Properties of Operations and Identity

In this math class video, the teacher explores the relationship between multiplication and division, focusing on identities such as a divided by B times B equals a, and a times B divided by B equals a. The video includes problem-solving exercises to demonstrate these identities, emphasizing the identity property of multiplication. The teacher uses examples and tape diagrams to illustrate how multiplying and dividing by the same number results in the original number, similar to the relationship between addition and subtraction.

What is the result of dividing a number by another and then multiplying by the same number?

• The original number

• Zero

• Half the original number

• Double the original number

If 12 divided by 3 is multiplied by 3, what is the result?

• 9

• 12

• 3

• 6

What does the identity property of multiplication state?

• Multiplying by one gives the original number

• Multiplying by zero gives zero

• Multiplying by a number gives a different number

• Multiplying by two doubles the number

In the expression 45 times a number divided by 15 equals 45, what must the number be?

• 0

• 15

• 45

• 1

What happens when you multiply a number by one?

• The number becomes zero

• The number halves

• The number remains the same

• The number doubles

What is the result of dividing a number by one?

• The number remains the same

• The number doubles

• The number halves

• The number becomes zero

How does the relationship between multiplication and division compare to addition and subtraction?

• Multiplication and division are more complex

• Addition and subtraction are unrelated

• They are similar in that reversing the operation returns the original number

• They are completely different

What is the result of multiplying a number by a fraction that equals one?

• The number becomes zero

• The number remains the same

• The number doubles

• The number halves

If you divide a number and then multiply by the same number, what is the outcome?

• The number becomes zero

• The number remains the same

• The number halves

• The number doubles

What is the result of adding and then subtracting the same number?

• The number halves

• The number doubles

• The number becomes zero

• The number remains the same