Docstoc

Multiplying and Dividing Integers (PowerPoint)

Document Sample
Multiplying and Dividing Integers (PowerPoint) Powered By Docstoc
					Integer Operations Review
      Integer Operations Review
One model that we can use for integers is a greenhouse.

In the Greenhouse, positive integers represent a temperature
   above 0ºC or an increase in temperature.

Negative integers represent a temperature below 0ºC or a
  decrease in temperature.

A hot coal will increase the temperature by exactly 1ºC.

An ice cube will decrease the temperature by exactly 1ºC.

There are unlimited amounts of each item in the Greenhouse.
       Integer Operations Review
Add:          (+5) + (+7)

What happens when we combine hot coals with hot coals?

             (+5) + (+7)
           = (+12)

We get a big pile of hot coals.
       Integer Operations Review
Add:         (-4) + (-9)

What happens when we combine ice cubes with ice cubes?

             (-4) + (-9)
           = (-13)

We get a big pile of ice cubes.
       Integer Operations Review
Add:         (-8) + (+5)

What happens when we combine ice cubes with hot coals?

             (-8) + (+5)
           = (-3)

The five hot coals melt five ice cubes. They cancel out.
      Integer Operations Review
Subtraction:

What are 2 different ways that we could lower the
 temperature in the Greenhouse by 6ºC ?

We could remove 6 hot coals, or
We could add 6 ice cubes.

Instead of subtracting an integer, we may add its opposite.
      Integer Operations Review
Subtract:     (-5) – (+13)
            = (-5) + (-13)
            = (-18)

Subtract:     (+15) – (-17)
            = (+15) + (+17)
            = (+32)
Multiplying and Dividing Integers


Multiplying and Dividing Integers is even easier !!!!



  You only need to remember 2 simple rules . . .
 Multiplying and Dividing Integers
RULES:

1) When multiplying or dividing 2 integers with the same
  signs, the answer will be positive.

2) When multiplying or dividing 2 integers with different
  signs, the answer will be negative.
Let’s see how this works:

Consider: (+3) x (-7) = ?

We can think of it this way:

Santa Claus makes 3 trips into the Greenhouse and
  leaves 7 ice cubes each time.

What happens to the temperature?
It drops by 21°C.

So, . . .    (+3) x (-7) = (-21)
Consider: (-5) x (-4) = ?

We can think of it this way:

A thief makes 5 trips into the Greenhouse and steals
  4 ice cubes each time.

What happens to the temperature?
It rises by 20°C.

So, . . .    (-5) x (-4) = (+20)
Consider: (-3) x (+8) = ?

We can think of it this way:

A thief makes 3 trips into the Greenhouse and steals
  8 hot coals each time.

What happens to the temperature?
It drops by 24°C.

So, . . .    (-3) x (+8) = (-24)
Consider: (+5) x (+6) = ?

We can think of it this way:

Santa Claus makes 5 trips into the Greenhouse and
  leaves 6 hot coals each time.

What happens to the temperature?
It rises by 30°C.

So, . . .    (+5) x (+6) = (+30)
 Multiplying and Dividing Integers
We have:

(+3) x (-7) = (-21)

(-5) x (-4) = (+20)

(-3) x (+8) = (-24)

(+5) x (+6) = (+30)
 Multiplying and Dividing Integers
We have:

(+3) x (-7) = (-21)

(-5) x (-4) = (+20)

(-3) x (+8) = (-24)

(+5) x (+6) = (+30)

We could try to think of examples for division, but . . .
It might be a little confusing . . .
    It might be a little confusing . . .




Just remember that multiplying and dividing are opposite operations.
 Multiplying and Dividing Integers
If:

(+3) x (-7) = (-21)

(-5) x (-4) = (+20)

(-3) x (+8) = (-24)

(+5) x (+6) = (+30)
 Multiplying and Dividing Integers
If:                   Then:

(+3) x (-7) = (-21)   (-21) ÷ (+3) = (-7)

(-5) x (-4) = (+20)

(-3) x (+8) = (-24)

(+5) x (+6) = (+30)
 Multiplying and Dividing Integers
If:                   Then:

(+3) x (-7) = (-21)   (-21) ÷ (+3) = (-7)

(-5) x (-4) = (+20)   (+20) ÷ (-5) = (-4)

(-3) x (+8) = (-24)

(+5) x (+6) = (+30)
 Multiplying and Dividing Integers
If:                   Then:

(+3) x (-7) = (-21)   (-21) ÷ (+3) = (-7)

(-5) x (-4) = (+20)   (+20) ÷ (-5) = (-4)

(-3) x (+8) = (-24)   (-24) ÷ (-3) = (+8)

(+5) x (+6) = (+30)
 Multiplying and Dividing Integers
If:                   Then:

(+3) x (-7) = (-21)   (-21) ÷ (+3) = (-7)

(-5) x (-4) = (+20)   (+20) ÷ (-5) = (-4)

(-3) x (+8) = (-24)   (-24) ÷ (-3) = (+8)

(+5) x (+6) = (+30)   (+30) ÷ (+5) = (+6)
 Multiplying and Dividing Integers
If:                               Then:

(+3) x (-7) = (-21)               (-21) ÷ (+3) = (-7)

(-5) x (-4) = (+20)               (+20) ÷ (-5) = (-4)

(-3) x (+8) = (-24)               (-24) ÷ (-3) = (+8)

(+5) x (+6) = (+30)               (+30) ÷ (+5) = (+6)

So we can see that the 2 simple rules also work for division.
 Multiplying and Dividing Integers
RULES:

1) When multiplying or dividing 2 integers with the same
  signs, the answer will be positive.

2) When multiplying or dividing 2 integers with different
  signs, the answer will be negative.

				
DOCUMENT INFO