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Multiplying and Dividing Integers. Multiplying and Dividing Integers. Ex) Consider: (+3) x (-7) = ?. Multiplying and Dividing Integers. Ex) Consider: (+3) x (-7) = ? Think of our Model:. Multiplying and Dividing Integers. Ex) Consider: (+3) x (-7) = ? Think of our Model:

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multiplying and dividing integers1
Multiplying and Dividing Integers

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

multiplying and dividing integers2
Multiplying and Dividing Integers

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

Think of our Model:

multiplying and dividing integers3
Multiplying and Dividing Integers

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

Think of our Model:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

multiplying and dividing integers4
Multiplying and Dividing Integers

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

Think of our Model:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

What is the overall effect?

multiplying and dividing integers5
Multiplying and Dividing Integers

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

Think of our Model:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

What is the overall effect? The temperature drops by 21°.

multiplying and dividing integers6
Multiplying and Dividing Integers

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

Think of our Model:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

What is the overall effect? The temperature drops by 21°.

So, (+3) x (-7) =

multiplying and dividing integers7
Multiplying and Dividing Integers

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

Think of our Model:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

What is the overall effect? The temperature drops by 21°.

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

multiplying and dividing integers9
Multiplying and Dividing Integers

Ex) (-5) x (-4) =

We need to make 5 trips into the greenhouse to remove . . .

four ice cubes each time.

multiplying and dividing integers10
Multiplying and Dividing Integers

Ex) (-5) x (-4) =

We need to make 5 trips into the greenhouse to remove . . .

four ice cubes each time.

The temperature will rise by 20° C.

multiplying and dividing integers11
Multiplying and Dividing Integers

Ex) (-5) x (-4) =

We need to make 5 trips into the greenhouse to remove . . .

four ice cubes each time.

The temperature will rise by 20° C.

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

multiplying and dividing integers13
Multiplying and Dividing Integers

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

We need to make 3 trips into the greenhouse to remove . . .

8 hot coals each time.

multiplying and dividing integers14
Multiplying and Dividing Integers

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

We need to make 3 trips into the greenhouse to remove . . .

8 hot coals each time.

Overall Effect:

multiplying and dividing integers15
Multiplying and Dividing Integers

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

We need to make 3 trips into the greenhouse to remove . . .

8 hot coals each time.

Overall Effect: A decrease in temperature of 24° C.

multiplying and dividing integers16
Multiplying and Dividing Integers

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

We need to make 3 trips into the greenhouse to remove . . .

8 hot coals each time.

Overall Effect: A decrease in temperature of 24° C.

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

multiplying and dividing integers18
Multiplying and Dividing Integers

Ex) (+5) x (+6) =

We are making 5 trips into the greenhouse to add . . .

6 hot coals each time.

multiplying and dividing integers19
Multiplying and Dividing Integers

Ex) (+5) x (+6) =

We are making 5 trips into the greenhouse to add . . .

6 hot coals each time.

Overall Effect:

multiplying and dividing integers20
Multiplying and Dividing Integers

Ex) (+5) x (+6) =

We are making 5 trips into the greenhouse to add . . .

6 hot coals each time.

Overall Effect: The temperature increases by 30° C.

multiplying and dividing integers21
Multiplying and Dividing Integers

Ex) (+5) x (+6) =

We are making 5 trips into the greenhouse to add . . .

6 hot coals each time.

Overall Effect: The temperature increases by 30° C.

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

multiplying and dividing integers23
Multiplying and Dividing Integers

We have:

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

multiplying and dividing integers24
Multiplying and Dividing Integers

We have:

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

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

multiplying and dividing integers25
Multiplying and Dividing Integers

We have:

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

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

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

multiplying and dividing integers26
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 integers27
Multiplying and Dividing Integers

We have:

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

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

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

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

Can we write some rules?

multiplying and dividing integers29
Multiplying and Dividing Integers

RULES:

1) When multiplying integers with the same signs, the answer will be

multiplying and dividing integers30
Multiplying and Dividing Integers

RULES:

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

multiplying and dividing integers31
Multiplying and Dividing Integers

RULES:

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

2) When multiplying integers with different signs, the answer will be

multiplying and dividing integers32
Multiplying and Dividing Integers

RULES:

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

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

multiplying and dividing integers33
Multiplying and Dividing Integers

RULES:

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

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

Will this be true for division?

multiplying and dividing integers34
Multiplying and Dividing Integers

If:

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

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

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

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

multiplying and dividing integers35
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 integers36
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 integers37
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 integers38
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 integers39
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)

Are the rules the same?

multiplying and dividing integers40
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)

Are the rules the same? Yes!

multiplying and dividing integers41
Multiplying and Dividing Integers

RULES:

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

multiplying and dividing integers42
Multiplying and Dividing Integers

RULES:

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

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