Multiplication & Division of Rational Numbers, & Properties

Multiplication & Division of Rational Numbers, & Properties

Review

• 8-(-3)

• What does minus a negative become?

• Solve: -2+3-(-6)

• Which direction on the number line do you go for negatives?

Commutative Property

• You can change the order of the numbers and get the same result.

• The positive or negative sign must stay with the number.

Multiple Choice

Which of the following correctly shows the commutative property?

• -2+3=1 and -3+2=1

• (-2)(3)=-6 & (-3)(-2)=-6

• -2+3=1 and 3+(-2)=1

• (-2)(3)=-6 & (-3)(2)=-6

Associative Property

• The grouping or parenthesis changes but the order of the numbers stays the same.

• (1+2)+3=6 and 1+(2+3)=6

• (2x3)x4=24 and 2x(3x4)=24

Multiple Choice

Which one is the associative property to:

(8 x 2) x 4

• 4 x 2 x 8

• (4 x 2) x 8

• 8 x (2 x 4)

• (8 x 2) x4

Distributive Property

Lesson 6.12

How do you multiply a number by a variable?

• To multiply a number by a variable, remember there is always a 1 in front of that variable if the variable is alone. 4(x)= 4x It is like multiplying 4 times 1x

Multiple Choice

3(2c - 5)

• 6c - 15
• 6c + 15
• 6c + 15
• -6c - 15

Multiple Select

4(a + 3)

• 4a + 3

• 4 + 3

• 4a + 12

• a + 12

What if I have more than one variables?

Then you multiply the number outside the parenthesis with each coefficient inside. For example: 3(2x + 3y +z) = 3(2x) + 3(3y) + 3(z)=

6x + 9y + 3z this is the answer because there are no like terms.

Multiple Choice

Simplify the expression:
4(5b - 6f - c)

• 20b - 24f - 4c
• 9b - 10f - 4c
• 45b - 46f - 4c
• 20b + 24f + 4c

Multiple Select

What situations allow for the answer to be the same as our original number?

• b + 1 =

• b * 1 =

• b + 0 =

• b * 0 =

Multiple Select

What situations allow for the answer to be the same as our original number?

• b + 1 =

• b * 1 =

• b + 0 =

• b * 0 =

Multiple Choice

-3 x (-5)

• Positive
• Negative

Multiple Choice

-20/5=

• -4

• 4

• -100

• 100

What if there are more than two number?

• (-2)(-3)(-4)?

• Count the number of negative signs.

• If there is an odd amount the answer will be negative.

• If there is an even amount the answer will be positive.

Multiple Choice

(-2)(-3)(-4)

• 24

• -24

• 9

• -9