Exploring Algebraic Properties in Rational Expressions

This video tutorial covers algebraic properties, focusing on the commutative and distributive properties. It explains how these properties can be used to create equivalent algebraic expressions and simplify expressions. The tutorial provides examples and practice options, emphasizing the importance of understanding these properties for mental math and algebraic simplification.

What is the learning target for this lesson?

• I can factor polynomials.

• I can graph linear equations.

• I can use algebraic properties to create equivalent algebraic expressions.

• I can solve quadratic equations.

What does the commutative property state about addition?

• You can only add numbers in ascending order.

• You can add numbers in any order.

• You cannot add numbers in any order.

• You can add numbers only if they are the same.

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

• 3 + 5 = 5 + 3

• 4 * 7 = 7 * 4

• 8 / 4 = 4 / 8

• 6 - 2 = 2 - 6

What does the distributive property state for any real numbers a, b, and c?

• a + (b * c) = a + b * c

• a * (b - c) = a * b + a * c

• a * (b + c) = a * b + a * c

• a - (b + c) = a - b + c

How can the distributive property be useful in mental math?

• It helps in dividing large numbers.

• It helps in adding large numbers.

• It is not useful in mental math.

• It simplifies the multiplication of large numbers.

What is the result of 9 * (37 - 27) using the distributive property?

• 70

• 80

• 90

• 100

What does it mean to distribute in the context of algebraic expressions?

• To divide the terms inside the parentheses.

• To multiply the number outside the parentheses by each term inside.

• To subtract the terms inside the parentheses.

• To add the terms inside the parentheses.

What is the simplified form of 3 * (2G + 5) using the distributive property?

• 6G + 15

• 2G + 15

• 5G + 6

• 3G + 10

How do you handle a minus sign when using the distributive property?

• Keep the minus sign and distribute it to each term inside the parentheses.

• Add the terms instead of subtracting.

• Ignore the minus sign.

• Change the minus sign to a plus sign.

What is the result of 3 * (7 - 4H) using the distributive property?

• 7 - 12H

• 21 - 4H

• 21 + 12H

• 21 - 12H