Integers

We indicate absolute value by putting two bars around the number.

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Because the absolute value​ of a number is the distance from zero, it is always positive.

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Absolute Value

Multiple Choice

What is the definition of absolute value?

• The distance a number is to zero

• A positive number

• A number that has a value with a different sign

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

The absolute value of zero is zero because...

• Zero is not a number.
• Zero is 0 distance from zero.  It is neither negative or positive.

Multiple Choice

Evaluate: |-12|

• 12

• -12

• 0

• 1.2

Multiple Choice

Evaluate the expression.
| –3 |

• 3
• -3
• 0.30
• 30

Multiple Choice

Evaluate the expression.
| 9 |

• 0.9
• 9
• -9
• 90

Multiple Choice

What is the definition of an opposite?

• The distance a number is to zero

• A number with the same digit(s) but opposite sign

Multiple Choice

What is the opposite of 23

• 23

• -23

• 2/3

• 0

Multiple Choice

What is the opposite of 0

• -0

• +0

• 0

• There is no opposite

Multiple Choice

What is the opposite of -12

• 12

• -12

• 0

Multiple Choice

0 _______ -2

• <

• >

• =

Multiple Choice

-6 _______ -3

• <

• >

• =

Multiple Choice

-14 _______ 14

• <

• >

• =

Multiple Choice

0 _______ -23

• <

• >

• =

Multiple Choice

17 _______ -18

• <

• >

• =

Multiple Choice

7 _______ -12

• <

• >

• =

Multiple Choice

Which is COLDER? $$-4^oF$$   or $$0^oF$$  

• $$-4^oF$$  

• $$0^oF$$  

• They are the same

Multiple Choice

Which is COLDER? $$4^oF$$   or $$0^oF$$  

• $$4^oF$$  

• $$0^oF$$  

• They are the same

Multiple Choice

Which has a HIGHER elevation?

25 feet below sea level or 6 feet below sea level

• 6 feet below sea level

• 25 feet below sea level

• They are the same

Multiple Choice

Which is the least integer?

• 1
• -1
• -2
• -8

Multiple Choice

Which is the greatest integer?

• -33
• -31
• -28
• -17

Multiple Choice

Order from least to greatest:
[-8, 7, -6, 5, -4, 3, -2]

• -2, 3, -4, 5, -6, 7, -8
• -2, -4, -6, -8, 3, 5, 7
• -6, -8, -4, -2, 7, 5, 3
• -8, -6, -4, -2, 3, 5, 7

Multiple Choice

Choose the set of integers that are in ascending order.

• -5, -3, 0

• -3, 0, -5

• 0, -3, -5

• -3, -5, 0

Multiple Choice

Select the set of integers that are in descending order.

• |-34| , |5| , -2

• |5| , |-34| , -2

• -2 , |-34| , |5|

• |5| , -2 , |-34|

Multiple Choice

-8 + -12

• -20
• 20
• -4
• 4

Multiple Choice

-4 + -13 = ?

• 9

• 17

• -9

• -17

Multiple Choice

A scuba diver dove down 25 feet, then swam up 11 feet. Which equation represents this and the diver's current position?

• -25 + - 11 = -36

• -25 + 11 = -14

• -25 + 11 = -36

• -25 + 11 = 14

Multiple Choice

-14 + 19 =

• -33

• 33

• -5

• 5

Multiple Choice

-632 + 632 =

• 1264

• -1264

• -1

• 0

Multiple Choice

18 + -7

• 25
• -25
• 11
• -11

Multiple Choice

(-2) + 9  x  10

• 88
• 110
• -70
• 72

Multiple Choice

5 + (-9) x 9

• 86
• -86
• -36
• -76

Multiple Choice

(9 + 8) x (-3)

• -15
• 51
• -51
• 15

Multiple Choice

(7 - 8) x 2²

• 2
• -4
• -25
• 25

Multiple Choice

Solve the following:
-14 ÷ 2 – 15

• -8
• -22
• 8
• 22

Multiple Choice

Solve the following:  
8 + (-4) ÷ 4

• -7
• 1
• -1
• 7

Multiple Choice

(2 + 1) + 9 = (1 + 2) + 9

• Transitive Property

• Commutative Property of Addition

• Associative Property of Addition

• Distributive Property

Multiple Choice

This is an example of which property:
$$\left(2\cdot3\right)\cdot4=2\cdot\left(3\cdot4\right)$$  

• Associative

• Commutative

• Inverse

• Identity

Multiple Choice

Which property of addition is this?
-3 + 0 = (-3)

• Commutative Property
• Associative Property
• Identity Property
• Inverse Property

Multiple Choice

Which property of addition is this?
-8 + 8 = 0

• Commutative Property
• Associative Property
• Identity Property
• Inverse Property

Multiple Choice

Which property of multiplication says that any number times zero will equal zero?

• Commutative Property
• Associative Property
• Multiplicative Property of Zero
• Identity Property

Multiple Choice

Which property of multiplication says that any number times one equals that number?

• Commutative Property
• Associative Property
• Identity Property
• Distributive Property

Multiple Choice

Which property is this?
a x (b + c) = (a x b) + (a x c) = ab + ac

• Commutative Property
• Associative Property
• Identity Property
• Distributive Property

Multiple Choice

Does 4 x (1 + 7) = (4 x 1) + (4 x 7)?

• Yes
• No

Multiple Choice

Does 6 x 7 = 7 x 6?

• Yes
• No

Multiple Choice

What is a³ x b² in expanded form?

• a x 3 x b x 2

• a x a x b x b x b

• ab⁵

• a x a x a x b x b

Multiple Choice

Write the following in index form; 2 x 2 x a x a x b

• 4a²b

• 2²a²b

• 2²ab³

• 4ab²

​Rules
of Exponents

Multiple Choice

• 1¹⁰
• 1²⁶
• z¹⁰
• z²⁶

Multiple Choice

x³⋅x² =

• x⁵

• x⁶

• x⁹

• x¹

Multiple Choice

Evaluate the expression using the quotient rule.

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

• y³/8
• y³/24
• y/24
• y³/8³

Multiple Choice

Evaluate (-3)²

• -9

• 9

• -6

• 6

Multiple Choice

-5²

• -25

• 25

• 5

• 52

Multiple Choice

(-5)²

• -25

• 25

• 5

• 52

Multiple Choice

(-2)³

• -8

• 8

• 6

• -6

Multiple Choice

$$(-1)^3$$  

• (-3) x (-1)

• (-1) x 3

• (-3) x (-3) x (-3)

• (-1) x (-1) x (-1)

Multiple Choice

$$\left(-7\right)^4$$  is the final product positive or negative?

• positive

• negative

• neither

• both

Multiple Choice

$$(-1.25)^{15}$$  

Mike says the final product is positive. Is he correct?

• Yes

• No

Square Roots

Multiple Choice

$$\sqrt{49}$$  

• 7

• 3

• 4

• 6

Multiple Choice

$$\sqrt{36}$$  

• 3

• 6

• 7

• 18

Multiple Choice

$$\sqrt{400}$$  

• 20

• 100

• 200

• 4

Multiple Choice

$$\sqrt{-144}$$  

• 12

• -12

• 72

• none of the above. There is no true square root of a negative number.

​Cube roots

​The opposite of cubing a number.

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​Think ____ x ____ x ____ (all the same number) = 64

Multiple Choice

$$\sqrt[3]{27}$$  

• 3

• 9

• 24

Multiple Choice

$$\sqrt[3]{8}$$  

• 4

• 3

• 2

• 1

Multiple Choice

Find the cube root. 

• -5
• 5
• 4
• -4