Basic Arithmetic and Algebra Concepts

This lesson covers using identity and inverse properties to write equivalent expressions. It begins with a temperature change problem, demonstrating how to represent changes using expressions. The lesson explores additive inverses, showing how the sum of a number and its inverse equals zero. A number puzzle is presented, emphasizing the unique solution of zero. The lesson continues with writing equivalent expressions by collecting like terms and removing parentheses. Finally, it covers using the multiplicative inverse and distribution to simplify expressions. Students are encouraged to practice these concepts through examples and exercises.

If the temperature starts at -12 degrees and rises by 12 degrees, what is the new temperature?

• -12 degrees

• 0 degrees

• 12 degrees

• 24 degrees

What is the result of adding a number to its additive inverse?

• Zero

• The number itself

• Negative of the number

• Double the number

What pattern is observed when adding any number to zero?

• The result is double the number

• The result is the number itself

• The result is negative of the number

• The result is zero

If you repeatedly add a number to itself and the result is the same as the original number, what must the number be?

• One

• Zero

• Negative one

• Two

What is the equivalent expression for 2x + (-2x) + 3?

• 3x

• 2x - 3

• 0 + 3

• 2x + 3

How do you simplify the expression 3x + (-3x) + 1?

• 1

• 0 + 1

• 3

• 3x + 1

What is the multiplicative inverse of -5?

• -1/5

• 5

• -5

• 1/5

How do you simplify the expression 3/4 * 4/3?

• 1

• 0

• 3/4

• 4/3

What is the result of multiplying 1/2 by 4?

• 1/2

• 2

• 1

• 4

What is the simplified form of 3x + 5 divided by 3?

• 1x + 5/3

• 3x + 5

• 1x + 1/3

• 3x/3 + 5/3