Exploring Algebraic Properties and Rational Expressions

The video tutorial covers algebraic properties including commutative, associative, and distributive properties. It explains how these properties apply to addition and multiplication, and provides examples to illustrate each concept. The tutorial also demonstrates how to simplify and evaluate expressions using these properties, offering two methods for evaluation: substituting values first or simplifying expressions before substitution.

What does the commutative property of addition state?

• The sum of two numbers is always even.

• The sum of two numbers is always greater than either number.

• The order of numbers does not affect the sum.

• The sum of two numbers is always positive.

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

• 2 + 3 = 3 + 2

• 2 + 3 = 5

• 2 * 3 = 6

• 2 * 3 = 3 * 2

What does the associative property of addition allow you to do?

• Multiply numbers before adding them.

• Change the order of numbers in addition.

• Group numbers differently without changing the sum.

• Add numbers only in pairs.

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

• 2 + 3 = 5

• 2 * (3 * 4) = (2 * 3) * 4

• 2 + (3 + 4) = (2 + 3) + 4

• 2 * 3 = 3 * 2

What is the main purpose of the distributive property?

• To expand expressions and remove parentheses.

• To group numbers differently.

• To simplify fractions.

• To change the order of numbers.

Which of the following expressions demonstrates the distributive property?

• a * b = b * a

• a + (b + c) = (a + b) + c

• a * (b + c) = a * b + a * c

• a + b = b + a

What is the first step in simplifying the expression 3(x - 4) - 2(4 - x)?

• Reorder the terms.

• Add the constants.

• Apply the distributive property.

• Combine like terms.

After applying the distributive property to 3(x - 4) - 2(4 - x), what is the next step?

• Combine like terms.

• Factor the expression.

• Reorder the terms.

• Add the constants.

When evaluating the expression 3a + b - a * b for a = 3 and b = -2, what is the first step?

• Simplify the expression.

• Substitute the values of a and b.

• Combine like terms.

• Apply the distributive property.

What is the final value of the expression 3a + b - a * b when a = 3 and b = -2?

• 11

• 9

• 7

• 5