Mathematics
Grade 6
15 min
Properties of addition
Properties of addition
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the Commutative Property of Addition.
Identify the Associative Property of Addition.
Identify the Identity Property of Addition.
Apply the properties of addition to simplify numerical expressions.
Use the properties of addition to solve problems more efficiently.
Explain the purpose and usefulness of each addition property.
Ever notice how you can add numbers in any order and still get the same sum? 🤔 Or how grouping numbers differently doesn't change the total?
In this lesson, you'll discover the special rules, or 'properties,' that addition follows. Understanding these properties will make solving math problems easier, help you simplify expressions, and build a strong foundation for future algebra.
Real-World Applications...
2
Key Concepts & Vocabulary
TermDefinitionExample
PropertyA rule or principle that is always true in mathematics.The Commutative Property is a rule that applies to addition.
AdditionThe mathematical operation of combining two or more numbers to find their sum or total.In $3 + 5 = 8$, addition is used to combine 3 and 5.
Commutative Property of AdditionThis property states that changing the order of the numbers being added does not change the sum.$2 + 7 = 9$ and $7 + 2 = 9$. The sum is the same.
Associative Property of AdditionThis property states that changing the way numbers are grouped (using parentheses) when adding three or more numbers does not change the sum.$(4 + 2) + 5 = 6 + 5 = 11$ and $4 + (2 + 5) = 4 + 7 = 11$. The sum is the same.
Identity Property of AdditionThis property states that the sum of any numb...
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Core Formulas
Commutative Property of Addition
$a + b = b + a$
This rule allows you to reorder numbers in an addition problem without changing the result. It's useful for rearranging terms to make calculations easier.
Associative Property of Addition
$(a + b) + c = a + (b + c)$
This rule allows you to regroup numbers in an addition problem without changing the result. It's helpful when adding three or more numbers, letting you choose which pair to add first.
Identity Property of Addition
$a + 0 = a$
This rule states that adding zero to any number leaves the number unchanged. Zero is the 'additive identity' because it preserves the identity of the number.
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Challenging
A student claims the two expressions (10+20)+30 and (20+10)+30 are equivalent because of the Associative Property. What is the error in the student's reasoning?
A.The student is correct; the grouping changed.
B.The student used the Identity Property, not the Associative Property.
C.The student confused the properties; the order of numbers changed, which is the Commutative Property.
D.The expressions are not equivalent.
Challenging
You need to calculate 18 + (45 + 82). Which expression uses both the Commutative and Associative properties to make the calculation easiest to perform mentally?
A.(18 + 82) + 45
B.18 + (82 + 45)
C.(45 + 18) + 82
D.(18 + 45) + 82
Challenging
Maria added a list of prices: $1.50 + $8.00 + $2.50. She got a total of $12.00. To check her work, her friend Tom calculated $8.00 + ($1.50 + $2.50). Tom also got $12.00. Which property or properties confirm that Tom's method of checking is valid?
A.The Identity Property
B.The Associative Property only
C.The Commutative Property only
D.Both the Commutative and Associative Properties
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