Properties of Operations on the set of Integers

What I know​

​Let us check your prior knowledge about the properties of operations on the set of integers by answering the questions that follows.

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Choose the letter of the best answer.​

Multiple Choice

Which operation below does not change the value of any nonzero number?

• Adding by One

• Dividing by Zero

• Multiplying by One

• Multiplying by Zero

Multiple Choice

Which of the following property states that changing the order of two numbers that are either being added or multiplied does not change the value.

• Closure property

• Commutative property

• Associative property

• Identity property

Multiple Choice

Which of the following property states that the two integers that are added and multiplied remain as integers? The set of integers is closed under addition and multiplication

• Closure property

• Commutative property

• Associative property

• Distributive property

Multiple Choice

When two numbers have been added / subtracted and then multiplied by a factor, the result will be the same when each number is multiplied by the factor and the products are then added / subtracted.

• Closure property

• Commutative property

• Associative property

• Distributive property

Multiple Choice

Which of the following property states that the sum of any number and 0 is the given number?

• Closure property

• Commutative property

• Associative property

• Identity property

Multiple Choice

Which of the following property is used in the expression 2 (3-5) = 2(3) – 2(5)?

• Additive Inverse

• Associative Property

• Additive Identity

• Distributive Property

Multiple Choice

Which of the following does not illustrate Inverse Property?

• 5 + 8 = 8 + 5

• ½ (2) = 1

• (-9) + (9) = 0

• (x) + (-x) = 0

Multiple Choice

Which of the following does not illustrate Distributive Property?

• a(b – c) = ab – ac

• 4(x + 3) = 4x + 12

• 3(5 * 6) = (3 5)6

• 2(7 – 5) = 14 – 10

Multiple Choice

Which Property of Multiplication is shown in (6 + 3) x 4 = 6(4) + 3(4)?

• Associative Property

• B Commutative Property

• Distributive Property

• Inverse Property

Multiple Choice

Which of the following property is used in the expression 4(1+7) = 4 + 28?

• Additive Inverse

• Associative Property

• Additive Identity

• Distributive Property

Multiple Choice

Which property of addition is used in (4 + 7) + 3 = 4 + (7 + 3)?

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

Multiple Choice

Which is an example of Identity Property of Addition?

• 1 + 3 = 4

• 2 + 4 = 4 + 2

• 3 + 0 = 3

• 5 + (6 + 3) = (5 + 6) + 3

Multiple Choice

Which of the following does not show the Commutative Property?

• a + 8 = 8 + a

• xy = yx

• m + n = n + m

• 3x(4) = 12x

Multiple Choice

Which property of addition does 5 + 0 = 5 illustrate?

• Commutative Property

• Distributive Property

• Identity Property

• Inverse Property

Multiple Choice

What property of integers justify 12 + 3 = 3 + 12

• Closure property

• Commutative property

• Identity property

• Inverse Property

​What's In

​This module is a continuation of the concepts on the Operations on Integers. Mastering the rules in the previous module will help speed you up in completing this module.

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​Perform the indicated operations. Apply the rules of the Operations on Integers

Multiple Choice

Choose with the correct number that will make it exact.

(8 +___ ) +___ = ___+ ( 5 + 1 )

What are the numbers?

What property is illustrated?

• (8 +5 ) + 1 = 8+ ( 5 + 1 )

  Associative property

• (8 +5 ) + 1 = 8+ ( 5 + 1 )

  Closure property

• (8 +5 ) + 1 = 8+ ( 5 + 1 )

  Distributivproperty

Multiple Choice

Identify the property used in each of the statements below.

(-7) + 0 = -7

• Additive Identity

• Distributive Property

• Commutative Property

• Multiplicative Identity

Multiple Choice

Identify the property used in each of the statements below.

6 (3 - 5) = 6(3) - 6(5)

• Additive Identity

• Distributive Property

• Commutative Property

• Multiplicative Identity

Multiple Choice

Identify the property used in each of the statements below.

(-8) + (-7) = (-7) + (-8)

• Additive Identity

• Distributive Property

• Commutative Property

• Multiplicative Identity

Multiple Choice

Identify the property used in each of the statements below.

(-13) x 1 = -13

• Additive Identity

• Distributive Property

• Commutative Property

• Multiplicative Identity

Multiple Choice

Identify the property used in each of the statements below.

-4 x - (1/4) = 1

• Additive Identity

• Distributive Property

• Commutative Property

• Multiplicative Inverse

Multiple Choice

Identify the property used in each of the statements below.

2 x (4 x 7) = (2 x 4) x 7

• Additive Identity

• Associative Property

• Commutative Property

• Multiplicative Inverse

Multiple Choice

Identify the property used in each of the statements below.

11 + (-11) = 0

• Additive Identity

• Associative Property

• Commutative Property

• Additive Inverse

Multiple Choice

Identify the property used in each of the statements below.

3(5) = 5(3)

• Additive Identity

• Associative Property

• Commutative Property

• Additive Inverse

Multiple Choice

Identify the property used in each of the statements below.

2 /5 • 5/2 = 1

• Additive Identity

• Associative Property

• Commutative Property

• Multiplicative Inverse

Multiple Choice

Identify the property used in each of the statements below.

(-3) (5 + 9) = (-3) (5) + (-3) (9)

• Distributive Property

• Associative Property

• Commutative Property

• Multiplicative Inverse

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Multiple Choice

To sum it up, let us complete the statements.

Commutative Property states that changing the ___ of two numbers that

• order

• positive

• negative

• zero

Multiple Choice

To sum it up, let us complete the statements.

Associative Property states that changing the ____of numbers that are either being added or multiplied does not change its value.

• order

• positive

• grouping

• zero

Multiple Choice

To sum it up, let us complete the statements.

Distributive Property states that when two numbers have been added/subtracted and then multiplied by a ___ , the result will be the same when each number is multiplied by the factor and the products are then added /subtracted.

• order

• positive

• grouping

• factor

Multiple Choice

To sum it up, let us complete the statements.

Additive Identity Property states that the sum of any number and 0 is the given number.___ is the additive identity.

• zero

• positive

• grouping

• factor

Multiple Choice

To sum it up, let us complete the statements.

Multiplicative Identity Property states that the product of any number and 1 is the given number, a • 1 = a.___ is the multiplicative identity.

• zero

• one

• grouping

• factor

Multiple Choice

To sum it up, let us complete the statements.

Additive Inverse Property states that the sum of any number and its ___is zero.

• zero

• one

• grouping

• Additive inverse

Multiple Choice

To sum it up, let us complete the statements.

The additive inverse of a positive number is the ___ of that number.

• zero

• one

• negative

• Additive inverse

Multiple Choice

To sum it up, let us complete the statements.

The additive inverse of a negative number is the ___ of that number.

• zero

• positive

• negative

• Additive inverse

Multiple Choice

To sum it up, let us complete the statements.

Multiplicative Inverse Property states that the ___ of any number and its multiplicative inverse or reciprocal is 1.

• product

• positive

• negative

• Additive inverse

Multiple Choice

To sum it up, let us complete the statements.

The multiplicative inverse of the number 𝒂 is ___.

• product

• 1/a

• negative

• Additive inverse

​Assessment

​I hope you had a good time going over this module. For you to determine how much you’ve learned, please answer the questions by choosing the letter of the best answer

Multiple Choice

Which of the following property is used in the expression 1 + 4 = 5?

• Additive Inverse

• Associative Property

• Closure Property

• Commutative Property

Multiple Choice

Which property of addition is used in 4 + 0 = 4?

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

Multiple Choice

Which is an example of Inverse Property of Addition?

• (-5) + (5) = 0

• 2(-3) = (-2)(3)

• 3 + 0 = 3

• 4 + (1 + 3) = (4 + 1) + 3

Multiple Choice

Which of the following does not show Distributive Property?

• 4(2 – 7) = 4(2) – 4(7)

• 5(x + 3) = 5x + 15

• a(b + c) = a + (b + c)

• a(3 + 4) = 3a + 4a

Multiple Choice

Which property of addition does (-x) + x = 0 illustrate?

• Commutative Property

• Distributive Property

• Identity Property

• Inverse Property

Multiple Choice

Which of the following does not illustrate Associative Property?

• 4(5 x 3) = 4(5) x 4(3)

• 2(3 x 7) = (2 x 3)7

• 5 + (3 + 8) = (5 + 3) + 8

• None of the above

Multiple Choice

Which of the following states that the sum of any number and 0 is the given number?

• Additive Identity Property

• Additive Inverse Property

• Multiplicative Identity Property

• Multiplicative Inverse Property

Multiple Choice

Which of the following does not illustrate Multiplicative Identity Property?

• ( 3 /4 ) ( 4/ 3 ) = 1

• (-9) (1) = -9

• 1/2 = ( 1/2 ) (1) 

• (m)(1) = m

Multiple Choice

Which Property is shown in (-x) + (-1) = (-1) + (-x)?

• Associative Property

• Commutative Property

•  Distributive Property

• Inverse Property

Multiple Choice

What is the additive inverse of x?

• 1/X

• –x

• x-1

• 1

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