§2.5 Multiplying and Dividing Negative Numbers

C2 Numbers & Operations

Mr. Fintelman (FNL)

Monday October 14th

2024

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C2 Numbers & Operations

Mr. Fintelman (FNL)

Monday October 14th

2024

Slide 1 - Tekstslide

Date

Monday October 14th 2024

Paragraph

§2.5 Multiplying and Dividing Negative Numbers

Pages from the handbook

Pag. 77-79

Subject

Multiplying negative numbers

Order of operations

Today is the day...

Slide 2 - Tekstslide

I can already…

… add and subtract negative numbers.

Prior Knowledge

Slide 3 - Tekstslide

Adding and subtracting with negative numbers

Slide 4 - Tekstslide

After this lesson, I can…

… multiply with negative numbers and use this in combination with the order of operations.

Goals

Slide 5 - Tekstslide

Negative numbers 2: Electric boogaloo!

I do (+) like (+) pancakes.

I don't (-) like (+) pancakes.

I do (+) hate (-) pancakes.

I don't (-) hate (-) pancakes.

Slide 6 - Tekstslide

Little reminder

We already know about adding and subtracting:

- 5 - - 3 = - 5 + 3 = - 2

2 + - 6 = 2 - 6 = - 4

- 3 + - 7 = - 3 - 7 = - 10

Slide 7 - Tekstslide

New

But don't know the rules of multiplication... or do we?

- 3 \times 4 =

- 2 \times - 6 =

5 \times - 1 =

8 \times 3 =

Slide 8 - Tekstslide

Multiple multiplications. Positive or negative?

- 100 \cdot 99 \cdot - 98 \cdot 97 \cdot . . . \cdot - 4 \cdot 3 \cdot - 2 \cdot 1 =

- 2 \cdot 3 \cdot - 5 \cdot - 8 =

- 3 \cdot - 2 \cdot - 2 \cdot - 1 \cdot 3 \cdot 3 \cdot 4 \cdot - 5 =

Slide 9 - Tekstslide

Multiple multiplications. Positive or negative?

- 100 \cdot 99 \cdot - 98 \cdot 97 \cdot . . . \cdot - 4 \cdot 3 \cdot - 2 \cdot 1 =

- 2 \cdot 3 \cdot - 5 \cdot - 8 =

- 3 \cdot - 2 \cdot - 2 \cdot - 1 \cdot 3 \cdot 3 \cdot 4 \cdot - 5 =

Negative

Positive

Slide 10 - Tekstslide

Exercise 64 (Homework) - Pag. 78

Slide 11 - Tekstslide

Exercise 66abc (Homework) - Pag. 79

timer

2:30

Slide 12 - Tekstslide

Exercise 66abc

9 - 5 \cdot - 3 =

9 + 15 =

24

- 3 - 0 \cdot - 5 + 6 =

- 3 + 6 =

3

- 2 - (0) \cdot - 6 =

- 2 - (5 - 5) \cdot - 6 =

- 2 - 0 =

- 2

Slide 13 - Tekstslide

Worktime

You work neatly by…

… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 62, 64, 66 and 67.

Assignments:

Pages: 77-79

Exercises: 62, 63, 64, 66 and 67.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 68

Slide 14 - Tekstslide

Now I can…

… multiply with negative numbers and use this in combination with the order of operations.

Reflection

Slide 15 - Tekstslide

Date

Tuesday October 15th 2024

Paragraph

§2.5 Multiplying and Dividing Negative Numbers

Pages from the handbook

Pag. 80-81

Subject

Dividing negative numbers

Today is the day...

Slide 16 - Tekstslide

I can already…

… multiply with negative numbers and use this in combination with the order of operations.

Prior Knowledge

Slide 17 - Tekstslide

Multiplying with negative numbers

Slide 18 - Tekstslide

After this lesson, I can…

… divide with negative numbers and use this in combination with the order of operations.

Goals

Slide 19 - Tekstslide

Negative numbers 3: Return of the Cheesiness

I do (+) like (+) pancakes.

I don't (-) like (+) pancakes.

I do (+) hate (-) pancakes.

I don't (-) hate (-) pancakes.

Slide 20 - Tekstslide

Multiplication Pyramid

Slide 21 - Tekstslide

Multiplication Pyramid

Slide 22 - Tekstslide

Trigger warning: Difficult language

Slide 23 - Tekstslide

Trigger warning: Difficult language

Slide 24 - Tekstslide

Exercise 72 (Homework) - Pag. 80

timer

3:30

Slide 25 - Tekstslide

Exercise 72a

(- 8 + - 6) - (- 9 \cdot 3) =

- 14 - - 27 =

- 14 + 27 =

13

Slide 26 - Tekstslide

Exercise 72bc

(- 8 \cdot - 5) \div (- 6 + 4) =

40 \div - 2 =

- 20

(- 12 \cdot - 5) - (- 20 \div 2) =

60 - - 10 =

60 + 10 =

70

Slide 27 - Tekstslide

Worktime

You work neatly by…

… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 62, 64, 66, 67, 70, 71, 72, 73 and 74.

Assignments:

Pages: 77-79

Exercises: 62, 63, 64, 66, 67, 70, 71, 72, 73 and 74.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 68

Slide 28 - Tekstslide

Now I can…

… divide with negative numbers and use this in combination with the order of operations.

Reflection

Slide 29 - Tekstslide

Date

Wednesday October 16th 2024

Paragraph

§2.5 Multiplying and Dividing Negative Numbers

Pages from the handbook

Pag. 81-82

Subject

Fraction bar

Today is the day...

Slide 30 - Tekstslide

I can already…

… multiply with negative numbers and use this in combination with the order of operations.
… divide with negative numbers and use this in combination with the order of operations.

Prior Knowledge

Slide 31 - Tekstslide

Multiplying and dividing with negative numbers

Slide 32 - Tekstslide

After this lesson, I can…

… do calculations that involve a fraction bar.

Goals

Slide 33 - Tekstslide

Let's solve this...

6 \div 2 (1 + 2)

Slide 34 - Tekstslide

Slide 35 - Video

Ambiguous problem

\frac{​ 6 ​ ​}{​ 2 ​} (1 + 2) =

\frac{​ 6 ​ ​}{​ 2 ( 1 + 2 ) ​} =

\frac{​ 6 ​ ​}{​ 2 ​} (3) =

3 (3) =

9

\frac{​ 6 ​ ​}{​ 2 ( 3 ) ​} =

\frac{​ 6 ​ ​}{​ 6 ​} =

1

Slide 36 - Tekstslide

Fraction bars are useful

Slide 37 - Tekstslide

Giving you a choice

Slide 38 - Tekstslide

Dividing by zero - Short version

Slide 39 - Tekstslide

Worktime

You work neatly by…

… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 62, 64, 66, 67, 70, 71, 72, 73, 74, 76, 77, 78, 79 and 80.

Assignments:

Pages: 77-79

Exercises: 62, 63, 64, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 and 80.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 68 and 81.

Slide 40 - Tekstslide

Dividing by zero - Actual mathematics

First, what is division?

Division is repeated subtraction.

So if we try to calculate...

So is our answer infinite?

15 \div 3 = 5

15 = 3 - 3 - 3 - 3 - 3 = 0

1 \div 0 = . . .

1 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - . . . = \infty ?

Slide 41 - Tekstslide

Dividing by zero - Actual mathematics

Let's use a different method...

So it seems right to say...

\frac{​ 1 ​ ​}{​ 0 ​} = \infty ?

\frac{​ 1 ​ ​}{​ 1 ​} = 1

\frac{​ 1 ​ ​}{​ 0 . 1 ​} = 10

\frac{​ 1 ​ ​}{​ 0 . 0 1 ​} = 100

\frac{​ 1 ​ ​}{​ 0 . 0 0 1 ​} = 1000

\frac{​ 1 ​ ​}{​ 0 ​} = \infty ?

Slide 42 - Tekstslide

Dividing by zero - Actual mathematics

But that also means that...

So...

\frac{​ 2 ​ ​}{​ 1 ​} = 2

\frac{​ 2 ​ ​}{​ 0 . 1 ​} = 20

\frac{​ 2 ​ ​}{​ 0 . 0 1 ​} = 200

\frac{​ 2 ​ ​}{​ 0 . 0 0 1 ​} = 2000

\frac{​ 2 ​ ​}{​ 0 ​} = \infty ?

\frac{​ 3 ​ ​}{​ 0 ​} = \infty ?

\frac{​ 1 4 5 ​ ​}{​ 0 ​} = \infty ?

Slide 43 - Tekstslide

Dividing by zero - Actual mathematics

Remember that earlier we established this:

So that means the following:

Correct?

15 \div 3 = 5

15 = 3 - 3 - 3 - 3 - 3 = 0

\frac{​ 1 5 ​ ​}{​ 3 ​} = 5 = \frac{​ 2 5 ​ ​}{​ 5 ​}

Slide 44 - Tekstslide

Dividing by zero - Actual mathematics

But that also means that...

And since we constantly divide by the same number, it should mean that...

Notice the problem?

\frac{​ 1 ​ ​}{​ 0 ​} = \infty = \frac{​ 2 ​ ​}{​ 0 ​} = \infty = \frac{​ 3 ​ ​}{​ 0 ​} = . . .

1 = 2 = 3 = . . .

0 \cdot \infty = 1

0 \cdot \infty = 2

0 \cdot \infty = 3

Slide 45 - Tekstslide

Dividing by zero - Actual mathematics

If we move towards zero from the opposite direction...

So it seems right to say...

\frac{​ 1 ​ ​}{​ 0 ​} = \infty ?

\frac{​ 1 ​ ​}{​ - 1 ​} = - 1

\frac{​ 1 ​ ​}{​ - 0 . 1 ​} = - 10

\frac{​ 1 ​ ​}{​ - 0 . 0 1 ​} = - 100

\frac{​ 1 ​ ​}{​ - 0 . 0 0 1 ​} = - 1000

\frac{​ 1 ​ ​}{​ 0 ​} = - \infty ?

Slide 46 - Tekstslide

Dividing by zero - Actual mathematics

Dividing by zero results in an 'error', but the reason is that it is left undefined by mathematicians. Since a lack of logic results in problems with set definitions of numbers.

Slide 47 - Tekstslide

Worktime

You work neatly by…

… reading the theory (again) before asking a question to your classmate.
… raising a hand before asking a question to the teacher.
… if the teacher is busy, remember your question and move on.

Help:

Exercises: 62, 64, 66, 67, 70, 71, 72, 73, 74, 76, 77, 78, 79 and 80.

Assignments:

Pages: 81-82

Exercises: 62, 63, 64, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79 and 80.

Assignments from the planning of WEEK 1:

Extra:

Exercises: 68 and 81.

Slide 48 - Tekstslide

Now I can…

… divide with negative numbers and use this in combination with the order of operations.

Reflection

Slide 49 - Tekstslide

§2.5 Multiplying and Dividing Negative Numbers

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