Multiplying and Dividing Integers

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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 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:

Make 3 trips into the greenhouse to add . . .

seven ice cubes each time.

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 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 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 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 Integers

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

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

four ice cubes each time.

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 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 Integers

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

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

8 hot coals each time.

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 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 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 Integers

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

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

6 hot coals each time.

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 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 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 Integers

We have:

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

Multiplying and Dividing Integers

We have:

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

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

Multiplying and Dividing Integers

We have:

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

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

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

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)

Can we write some rules?

Multiplying and Dividing Integers

RULES:

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

Multiplying and Dividing Integers

RULES:

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

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 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 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 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)

Are the rules the same?

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 Integers

RULES:

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

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.