Find the additive inverse of 7.
The additive inverse of 7 is -7.
What is the multiplicative inverse of 1/4?
The multiplicative inverse of 1/4 is 4.
True or False: a + b = b + a is an example of the commutative property.
True.
Provide an example of the associative property in multiplication.
Example: (2 × 3) × 4 = 2 × (3 × 4).
Solve: 5 × (2 + 3) - 4.
5 × (2 + 3) - 4 = 5 × 5 - 4 = 25 - 4 = 21.
Simplify the expression using the associative property: (2 + 3) + 4.
(2 + 3) + 4 = 5 + 4 = 9.
What is the inverse property of addition?
The inverse property of addition states that for every number a, there exists a number -a such that a + (-a) = 0.
Give an example of the commutative property in multiplication.
Example: 2 × 3 = 3 × 2.
True or False: The inverse property states that a + (-a) = 0.
True
Rewrite the expression 7 × 9 using the commutative property.
9 × 7 = 7 × 9.
What is the correct order of operations in mathematics?
The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
True or False: (a + b) + c = a + (b + c) is an example of the associative property.
True
What is the value of 12 ÷ (2 + 4) + 3 × 2?
12 ÷ (2 + 4) + 3 × 2 = 12 ÷ 6 + 6 = 2 + 6 = 8.
Expand the expression: 5(x + 2).
5(x + 2) = 5x + 10.
How can you use the associative property to solve 5 × (2 × 3)?
5 × (2 × 3) = (5 × 2) × 3 = 30.
What does the commutative property state about addition?
The commutative property states that changing the order of the numbers does not change the sum for addition
What does the distributive property state?
The distributive property states that a(b + c) = ab + ac.
Simplify: 3(2 + 4).
3(2 + 4) = 3 × 2 + 3 × 4 = 6 + 12 = 18.
Use the distributive property to simplify: 2(3x + 4).
2(3x + 4) = 6x + 8.
What is the associative property of addition?
The associative property states that the way numbers are grouped does not change their sum or product.
Explain how the inverse property applies to the number 5.
The inverse property applies as 5 + (-5) = 0.
How does the commutative property apply to the expression x + 3?
The commutative property applies as x + 3 = 3 + x.
Simplify the expression: 3 + 4 × 2.
3 + 4 × 2 = 3 + 8 = 11.
Explain how the distributive property can be used in the expression 7(x - 3).
7(x - 3) = 7x - 21.
Evaluate: 8 + (3 × 2^2) - 5.
8 + (3 × 2^2) - 5 = 8 + (3 × 4) - 5 = 8 + 12 - 5 = 15.