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Properties of Operations in Addition and Subtraction Facts & Worksheets

Addition is about combining quantities while subtraction is about “taking away.” But in fact, addition and subtraction are tied together.

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Addition is about combining quantities while subtraction is about “taking away.” But in fact, addition and subtraction are tied together. Addition equations can be solved by subtraction, and subtraction equations can be solved by addition.

See the fact file below for more information on the properties of operations in addition and subtraction or alternatively, you can download our 31-page Properties of Operations in Addition and Subtraction worksheet pack to utilise within the classroom or home environment.

Key Facts & Information

PROPERTY OF ADDITION: COMMUTATIVE PROPERTY

  • Commutative property states that numbers can be added in any order you want and you will still get the same answer.
  • Remember that addition is just counting the objects or putting objects or numbers together, which is commutative property is applicable.
  • For example, there two groups. One group has one (1) button and the other one has two (2) buttons.
  • Doing addition, we will get a total of three (3) buttons.
  • Now, what if we changed the distributions. Let’s say, Group 1 now has two (2) buttons and Group 2 now has only one (1) button. How many would be the total?
  • The total would still be three (3).
  • Following the commutative property of addition, no matter what group has the two (2) yellow buttons and the one (1) red button, the total would still be three (3) buttons.
  • Applying this property in an equation.

PROPERTY OF ADDITION: ASSOCIATIVE PROPERTY

  • Another property of addition is the associative property.
  • Associative property states that regardless of how numbers or objects are grouped together, the total sum would still be the same.
  • Following (A+B)+C, we are going to add the number of cars Tom and Sam have.
  • Tom has two (2) cars while Sam has one (1) car, then they have a total of three (3) cars. Then, we will add the number of cars Chris has, which is three (3). The total number of cars is then equal to six (6).
  • Now, let’s try applying the associative property.
  • Following A+(B+C), we are going to add the number of cars Sam and Chris have, we will have four (4) cars.
  • Then, add the number of cars Tom has, which is two (2), the total
    then will be six (6).
  • The total number of cars are both six (6) regardless of if we added the number of cars Tom and Sam have and then added Chris’ number of cars, or if we added Sam and Chris’ number of cars first and then added Tom’s cars, this is due to the associative property.

PROPERTY OF ADDITION: ADDITIVE IDENTITY PROPERTY

  • Another property of addition is the additive identity property, which states that the sum of any number and zero is the number itself.
  • For example, there are two kids. One kid has 3 candies while the other one does not have any candy, thus, zero (0). What is the total number of candies they both have?
  • Following the additive identity property of addition, if we add three (3) and zero (0) we will get three (3).

PROPERTY OF SUBTRACTION: SUBTRACTIVE PROPERTY OF ZERO

  • The commutative property and associative property are not applicable to subtraction, but subtraction has a property called subtractive property of zero.
  • Subtractive property states that if we subtract zero (0) from any number, the answer or difference will be the non-zero number.
  • For example, one person, whom we will call Tom, has 3 water bottles.
  • A friend, whom we will call Sam, asked Tom for one water bottle but Tom decided not to give him any.
  • Following the subtractive property of zero, what would the answer be?
  • The answer is three (3). According to the property, any number minus zero is that number. Therefore, three (3) minus zero (0) is equal to three (3).

ADDITION AS SUBTRACTION

  • An addition equation can also be expressed as a subtraction equation.

SUBTRACTION AS ADDITION

  • Just like how addition equations can be expressed as subtraction equations, subtraction equations can also be expressed as addition equations.

Properties of Operations in Addition and Subtraction Worksheets

This is a fantastic bundle which includes everything you need to know about the properties of operations in addition and subtraction across 31 in-depth pages. These are ready-to-use Properties of Operations in Addition and Subtraction worksheets that are perfect for teaching students about the addition which is about combining quantities while subtraction is about “taking away.” But in fact, addition and subtraction are tied together. Addition equations can be solved by subtraction, and subtraction equations can be solved by addition.

Complete List Of Included Worksheets

  • Lesson Plan
  • Properties of Operations in Addition and Subtraction
  • Add Them
  • Plus To Minus
  • Commutative
  • Associative
  • Subtract Them
  • Minus To Plus
  • Zero
  • Solve All
  • Coloring Time
  • Answer

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Use With Any Curriculum

These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.

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