Determine Which of the Following Statements Are True

1.7  Properties of Real Numbers:

Determine which of the following statements are true:

1.  3 + (4 + 5) = 3 + (4 + 5)

2.  3 + (4 ∙ 5) = (3 + 4) ∙ 5

3.  3 ∙ (4 ∙ 5) = (3 ∙ 4) ∙ 5

Do you think that the statements that are true would work with numbers other than 3, 4, and 5?

4.  Try one other set of numbers to see if they work.

The true statements above show the number property called the associative property of real numbers.

5.  State the associative property using the variables a, b, and c, instead of the numbers:

Associative property: ______

or ______

Note that the associative property allows us to simplify expressions. For example:

5 ∙ (3 ∙ x)

= (5 ∙ 3) ∙ x

= 15x

Determine which of the following are true:

6.  3 + 4 = 4 + 3

7.  3 ∙ 4 = 4 ∙ 3

From your experience, are these statements true with numbers other than 3 and 4?

8.  Try one other set of numbers to see that they are true.

The true statements above show the number property called the commutative property of real numbers.

9.  State the commutative property using the variables a, and b instead of the numbers given:

Commutative property: ______

or ______

Note that the commutative property allows us to simplify expressions.

Determine which of the following are correct simplifications using the commutative property:

10.  3x ∙ 5y = 3∙5∙x∙y = 15xy

11.  5x + 3y = 5∙3 + x∙y = 15 + xy

Determine which of the following statements are true:

12.  3∙(4 + 5) = 3∙4 + 3∙5

13.  3 + (4 ∙ 5) = 3+4 ∙ 3+5

Do you think that the statements that are true would work with numbers other than 3, 4, and 5?

14.  Try one other set of numbers to see if it works.

The true statements above show the number property called the distributive property of real numbers.

15.  State the distributive property using the variables a, b, and c, instead of the numbers given:

Distributive property: ______

Note that the distributive property allows us to simplify expressions.

Use the distributive property to simplify the following:

16.  3(5x + 2) =

17.  – (5x + 2y – 7) =

We can also use the distributive property in reverse to factor expressions (i.e., to write as a product). For Example if there is a common factor of 2:

6x + 4

= 2∙3x + 2∙2

= 2(3x + 2)

Or if there is a common factor of x:

9x + 13x

= x(9 + 13)

= x(22)

= 22x

18.  Use the distributive property on the answer of each of the simplifications above to confirm that it is equal to the original expression.

Factor out the GCF from the following expressions:

19.  8y – 24

20.  5x + 3x

21.  3xy + 7xy =

22.  =

23.  =

Look back at the previous examples 20 – 23.

24.  What can we do when adding or subtracting variables that are the same?

25.  Does this conclusion work for 3x + 5y?

26.  Does this conclusion work for ?

27.  Does this conclusion work for ?

28.  Conclusion: When adding and subtracting variables we need: