Properties of Operations in Mathematics

This video tutorial covers four examples of properties of real numbers: the commutative property of multiplication, the distributive property, and the associative properties of both multiplication and addition. Each property is explained with examples, demonstrating how the order or grouping of numbers affects the outcome of operations. The commutative property shows that the order of multiplication does not change the result. The distributive property illustrates how a number can be distributed across terms within parentheses. The associative properties highlight how the grouping of numbers in addition or multiplication does not affect the sum or product.

What property is demonstrated when the order of factors in a multiplication changes?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

Which property is used when a term is multiplied across terms inside parentheses?

• Associative Property

• Distributive Property

• Commutative Property

• Inverse Property

In the expression 9a - 4a = (9 - 4)a, which property is being applied?

• Identity Property

• Associative Property

• Distributive Property

• Commutative Property

What is the result of changing the grouping of factors in a multiplication?

• Identity Property

• Commutative Property

• Distributive Property

• Associative Property

Which property is illustrated by the equation 2 x (10b) = (2 x 10) x b?

• Identity Property

• Associative Property

• Distributive Property

• Commutative Property

Which property is often expressed as a(bc) = (ab)c?

• Distributive Property

• Commutative Property

• Identity Property

• Associative Property

What property is shown when the grouping of terms in a sum changes?

• Identity Property

• Commutative Property

• Distributive Property

• Associative Property

In the expression (4x + 8) + 7 = 4x + (8 + 7), which property is being used?

• Identity Property

• Commutative Property

• Distributive Property

• Associative Property

Which property is demonstrated by rearranging the grouping of addends?

• Inverse Property

• Distributive Property

• Commutative Property

• Associative Property

What is the formal expression of the associative property of addition?

• a + 0 = a

• a(b + c) = ab + ac

• a + b = b + a

• (a + b) + c = a + (b + c)