Mixed Calculations

Laws of Math

​The Basic Laws of Math

• Commutative Law

• Associative Law

• Distributive Law

​Commutative Law of Multiplication

​Commutative Law of Addition

Commutative Law

• The commutative law states that the order in which you add or multiply two real numbers does not affect the result.

Multiple Choice

Which one of the following illustrates the Commutative Law of addition?

• 5 + 7 = 7 + 5

• 5 + 7 = 4 + 8

• 5 + 7 = 3 + 9

• 5 + 7 = 10 + 2

Multiple Choice

Which of the following illustrates the Commutative Law of multiplication?

• 3 × 4 = 4 × 3

• 3 × 4 = 12 × 1

• 3 × 4 = 6 × 2

• 3 × 4 = 2 × 6

​Associative Law of Multiplication

​Associative Law of Addition

Associative Law

• The associative law states that when you add or multiply three real numbers, the grouping (or association) of the numbers does not affect the result.

Multiple Choice

What law is shown in the equation?

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

• Commutative Law of Addition

• Commutative Law of Multiplication

• Associative Law of Addition

• Associative Law of Multiplication

Multiple Choice

What law is shown in the equation?

9 x (3 x 2) = (9 x 3) x 2 

• Associative Law of Addition

• Associative Law of Multiplication

• Commutative Law of Addition

• Commutative Law of Multiplication

Multiple Choice

5 × (2 × 9) is also equal to:

• 5 x (2 - 9)

• 5 x (2 + 9)

• (5 x 2) x 9

• (5 x 2) + 9

Multiple Choice

Which one of the following illustrates the Associative Law of addition?

• 3 + ( 2 + 4) = (4 + 4) + 1

• 3 + (2 + 4) = (3 + 2) + 4

• 3 + (2 + 4) = (5 + 2) + 2

• 3 + (2 + 4) = (2 + 6) + 1

Multiple Choice

Which of the following illustrates the Associative Law of multiplication?

• 4 × (3 × 6) = (3 × 12) × 2

• 4 × (3 × 6) = (6 × 6) × 2

• 4 × (3 × 6) = (4 × 3) × 6

• 4 × (3 × 6) = (3 × 8) × 3

Multiple Choice

What law is shown in the equation?

9 + (3 x 2) = (3x 2) + 9 

• Associative Law of Addition

• Associative Law of Multiplication

• Commutative Law of Addition

• Commutative Law of Multiplication

Distributive Property

Distributive Property

There are two steps to the

distributive property.

4 x (20 + 8) = (4 x 20) + (4 x 8)

= 80 + 32
= 112

1) Multiply each part by 4. (distribute the 4)

2) Add/ Subtract the two products.

Multiple Select

Using the Distributive Law, rewrite the equation:

81 x 450 + 81 x 550 = ?

Choose ALL that apply

• 81 x (450+550) =?

• 81 x ( 1000 ) =?

• 1000 x (81 + 81) =?

• 2 x (450 + 550) =?

• 81 (450 + 550) =?

Multiple Select

Using the Distributive law, rewrite the equation:

50 x 161 - 50 x 81 = ?

Choose ALL that apply.

• 50 (161 - 81) = ?

• (161 - 81) x (50 - 50) = ?

• 50 x (161 - 81) = ?

• 50 x (80) = ?

• 50 x (81 - 161) = ?

Multiplying a number by itself

Multiple Choice

In this expression
$$3^4$$  
3 is the ...

• base

• exponent

Multiple Choice

In this expression
$$3^4$$  
4 is the ...

• base

• exponent

Multiple Choice

In this expression
$$5^2$$  
The base is ...

• 2

• 5

Multiple Select

Which two mathematical expression are equal to:

5 x 5 x 5

• $$3^5$$  

• $$15$$   

• $$125$$  

• $$5^3$$  

​"three raised to the power of 2"

"three squared"

​"four raised to the power of 3"

"four cubed"

Multiple Select

Which expressions are equal to:

4 x 4 x 4

Choose ALL that apply.

• $$4^3$$  

• "four cubed"

• 12

• 64

• "4 raised to the power of 3"

Multiple Choice

Evaluate:
2⁵

• 10

• 16

• 32

• 124

Reminder

When multiplying, be mindful of the signs

Negative x Negative = Positive

Positive x Positive = Positive

Negative x Positive = Negative

​Look closely at the two examples at the right.

• What have you noticed?

• Write a rule that we can use to remember how to solve it.

Open Ended

Write a rule to solve it.

​Look closely at the three example equations.

• What have you noticed?

• Write a rule that we can use to remember how to solve it.

Open Ended

Write a rule to solve it.

Multiple Choice

How would you represent
2 x 2 x 2 x 2 x 2 ?

• 2 x 5

• 2 x 2 x 5

• 5²

• 2⁵

Multiple Choice

Calculate $$\left(-2\right)^4\times-10^2$$  

• $$-1600$$  

• $$-1800$$  

• $$-1500$$  

• $$-1700$$  

Multiple Choice

What is the value of
9²

• 18

• 81

• 729

• 9

Multiple Choice

Express $$\left(-2\right)\times\left(-2\right)\times\left(-2\right)\times\left(-2\right)\times\left(-2\right)\times\left(-2\right)$$ using exponents. 

• $$\left(-2\right)^5$$  

• $$\left(-2\right)^6$$  

• $$\left(-2\right)^4$$  

• $$\left(-2\right)^7$$  

Multiple Choice

How would you represent 8⁶ ?

• 8 x 6

• 8 x 8 x 6

• 8 x 8 x 8 x 8 x 8 x 8

• 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

Multiple Choice

Calculate $$\left(-9\right)^2\div\left(-3\right)$$  

• $$-27$$  

• $$-81$$  

• $$-18$$  

• $$-36$$  

Multiple Choice

Calculate $$\left(-3\right)^2\times5$$  

• $$45$$  

• $$15$$  

• $$54$$  

• $$63$$  

Multiple Choice

Calculate $$-12^2\div6^2$$  

• $$-4$$  

• $$6$$  

• $$36$$  

• $$48$$  

Multiple Choice

Calculate $$\left(-4\right)^2\div2^2$$  

• $$4$$  

• $$8$$  

• $$-8$$  

• $$16$$  

Multiple Choice

Evaluate
3⁶

• 81

• 18

• 729

• 243

Multiple Choice

Calculate $$2^2\times\left(-3\right)$$  

• $$-12$$  

• $$12$$  

• $$18$$  

• $$-18$$  

Multiple Choice

Calculate $$\left(-3\right)^3$$  

• $$-27$$  

• $$27$$  

• $$-9$$  

• $$9$$