PA_VA_Unit 2 Review

Negative Numbers and Temperature Review

(positive and negative counting numbers are called integeers)

Lets review negative numbers and number lines because...

• You are learning about them in pre-algebra

• You use negative numbers in real life for temperature, elevation, and money

• Number lines are a tool you can use to help understand negative numbers

Multiple Choice

Is -2 a negative or positive number?

• Negative

• Postive

What is colder -2 or 2 degrees?

• First I see which number is further to the left

• The further away a number is from 0 in the negatives, the colder it is

• The further away a number is in the positives, the warmer it is

• -2 is further to the left, so I know that it's colder

Multiple Choice

What is colder, -4 or 4 degrees?

• -4

• 4

How do you know -4 is colder

- 4 is further to the left from the 0, the further to the left, the colder it is.

Multiple Choice

What is colder -2 or -16?

• -2

• - 16

Multiple Choice

What is warmer, 2 or 66 degrees?

• 2

• 66

Add Integers (Same & Different Signs)

~ ​Review ~

​ add numbers & keep the sign!

​Remember: When adding integers with the same sign

Multiple Choice

-4 + (-3) = ?

• -7

• 7

• -1

• 1

Multiple Choice

-4 + (-6) + (-3) = ?

• -5

• -10

• -13

• -7

​ > subtract from the larger number

​Remember: When adding integers with the DIFFERENT signs

​ > then keep sign of the stronger integer

Multiple Choice

$$-3\ +\ 17$$  Which sign is stronger?

• positive!

• negative! 

​-3 + 17

three negatives

​positive is stronger! so the sum will be positive!

seventeen positives

​-3 + 17 = 14

three negatives      seventeen positives

​17 - 3 = 14

​keep positive!

​O

​->

​->

Multiple Choice

$$8\ +\ \left(-20\right)$$   Which sign is stronger? 

• positive! 

• negative! 

Positive and Negative Numbers

Understand, Compare and Order

Examples of Positive and Negative Numbers

Altitude - above sea level is positive, below sea level is negative.

Temperature - temperatures above zero are positive, below zero are negative.

Money - savings and deposits are positive, loans and withdrawals are negative.

Science - protons have a positive charge and electrons have a negative charge.

Sports- a gain of yards/points is positive, loss of yards/points is negative

Multiple Select

Select ALL the scenarios that describe a positive integer

• Loan of $10

• deposit of $20

• 4 feet below sea level

• $$8\degree$$   above freezing

• gain of 6 pts 

Multiple Select

Select ALL the scenarios that describe a negative integer.

• a loan of $40

• 12 feet above sea level

• $$2\degree$$ below freezing

• gain of 15 yards

• a withdrawl of $100

Multiple Choice

The opposite of a negative is always a ___________

• positive
• negative
• absolute value
• inequality

Multiple Choice

How do you know that 5 and -5 are opposites? 

• Because they both have a 5 
• They are the same distance from 0 and on opposite sides of 0 
• Because they are the same 
• They both are on a number line 

Multiple Choice

What is the opposite of the integer on the number line?

• 0

• -7

• 7

• 1

Multiple Choice

What is the opposite of the integer on the number line?

• 2

• -1

• 1

• 0

Multiple Choice

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

What is the absolute value of |-26|

• 26

• -26

Multiple Choice

|20|

• 20

• -20

Comparing Integers

• You can use a number line to compare integers

• A number farther to the left is less than a number farther to the right.

• A number farther to the right is greater than a number farther to the left.

Multiple Choice

Compare these Integers using the symbols:

< , > , or =

3 ____ -6

• <

• >

• =

Multiple Choice

Compare these Integers using the symbols:

< , > , or =

18 _____ 23

• >

• <

• =

Multiple Choice

Compare these Integers using the symbols:

< , > , or =

11 _____ -23

• >

• <

• =

Multiple Choice

Order from least to greatest:

[1, -2, 5, -5, 3, -1]

• -1, 1, -2, 3, 5, -5

• 1, -1, -2, 3, -5, 5

• 5, -5, 3, -2, -1, 1

• -5, -2, -1, 1, 3, 5

Multiple Choice

Order from least to greatest:

[1, -2, 5, -5, 3, -1]

• -1, 1, -2, 3, 5, -5

• 1, -1, -2, 3, -5, 5

• 5, -5, 3, -2, -1, 1

• -5, -2, -1, 1, 3, 5

Exponents and Perfect Squares

Introduction

The exponent tells you how many times you are multiplying the base by itself

(Exponents are REPEATED multiplication!)

Examples:

5² = 5 x 5 = 25

2³ = 2 x 2 x 2 = 8

1⁵ = 1 x 1 x 1 x 1 x 1 = 1

Multiple Choice

Which of the following is true?

• 4² = 8

• 4² = 16

• 4² = 6

• 4² = 2

Multiple Choice

Which of the following is equivalent to this exponent: 9³

• 9 x 3

• 9 x 9 x 9

• 9 + 9 + 9

• 93

Multiple Choice

Which of the following is equivalent to this expression: 8 x 8 x 8 x 8

• 32

• 8⁴

• 4⁸

• 84

Multiple Choice

Which answer shows 2 * 2 * 2 * 2 in exponential form?

• 2²

• 2⁴

• 4²

• 4⁴

Multiple Select

Solve: 3² + 4³

• 18

• 576

• 73

• 12

Square Roots

​What is a square root?

A square root is the inverse of "squaring" a number

​Squaring a number just means that a number is multiplied by itself ​TWO times, or said differently, a number to the power of TWO

Some text here about the topic of discussion

​s =5mm

​

​

​​​

A = s • s or ​ A = s²

This square has 5 mm sides​

​ We find the area of the square by

multiplying one side length times another side length

​Five squared is 5²

Why is it called squaring a number?

Some text here about the topic of discussion

A square has sides that are all the same length,​

SYMBOL FOR SQUARE ROOT

√

Multiple Choice

What is $$\sqrt[]{49}$$  =

• 9

• 5

• 7

• 4

Just find the square root of each part of the fraction

You can input this on a scientific calculator

Sometimes there is a fraction under the radical sign (that's what we call the square root symbol)

​

​Square root of a fraction

What happens if there is a fraction??

Some text here about the topic of discussion

Like this:

and simplified 6/8 = 3/4

​

​Since the square root of 36 is 6 and square root of 64

is 8, you just write those numbers in the form of a fraction

since they were already in a fraction.

​

If it needs to be reduced, you still have to reduce it.

Some text here about the topic of discussion

Multiple Choice

√256

• 14
• 16
• 13
• 17

PEMDAS

• Parenthesis

• Exponents

• Multiplication/Division (in the order they are seen in the problem)

• Addition/Subtraction (in the order they are seen in the problem)

Multiple Choice

What does the "E" in PEMDAS stand for?

• Equal

• Equation

• Exponent

Multiple Choice

What does the "M" in PEMDAS stand for?

• Multiply

• More

• Minus

Multiple Choice

What does the "D" in PEMDAS stand for?

• Divide

• Dozen

• Dime

Multiple Choice

What does the "A" in PEMDAS stand for?

• Addition

• Any

• Above

Multiple Choice

What does the "S" in PEMDAS stand for?

• Square

• Scale

• Subtract

Multiple Choice

SOLVE THE PARENTHESIS FIRST

55+(20-5)=

What do the PARENTHESIS "break down" to?

• 5

• 40

• 15

• 70

Multiple Choice

Solve this equation using the PEMDAS rules:

3 x 2 + 4

• 10

• 9

• 18

Multiple Choice

Which operation would you do first?
10 - 7 + 8 ÷ 1

• Subtraction

• Addition

• Division

• Multiplication

Multiple Choice

Use PEMDAS to solve the following equation.

$$39\div3\ \times2$$  

• 13

• 58.5

• 6.5

• 26

What is a one-step equation?

An equation where you only need to do one operation to solve for x.

What is an operation?

• addition

• subtraction

• multiplication

• division

To solve a one-step equations, you need to use the INVERSE operation.

Inverse means opposite

Multiple Choice

What is the inverse (opposite) of addition?

Multiple Choice

What is the inverse (opposite) of subtraction?

Multiple Choice

What is the inverse (opposite) of multiplication?

Multiple Choice

What is the inverse (opposite) of division?

Multiple Choice

How do you solve?

$$x+5=10$$  

• $$-5\ on\ both\ sides$$  

• $$+5\ on\ both\ sides$$  

• $$\div5\ on\ both\ sides$$  

• $$\times5\ on\ both\ sides$$  

Multiple Choice

How do you solve?

$$x-3=4$$  

• $$-3\ on\ both\ sides$$  

• $$+3\ on\ both\ sides$$  

• $$\times3\ on\ both\ sides$$  

• $$\div3\ on\ both\ sides$$  

Solve the following problems for X

Multiple Choice

Solve:

$$x-3=12$$  

• $$x=9$$  

• $$x=15$$  

• $$x=4$$  

Multiple Choice

Solve:

$$3x=12$$  

• $$x=9$$  

• $$x=15$$  

• $$x=4$$  

Solving Two-Step Equations

Multiple Select

Which two operations are in this equation? (pick both operations)

$$2x+5=11$$  

• addition

• subtraction

• multiplication

• division

Step One

The first step is to UNDO the addition or subtraction using inverse operations

Multiple Choice

Which equation shows the results of undoing the addition in the equation?

$$2x+5=11$$  

• $$2x=6$$  

• $$2x=16$$  

Step Two

The second step is to UNDO the multiplication or division using inverse operations

Multiple Choice

Which equation shows the results of undoing the multiplication in the equation?

 

$$2x=6$$  

• $$x=3$$  

• $$x=\frac{1}{3}$$  

• $$x=18$$  

• $$x=4$$  

• $$x=8$$

Multiple Choice

What is the first step to solve this equation:

11 - 3x = 44

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.

Multiple Choice

What is the first step to solve this equation?

3k + 5 = 23

• Multiply both sides by 3

• Subtract both sides by 3

• Divide both sides by 3

• Subtract both sides by 5

Multiple Choice

What is the second step to solve this equation?

3k + 5 = 23

• Multiply both sides by 3

• Subtract both sides by 3

• Divide both sides by 3

• Subtract both sides by 5

Multiple Choice

The steps in solving 5b - 6 = 24 are:

• Add 6 to both sides and divide both sides by 5

• Add 6 to both sides and multiply both sides by 5

• Subtract 6 from both sides then multiply both sides by 5

• Subtract 6 from both sides then divide both sides by 5

Multiple Choice

Solve this 2 step equation for a

• a= -2

• a= -7.5

• a= 2

• a= 6

Multiple Choice

solve 3n + 4 = 7 

• 1
• -1
• 3.67
• 2

​THE END OF THE REVIEW
READY FOR THE QUIZ?