a bakery can bake 12 dozen cookies in 12 minutes. if the bakery’s pace stays the same, how many...

A bakery can bake 12 dozen cookies in 12 minutes. If the bakery’s pace stays the same, how many cookies can it bake in 1 ½ hours?

Bellringer

Multiplication of Integers

TLW compute fluently with multiplication of integers.

Negative Times Negativeis What?

Some people think of negative as meaning “not.”

Consider the sentence: “I am not going to the store.”

It is the negative version of “I am going to the store.”

So what do two “nots” mean?

Consider this sentence: “You may tell me NOT to go to the store, but I’m not going to do what you say!”

The two “nots” cancel each other out, just like two negatives.

I am insisting that I WILL go to the store!

Deposits and Withdrawals

A positive integer is like a deposit, and a negative integer is like a withdrawal.

Transaction Representation

• Add 3 deposits of $100

•(3)(100)

• Increase of $300

Result

Transaction Representation

• 4 withdrawals of $20

• (4)(-20)

• Decrease of $80

Result

Symbolism

= love

= hate

Character Symbolism

If you love to love means you love.

X =

Pos. X Pos. = Pos.

If you hate to hate means you love.

X =

Neg. X Neg. = Pos.

If you love to hate means you hate.

X =

Pos. X Neg. = Neg.

If you hate to love means you hate.

X =

Neg. X Pos. = Neg.

Multiplying Two Integers

(+7)(+3) = (-7)(-3) = (+7)(-3) = (-7)(+3) =

+21

+21

-21-21

Multiplying Three Integers

(+5)(+3)(+2) = (+15)(+2)

= +30

Multiplying Three Integers

(+5)(+3)(-2) = (+15)(-2)

= -30

Multiplying Three Integers

(-5)(-3)(-2) = (+15)(-2)

= -30

CHECK IT OUT!

Is the product positive or negative when an odd number of negative numbers are multiplied?

NEGATIVE

RULES

When multiplying an ODD number of negatives, the product is always NEGATIVE.

When multiplying an EVEN number of negatives, the product is always POSITIVE.