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If Aiden originally buys 1 chocolate cupcake and 2 vanilla cupcakes, what is the total number of cupcakes sold by him and Gabrielle if she buys 4 strawberry cupcakes?
If Aiden originally buys 1 chocolate cupcake and 2 vanilla cupcakes, what is the total number of cupcakes sold by him and Gabrielle if she buys 4 strawberry cupcakes?
Which of the following best describes the commutative property?
Which of the following best describes the commutative property?
Using the commutative property, what is the sum of 25 + 28 + 15 if rearranged to 15 + 25 + 28?
Using the commutative property, what is the sum of 25 + 28 + 15 if rearranged to 15 + 25 + 28?
What is the result of the operation 3 x 5 based on the commutative property?
What is the result of the operation 3 x 5 based on the commutative property?
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What will be the total if Gabrielle decides to buy 2 chocolate cupcakes and 4 strawberry cupcakes instead of 4 strawberry cupcakes?
What will be the total if Gabrielle decides to buy 2 chocolate cupcakes and 4 strawberry cupcakes instead of 4 strawberry cupcakes?
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In the expression 16 + 8 + 4, rearranging it to 4 + 16 + 8 highlights which property?
In the expression 16 + 8 + 4, rearranging it to 4 + 16 + 8 highlights which property?
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If you add the numbers 123, 66, and 77, which of the following combinations using the commutative property yields the same total?
If you add the numbers 123, 66, and 77, which of the following combinations using the commutative property yields the same total?
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Which statement correctly applies the associative property?
Which statement correctly applies the associative property?
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What is the result of applying the commutative law in the calculation of $4 × 9 × 5$?
What is the result of applying the commutative law in the calculation of $4 × 9 × 5$?
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Which equation illustrates the associative property with addition correctly?
Which equation illustrates the associative property with addition correctly?
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Using the associative property, what is the value of $2 × (3 × 4)$?
Using the associative property, what is the value of $2 × (3 × 4)$?
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If $5 × 15 × 2$ is rearranged using the commutative law, which of the following is a valid equivalent expression?
If $5 × 15 × 2$ is rearranged using the commutative law, which of the following is a valid equivalent expression?
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What is the correct expression when applying the distributive property to $3(4 + 5)$?
What is the correct expression when applying the distributive property to $3(4 + 5)$?
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Which of the following statements about the commutative and associative properties is incorrect?
Which of the following statements about the commutative and associative properties is incorrect?
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What is the result of applying the associative law to $31 + 9 + 6$?
What is the result of applying the associative law to $31 + 9 + 6$?
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When applying the associative property to multiplication, what is $6 × (4 × 3)$ equivalent to?
When applying the associative property to multiplication, what is $6 × (4 × 3)$ equivalent to?
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Which property states that the order of numbers does not affect their sum or product?
Which property states that the order of numbers does not affect their sum or product?
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The sum of 10 + 20 is the same as 20 + 10.
The sum of 10 + 20 is the same as 20 + 10.
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Define the associative property in your own words.
Define the associative property in your own words.
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The commutative property applies to both addition and __________.
The commutative property applies to both addition and __________.
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Match the following operations with their associated properties:
Match the following operations with their associated properties:
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If you arrange the numbers 8, 4, and 2 for addition in the order of 4 + 2 + 8, which property are you demonstrating?
If you arrange the numbers 8, 4, and 2 for addition in the order of 4 + 2 + 8, which property are you demonstrating?
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The associative property only applies to addition.
The associative property only applies to addition.
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Calculate the result of $3 + (4 + 5)$ and also calculate $(3 + 4) + 5$ to demonstrate the associative property.
Calculate the result of $3 + (4 + 5)$ and also calculate $(3 + 4) + 5$ to demonstrate the associative property.
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In the statement $3(4 + 5)$, the __________ property allows us to distribute 3 across (4 + 5).
In the statement $3(4 + 5)$, the __________ property allows us to distribute 3 across (4 + 5).
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Which of the following statements correctly describes the associative property?
Which of the following statements correctly describes the associative property?
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The commutative property applies only to addition and not to multiplication.
The commutative property applies only to addition and not to multiplication.
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What is the result of applying the associative law to the expression $9 + (17 + 39)$?
What is the result of applying the associative law to the expression $9 + (17 + 39)$?
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In the equation $2 × (3 × 4)$, applying the associative property results in _____ × 4.
In the equation $2 × (3 × 4)$, applying the associative property results in _____ × 4.
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Match the property to its definition:
Match the property to its definition:
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Using the distributive property, what is $5(2 + 3)$ equivalent to?
Using the distributive property, what is $5(2 + 3)$ equivalent to?
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The expression $4 × 5 × 9$ is equal to $5 × 9 × 4$ according to the commutative property.
The expression $4 × 5 × 9$ is equal to $5 × 9 × 4$ according to the commutative property.
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What is the result of applying the associative law to the expression $2 × 3 × 4$?
What is the result of applying the associative law to the expression $2 × 3 × 4$?
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The expression $9 + (3 + 5)$ can be rewritten as $(____ + 3) + 5$.
The expression $9 + (3 + 5)$ can be rewritten as $(____ + 3) + 5$.
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Which equation illustrates the commutative property with multiplication?
Which equation illustrates the commutative property with multiplication?
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Study Notes
Arithmetic Laws - Lesson 1
- Arithmetic laws are used to simplify calculations.
- Three main properties: Commutative, Associative, and Distributive.
Commutative Property
- Changing the order of numbers in an addition or multiplication problem doesn't change the result.
- Example: 3 + 5 = 5 + 3 = 8
- Example: 3 x 5 = 5 x 3 = 15
Associative Property
- Changing the grouping of numbers in an addition or multiplication problem doesn't change the result.
- Example: (3 + 4) + 5 = 3 + (4 + 5) = 12
- Example: (3 x 4) x 5 = 3 x (4 x 5) = 60
Distributive Property
- Distributes multiplication over addition or subtraction.
- Example: a x (b + c) = (a x b) + (a x c)
- Example: a x (b - c) = (a x b) - (a x c).
- Real-world Application:
- A person buys two, 2-packs of cookies at 2each,andtwo,3−packsofcookiesat2 each, and two, 3-packs of cookies at 2each,andtwo,3−packsofcookiesat3 each. What's the total cost? 2 x (2 + 2 x 3). 2 x 2 + 2 x 2 x 3 = 4 + 12 = 16.
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Description
This quiz covers the fundamental arithmetic laws that simplify calculations, including the Commutative, Associative, and Distributive properties. Test your understanding of these properties with examples and real-world applications to see how they operate in math problems.
