AM

Marshall has $1.8 billion. He spends $2.7 billion on a new

skyscraper. He got a loan to cover the extra costs.

How much will he owe the bank?

Use a number line to represent the two numbers.

ex.

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November 30, 2016

Nov 30­10:24 AM

Converting Between Mixed Numbers and Improper Fractions

Sep 18­9:21 AM

Improper Fractions to Mixed Numbers

Mixed Numbers to Improper Fractions

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November 30, 2016

Sep 18­9:27 AM

Converting Whole Numbers to Fractions

Nov 23­10:18 AM

Equivalent Fractions

To make equivalent fractions, multiply the top and the

bottom by the same number.

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November 30, 2016

Nov 23­10:36 AM

Simplifying Fractions

Find the largest factors that divide evenly into both the

numerator and the denominator

Oct 15­9:02 AM

Writing a rational number between two given numbers:

ex. Write a rational number between 1 and 2.

ex. Find a rational number between -3 and -4.

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November 30, 2016

Oct 15­9:11 AM

ex. Find a rational number between 1.25 and -3.26.

ex. Find a rational number between -0.25 and -0.26.

Oct 15­9:34 AM

ex. Find a rational number between and .

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November 30, 2016

Oct 16­9:03 AM

Ordering rational numbers in decimal OR fraction form

ex. Use a number line to order these numbers from least to

greatest:

0.35 2.5 -0.6 1.7 -3.2 -0.6

Oct 16­9:17 AM

ex. Use a number line to order these numbers from least to

greatest:

- 38

59

- 104

-114

710 3

8

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November 30, 2016

Oct 17­9:10 AM

Ordering Rational Numbers in Fraction and Decimal Form

ex. Order these rational numbers from least to greatest:

Steps: Convert to either ALL ___________ or ALL ___________.

Place on the number line, using the ___________

number form.

- 103

2.7 -225

37

-3.41.13

Nov 2­9:57 AM

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November 30, 2016

Nov 5­9:04 AM

Studying for Math Tests

1. Use your _____________.

2. Find ______ examples.

3. Copy the questions on _____________ piece of paper.

4. Try the question ____________ looking at your notes.

5. __________ to see if you are right!

6. If you're right, move on to the __________ question.

7. If not, find your __________, ____________ it, and then try

__________.

8. If you don't understand what went wrong, even after

checking for your error, then look over the

_________________ in your notes, ask a ____________ who is

confident about the topic, or __________ the teacher.

I CAN study for a math test. Again.

Nov 23­3:10 PM

What happens now?

• Study Notes

• Chapter 3a Test

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November 30, 2016

Sep 15­9:32 AM

ex.

3.2 Adding Rational Numbers

Sep 15­9:42 AM

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November 30, 2016

Oct 20­9:39 AM

Steps:

• Find a common denominator. Use equivalent fractions

to set this up.

• Add the numerators.

• DON'T FORGET ABOUT THE +/- SIGNS!!!1. Find a common

denominator

2. Multiply both top

and bottom of

fraction(s) to make

them equivalent

3. Add tops

4. Leave bottoms the

same

5. Convert to mixed

number answer, if

needed

Oct 21­9:00 AM

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November 30, 2016

Oct 21­9:05 AM

Oct 21­9:13 AM

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November 30, 2016

Oct 21­9:16 AM

Oct 23­8:57 AM

ex. At the beginning of June, The Frosty Snow Blower

Company was $235.46 in debt. By the end of August,

the company had increased its debt by $156.71.

How much are they in debt for at the end of August?

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November 30, 2016

Dec 4­10:31 AM

Same process as adding but we take away instead.

• Convert mixed numbers to improper fractions.

• Find the lower common denominator (LCD).

• Make equivalent fractions so that the fractions have the

same denominator.

• Subtract (just the numerator - top).

• Reduce.

• Convert any improper fractions to mixed numbers.

3.3 Subtracting Rational Numbersex.

Oct 23­9:42 AM

ex.

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November 30, 2016

Oct 29­9:04 AM

ex. -2.3-(-3.9) ex. -2.3+(-3.9)

Oct 30­8:56 AM

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November 30, 2016

Oct 30­9:35 AM

A diver jumps off a cliff that is 14.7 m above sea level.

After hitting the water, he plunges 3.8 m below the

surface of the water before returning to the surface.a) Use rational numbers to represent the difference in

heights from the top of the cliff to the bottom of his dive

(use +/- decimals to write out the expression).

ex.

Oct 21­4:40 PM

b) The water is 5.6 m deep. What is the distance from the

ocean floor to the bottom of the dive?

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November 30, 2016

Nov 23­3:10 PM

What happens now?

• Study Notes

• Chapter 3b Test

Nov 12­9:10 AM

5.4 Multiplying Rational NumbersPart A - Fractions

Steps:

• Convert any mixed # to improper fractions

• Multiply the tops straight across

• Multiply the bottoms straight across

• Check your signs to make sure you did it right

• Reduce

Optional: You can cross cancel before Step 2, if you

would like to skip Step 5

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November 30, 2016

Jan 5­9:52 AM

ex.

ex.

Nov 12­9:24 AM

ex.

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November 30, 2016

Nov 13­8:50 AM

When multiplying by decimals, sometimes you get a

___________ answer than you expect.

When multiplying by a number between _____ and _____ or

_____ and _____, your answer will be smaller than the original

number.

Part B: Decimals

Nov 13­9:09 AM

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November 30, 2016

Nov 14­8:58 AM

ex. On February 5, 2008, the price of a share in CIBC

changed by -$1.640. A person owns 35 shares. By how

much did those shares change in value that day?

Part C: Word Problems

Jan 11­10:31 AM

The Commutative Property of Addition and Multiplication

This means:

When you multiply or add, the order of the numbers

doesn't matter.

This does not work

for subtraction and

division.

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November 30, 2016

Jan 11­9:51 AM

3.5 Dividing Rational Numbers

Steps:

1. Convert any mixed numbers to improper fractions.

2. Flip the second fraction and change the division sign to

multiplication.

3. Cross-cancel (if you like).

4. Multiply denominators and multiply numerators.

5. Simplify and convert to mixed, if necessary.

Part A - Fractions

Nov 20­9:01 AM

ex. ex.

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November 30, 2016

Jan 11­9:59 AM

ex. ex.

Jan 11­10:03 AM

ex. ex.

Part B: Decimals

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November 30, 2016

Nov 24­9:15 AM

A person has 54 shares in WestJet Airlines. On February 6,

2008, these shares lost $17.28 in value.

How much was the change in value of 1 share?

ex.

Part C: Word Problems

Nov 26­9:05 AM

3.6 Order of Operations with Rational Numbers

• Brackets

• Exponents

• Division

• Multiplication

• Addition

• Subtraction

Watch the process, then copy down the example:

ex.

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November 30, 2016

Jan 19­10:49 AM

Be careful when using different operations with fractions!

If you are adding/subtracting = find a ________________

denominator.

If you are multiplying/dividing = use __________-_____________

or ________________ your answer before continuing.

ex.

Nov 28­8:53 AM

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November 30, 2016

Jan 19­10:55 AM

To convert a temp. in degrees F to degrees C, we use the

formula:

Using this formula, find the temp. in degrees C in Fort

Simpson, NWT, if the temp. is -9.4 degrees F.

ex.

Hint: Start with writing out the formula.

Nov 28­9:26 AM

A can of soup is a cylinder with a radius of 3.5 cm and a

height of 11.5 cm.

ex.

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November 30, 2016

Oct 21­4:33 PM