Exploring Algebraic Properties of Rational Expressions

This video tutorial covers various algebraic properties, including commutative, associative, distributive, identity, inverse, zero, reflexive, symmetric, transitive, and substitution properties. Each property is explained with examples to illustrate how they apply to both numbers and variables, helping students understand how to manipulate and solve equations effectively.

What does the commutative property of addition state?

• Multiplying a number by zero gives zero.

• The grouping of numbers does not affect the sum.

• Adding zero to a number gives the same number.

• The order of numbers does not affect the sum.

Which of the following is an example of the commutative property of multiplication?

• 7 * (3 + 2) = 7 * 3 + 7 * 2

• 7 * 3 = 3 * 7

• 7 + 0 = 7

• 7 + 3 = 3 + 7

What does the associative property of addition state?

• Multiplying a number by zero gives zero.

• The grouping of numbers does not affect the sum.

• Adding zero to a number gives the same number.

• The order of numbers does not affect the sum.

Which of the following is an example of the associative property of multiplication?

• 2 * 0 = 0

• 2 * 3 = 3 * 2

• 2 + (3 + 4) = (2 + 3) + 4

• 2 * (3 * 4) = (2 * 3) * 4

What does the distributive property state?

• The order of numbers does not affect the sum.

• The grouping of numbers does not affect the sum.

• Adding zero to a number gives the same number.

• Multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products.

What is the identity property of multiplication?

• Multiplying a number by one gives the same number.

• Multiplying a number by zero gives zero.

• Multiplying a number by its reciprocal gives one.

• Adding zero to a number gives the same number.

What is the additive inverse of a number?

• The number multiplied by one.

• The number multiplied by zero.

• The number itself.

• The negative of the number.

What does the zero property of multiplication state?

• Multiplying a number by its reciprocal gives one.

• Multiplying a number by one gives the same number.

• Adding zero to a number gives the same number.

• Multiplying a number by zero gives zero.

What does the symmetric property state?

• If a = b, then a + b = b + a.

• If a = b, then a can be substituted for b.

• If a = b and b = c, then a = c.

• If a = b, then b = a.

What does the transitive property state?

• If a = b and b = c, then a = c.

• If a = b, then b = a.

• If a = b, then a + b = b + a.

• If a = b, then a can be substituted for b.