Questions and Answers
Name the property: $x + 2 = 2 + x$
commutative property of addition
Name the property: $7x = x(7)$
commutative property of multiplication
Name the property: $5(4 x) = (5 4)x$
associative property of multiplication
Name the property: $6(x + 4) = 6 x + 6 4$
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Name the property: $(ab)c = a(bc)$
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Name the property: $xyz = yzx$
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Name the property: $(w + v) + z + u = w + (v + z) + u$
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Name the property: $2(x + y) = 2x + 2y$
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Name the property: $(8 + x)5 = 5(8 + x)$
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Name the property: $3(5 + b) = 15 + 3b$
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Study Notes
Properties of Addition and Multiplication
- The commutative property of addition states that changing the order of the addends does not change the sum, as seen in the equation x + 2 = 2 + x.
- The commutative property of multiplication indicates that changing the order of the factors does not affect the product, exemplified by 7x = x(7).
Associative Properties
- The associative property of multiplication shows that the grouping of factors can be changed without changing the product, demonstrated by the equation 5(4 x) = (5 4)x and the expression (ab)c = a(bc).
- The associative property of addition highlights that the grouping of addends can be rearranged without altering the sum, as illustrated by (w + v) + z + u = w + (v + z) + u.
Distributive Property
- The distributive property allows for the multiplication of a sum by multiplying each addend separately and then adding the results, shown in two forms: 6(x + 4) = 6x + 6(4) and 2(x + y) = 2x + 2y.
- Another instance of the distributive property is demonstrated in 3(5 + b) = 15 + 3b.
Additional Commutative Examples
- The formula (8 + x)5 = 5(8 + x) reinforces the commutative property of multiplication, showcasing that the multiplication order of an expression does not matter.
- The equation xyz = yzx further exemplifies the commutative property of multiplication by changing the order of variables.
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Description
Test your knowledge on the different properties of operations in mathematics with these flashcards. From the commutative property of addition and multiplication to the distributive property, this quiz will help you reinforce your understanding of these fundamental concepts. Perfect for students in algebra and math courses.
