Wednesdayweek2

AGENDA 1/16/13

• 1. Review: Prime Factorization, Solving One-Step Equations

• 2. Objectives for 2.1

REVIEW “QUIZ”

• 1. 134 is prime or composite?• 2. Find the prime factorization of 88.• 3. Solve • 4. Solve • 5. Solve • 6. Solve

OBJECTIVES FOR 2.1

1. Define the set of integers.

The collection of positive whole numbers, the negatives of the whole numbers, and 0 is called the set of integers.

0 1 2 3 4 5-1-2-3-4-5 6 7 8 9 10-6-7-8-9-10

Working with Signed Numbers

Algebra uses NEGATIVE and POSITIVE numbers.

Algebra also uses variables, or letters to represent the unknown values.

The Number Line

0 1 2 3 4 5-1-2-3-4-5

The numbers in red are the numbers we have worked with so far.

Algebra uses all of the numbers on the number line, both positive and negative.

OBJECTIVES FOR 2.1

2. Graph integers on the number line.

To graph a number means to make a drawing that represents the number.

0 1 2 3 4 5-1-2-3-4-5 6 7 8 9 10-6-7-8-9-10

Graph -4, -2, 0, and 3 on a number line.

Using the Number Line

0 1 2 3 4 5-1-2-3-4-5 6 7 8 9 10-6-7-8-9-10

• The arrows at both ends of the number line mean that the positive and negative numbers go on forever.

•Positive numbers are to the right of zero.

•Negative numbers are to the left of zero.

•A number on the number line is greater than any number to its left.

•A number on the number line is less than any number to its right.

ZERO is neither positive nor negative.

Using the Number Line

Positive numbers do not have to be written with a plus sign. Positive 8 is simply written as 8.

Negative numbers MUST be written with a negative sign in front of them (-8)

Graphing Integers on the Number Line

0 1 2 3 4 5 6 7 8 9-9 -8 -7 -6 -5 -4 -3 -2 -1

A BC D E FGH

1. +6

2. -3

3. 9

4. -8

5. 1

6. -6

7. 0

8. - 9

9. -5 10. 4

I J

JD

B

A

F

G I

H

C

E

OBJECTIVES FOR 2.1

3. Use inequality symbols to compare integers.

¿𝒎𝒆𝒂𝒏𝒔 𝒊𝒔 𝒍𝒆𝒔𝒔𝒕𝒉𝒂𝒏

0 1 2 3 4 5-1-2-3-4-5 6 7 8 9 10-6-7-8-9-10

−3<3𝑏𝑒𝑐𝑎𝑢𝑠𝑒−3 𝑖𝑠 𝑡𝑜 h𝑡 𝑒 𝑙𝑒𝑓𝑡 𝑜𝑓 3𝑜𝑛 h𝑡 𝑒𝑛𝑢𝑚𝑏𝑒𝑟 𝑙𝑖𝑛𝑒

OBJECTIVES FOR 2.1

3. Use inequality symbols to compare integers.

−𝟓𝟔 ≤−𝟓𝟕

−𝟑≤−𝟑

−𝟏𝟒 ≥−𝟏𝟗

−𝟖≥−𝟖

false

true

false

false

Absolute Value is the distance from a number to zero on the number line.

Absolute Value is neither positive or negative.

The absolute value of -5 is 5 .

What is the absolute value of -7?

OBJECTIVES FOR 2.1

4. Find the absolute value of an integer.

OBJECTIVES FOR 2.1

5. Find the opposite of an integer.

The opposite of negative 5 is positive 5.

− (−𝟓 )=𝟓

|−𝟒|=¿

−|𝟒|=¿

−|−𝟗𝟗|=¿

Homework Time!

Assignment 1 is due tomorrow and it would be a great use of you time to “get ‘er done”. If you’ve already finished, try working ahead on assignment #2.

Know the Rules: Same Sign

Adding Two SAME-Signed Numbers:

Add and give the total of the signed numbers.

(-5) + (-5) = -10

5 + 5 = 10

(-3) + (-2) = -5

Know the Rules: Different Signs

Adding when the signs are different:

Subtract and keep the sign of the bigger number.

8 + (-15)

Subtract :

15-8 =7

The sign of the larger number is negative So, the answer is -7

Adding a Series of Signed Numbers

Simplify (-9) + (10) + (-8) + (4) =

Step 1: Add the positive numbers.

Step 2: Add the negative numbers.

Step 3: Add sums together.

THIS IS WHERE IT GETS WEIRD.

If you get confused, try not to get wrapped up in the WHY of all the rules.

Sometimes some rules don’t make sense, but we accept that we must follow them anyway.

You’ve been warned!

Know the Rules: Subtracting

Change the minus to plus and change the sign of the number on the right ONLY.

(-8) - (3)= -11Different Signs

Same Signs (-8) - (-3)= -5ADD THE

OPPOSITE!!

!

Subtracting Signed Numbers

To subtract signed numbers:

Step 1: Change the sign of the number being subtracted.

Step 2: Follow the signs for adding signed numbers.

-8

Subtracting in a Series of Signed Numbers

This is where it gets weird.

Step 1: To solve a series of signed numbers, start by changing the signs of numbers being subtracted.

Step 2: Find the sum of the positive numbers.

Step 3: Find the sum of the negative numbers.

Step 4: Find the difference. Follow the rules of addition.

6 + 4 = 10

-2+ (-5) = -7

10- 7 = 3

Samech

ange

change

Review: Rules Subtraction:

Add the opposite

Addition:

Different signs, subtract and keep the sign of the larger number

Same signs, add and keep the sign

-1 + 3 = ?

1. -42. -23. 24. 4

Answer Now

-6 + (-3) = ?

1. -92. -33. 34. 9

Answer Now

Which is equivalent to-12 – (-3)?

1. 12 + 32. -12 + 33. -12 - 34. 12 - 3

Answer Now

7 – (-2) = ?

1. -92. -53. 54. 9

Answer Now

Here is One Way to Remember

A negative times a negative is a positive.

A negative times a positive is a negative.

Multiplying Signed Numbers

If you gain 2 pounds a week for 5 weeks, you will weigh 10 pounds more than you weigh now.

If you lose 2 pounds a week for 5 weeks, you will weigh 10 pounds less than you weigh now.

(+2)(+5) = +10

(-2)(+5) = -10

Step 1: Multiply.

Step 2: If same signs, make the product positive.

Step 3: If different signs, make the product negative.

If you have been gaining 2 pounds a week for 5 weeks, you weighed 10 pounds less five weeks ago.

If you have been losing 2 pounds a week for 5 weeks, you weighed 10 pounds more 5 weeks ago.

Multiplying Signed Numbers

(+2)(-5) = -10

(-2)(-5) = +10

Step 1: Multiply.



Multiplying 3 or more signed numbers

What is (-6)(+2)(-4)?

Rule: Step 1: Multiply.

Step 2: If there are even negative signs, the final product is POSITIVE.

Step 2: If there are an odd number of negative signs, the final product is NEGATIVE.

48

Rule

Step 1: Multiply.



Dividing Signed Numbers (Integers)

The rule for dividing is similar to the rules for multiplying.

Same signs = positive

Different signs = negative

-523

=

Division Word Problems: Integers

The population of a small town is dropping at a rate of 255 people per year. How long will it take for the change in population to be 2,040 people?

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