Arithmetic Laws - Lesson 1

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Questions and Answers

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?

7 (correct)
4
6
5

Which of the following best describes the commutative property?

Numbers may be swapped without changing the result. (correct)
Order changes the results of the operation.
Only applicable to addition, not multiplication.
Changing the grouping of numbers affects the total.

Using the commutative property, what is the sum of 25 + 28 + 15 if rearranged to 15 + 25 + 28?

68 (correct)
58
70
25

What is the result of the operation 3 x 5 based on the commutative property?

15 (C) Signup and view all the answers

What will be the total if Gabrielle decides to buy 2 chocolate cupcakes and 4 strawberry cupcakes instead of 4 strawberry cupcakes?

8 (A) Signup and view all the answers

In the expression 16 + 8 + 4, rearranging it to 4 + 16 + 8 highlights which property?

Commutative Property (B) Signup and view all the answers

If you add the numbers 123, 66, and 77, which of the following combinations using the commutative property yields the same total?

123 + 77 + 66 (B) Signup and view all the answers

Which statement correctly applies the associative property?

2 + (3 + 4) = 9 (D) Signup and view all the answers

What is the result of applying the commutative law in the calculation of $4 × 9 × 5$?

180 (B) Signup and view all the answers

Which equation illustrates the associative property with addition correctly?

$6 + (4 + 5) = (6 + 4) + 5$ (A), $2 + 4 + 5 = (2 + 4) + 5$ (B), $3 + (2 + 1) = (3 + 1) + 2$ (C) Signup and view all the answers

Using the associative property, what is the value of $2 × (3 × 4)$?

24 (C) Signup and view all the answers

If $5 × 15 × 2$ is rearranged using the commutative law, which of the following is a valid equivalent expression?

$15 × 5 × 2$ (B), $5 × 2 × 15$ (C) Signup and view all the answers

What is the correct expression when applying the distributive property to $3(4 + 5)$?

$3 × 4 + 3 × 5$ (A) Signup and view all the answers

Which of the following statements about the commutative and associative properties is incorrect?

The associative property only applies to addition. (D) Signup and view all the answers

What is the result of applying the associative law to $31 + 9 + 6$?

46 (B) Signup and view all the answers

When applying the associative property to multiplication, what is $6 × (4 × 3)$ equivalent to?

$(6 × 4) × 3$ (A), $(6 × 3) × 4$ (C) Signup and view all the answers

Which property states that the order of numbers does not affect their sum or product?

Commutative Property (D) Signup and view all the answers

The sum of 10 + 20 is the same as 20 + 10.

True (A) Signup and view all the answers

Define the associative property in your own words.

The associative property states that the way numbers are grouped does not affect their sum or product. Signup and view all the answers

The commutative property applies to both addition and __________.

multiplication Signup and view all the answers

Match the following operations with their associated properties:

3 + 5 = 5 + 3 = Commutative Property (2 + 3) + 4 = 2 + (3 + 4) = Associative Property 5 × (2 + 3) = 5 × 2 + 5 × 3 = Distributive Property 4 + 0 = 4 = Identity Property Signup and view all the answers

If you arrange the numbers 8, 4, and 2 for addition in the order of 4 + 2 + 8, which property are you demonstrating?

Commutative Property (A) Signup and view all the answers

The associative property only applies to addition.

False (B) Signup and view all the answers

Calculate the result of $3 + (4 + 5)$ and also calculate $(3 + 4) + 5$ to demonstrate the associative property.

$12$ Signup and view all the answers

In the statement $3(4 + 5)$, the __________ property allows us to distribute 3 across (4 + 5).

distributive Signup and view all the answers

Which of the following statements correctly describes the associative property?

Grouping of numbers does not impact the sum or product. (D) Signup and view all the answers

The commutative property applies only to addition and not to multiplication.

False (B) Signup and view all the answers

What is the result of applying the associative law to the expression $9 + (17 + 39)$?

65 Signup and view all the answers

In the equation $2 × (3 × 4)$, applying the associative property results in _____ × 4.

6 Signup and view all the answers

Match the property to its definition:

Commutative Property = Order of numbers can change and still yield the same result. Associative Property = Grouping of numbers does not affect the sum or product. Distributive Property = Expanding a multiplication over addition or subtraction. Signup and view all the answers

Using the distributive property, what is $5(2 + 3)$ equivalent to?

$5 × 2 + 5 × 3$ (C) Signup and view all the answers

The expression $4 × 5 × 9$ is equal to $5 × 9 × 4$ according to the commutative property.

True (A) Signup and view all the answers

What is the result of applying the associative law to the expression $2 × 3 × 4$?

24 Signup and view all the answers

The expression $9 + (3 + 5)$ can be rewritten as $(____ + 3) + 5$.

9 Signup and view all the answers

Which equation illustrates the commutative property with multiplication?

$3 × 4 = 4 × 3$ (A) Signup and view all the answers

Flashcards

Commutative Property of Addition

The order of numbers in addition does not change the sum.

Commutative Property of Multiplication

The order of numbers in multiplication does not change the product.