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Fun With Math: Understanding Number Properties!

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Fun With Math: Understanding Number Properties!
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Ayanna Stewart

@ayannastewart_znof

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Understanding number properties in math is essential for mastering basic arithmetic operations and algebraic concepts. This comprehensive guide explores fundamental properties including commutative, associative, distributive, and identity properties, with detailed examples of commutative and associative properties and demonstrations of the distributive property in addition and multiplication.

  • The commutative property allows numbers to be rearranged in addition and multiplication without affecting the result
  • The associative property demonstrates how regrouping numbers maintains the same outcome
  • The distributive property shows how multiplication can be distributed over addition or subtraction
  • Identity properties reveal how zero and one interact uniquely with numbers in addition and multiplication respectively

10/22/2023

64

Number Properties Commutative Property: The numbers in any multiplication or division equation can be moved or swapped from their position w

View

Page 2: Distributive and Identity Properties

The second page explores two additional fundamental properties that expand our understanding of number relationships and mathematical operations.

Definition: The distributive property shows that multiplying a sum by a number equals the sum of each addend multiplied by that number.

Example: For the expression 2(5+3), it can be solved as 2(5) + 2(3) = 10 + 6 = 16.

Vocabulary: An addend is any number being added in an addition problem.

Definition: The identity property comes in two forms:

  • The identity property of addition states that adding zero to any number yields the same number
  • The identity property of multiplication states that multiplying any number by one yields the same number

Example: For addition identity: 3 + 0 = 3, 14 + 0 = 14 For multiplication identity: 2 × 1 = 2, 7 × 1 = 7

Highlight: The distributive property is particularly useful in algebra and mental math, while identity properties help understand the special roles of zero and one in mathematics.

Number Properties Commutative Property: The numbers in any multiplication or division equation can be moved or swapped from their position w

View

Page 1: Commutative and Associative Properties

The first page introduces two fundamental mathematical properties that govern how we can manipulate numbers in equations. These properties form the foundation for more complex mathematical operations.

Definition: The commutative property states that numbers in multiplication or addition equations can be rearranged without changing the final result.

Example: In addition, 4 + 7 = 11 is equivalent to 7 + 4 = 11. Similarly, in multiplication, 6 × 2 = 12 is the same as 2 × 6 = 12.

Definition: The associative property demonstrates that regrouping numbers in an equation doesn't affect the final sum or product.

Example: In addition, (3 + 1) + (5 + 1) = 10 gives the same result as (5 + 3) + (1 + 1) = 10. For multiplication, 2 × (3 × 3) = 18 equals 3 × (2 × 3) = 18.

Highlight: These properties are essential tools for mental math and algebraic problem-solving, allowing flexible approaches to calculations.

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Subjects

/

Arithmetic

/

Proportions

/

Writing & Solving Proportions

Fun With Math: Understanding Number Properties!

user profile picture

Ayanna Stewart

@ayannastewart_znof

·

1 Follower

Follow

Understanding number properties in math is essential for mastering basic arithmetic operations and algebraic concepts. This comprehensive guide explores fundamental properties including commutative, associative, distributive, and identity properties, with detailed examples of commutative and associative properties and demonstrations of the distributive property in addition and multiplication.

  • The commutative property allows numbers to be rearranged in addition and multiplication without affecting the result
  • The associative property demonstrates how regrouping numbers maintains the same outcome
  • The distributive property shows how multiplication can be distributed over addition or subtraction
  • Identity properties reveal how zero and one interact uniquely with numbers in addition and multiplication respectively

10/22/2023

64

 

6th/7th

 

Arithmetic

7

Number Properties Commutative Property: The numbers in any multiplication or division equation can be moved or swapped from their position w

Page 2: Distributive and Identity Properties

The second page explores two additional fundamental properties that expand our understanding of number relationships and mathematical operations.

Definition: The distributive property shows that multiplying a sum by a number equals the sum of each addend multiplied by that number.

Example: For the expression 2(5+3), it can be solved as 2(5) + 2(3) = 10 + 6 = 16.

Vocabulary: An addend is any number being added in an addition problem.

Definition: The identity property comes in two forms:

  • The identity property of addition states that adding zero to any number yields the same number
  • The identity property of multiplication states that multiplying any number by one yields the same number

Example: For addition identity: 3 + 0 = 3, 14 + 0 = 14 For multiplication identity: 2 × 1 = 2, 7 × 1 = 7

Highlight: The distributive property is particularly useful in algebra and mental math, while identity properties help understand the special roles of zero and one in mathematics.

Number Properties Commutative Property: The numbers in any multiplication or division equation can be moved or swapped from their position w

Page 1: Commutative and Associative Properties

The first page introduces two fundamental mathematical properties that govern how we can manipulate numbers in equations. These properties form the foundation for more complex mathematical operations.

Definition: The commutative property states that numbers in multiplication or addition equations can be rearranged without changing the final result.

Example: In addition, 4 + 7 = 11 is equivalent to 7 + 4 = 11. Similarly, in multiplication, 6 × 2 = 12 is the same as 2 × 6 = 12.

Definition: The associative property demonstrates that regrouping numbers in an equation doesn't affect the final sum or product.

Example: In addition, (3 + 1) + (5 + 1) = 10 gives the same result as (5 + 3) + (1 + 1) = 10. For multiplication, 2 × (3 × 3) = 18 equals 3 × (2 × 3) = 18.

Highlight: These properties are essential tools for mental math and algebraic problem-solving, allowing flexible approaches to calculations.

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Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying