1TH/vwo § 9.2 Simplifying formulas-long

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

§ 9.2 Simplifying formulas

The simpler the formulas,

the more we like them!  

First a little REFRESH on Positive and Negative terms.

see next slides

- 8 - 6 =

1. -2
2. 2
3. 14
4. -14

Who believes in fairytales?

A few examples:

In Hans und Gretel, or in this one:

'Whenever I see two minuses, I write down a plus.'

 Hans und Gretel is a nice 

but frightening story: 

But what about:

'Whenever I see two minuses, I write down a plus.'

Now the other one:

 'Whenever I see two minuses, I write down a plus.'

This is NOT TRUE:

7 + 8 = 15                        and                            - 7 - 8 = - 15

When do two minuses make plus?

When MULTIPLYING:          - 5 x - 6 = 30 !

6 - 8 =

1. -2
2. 2
3. 14
4. -14

8 -6 -7 =

1. 5
2. -5
3. 21
4. -21

5 - 6 + 7 =

1. 6
2. 18
3. -6
4. 8

Like terms ......

                                     are the terms I like !

f=8h−4h+6−3

f=8h+6−4h−3

8h and 4h are like terms

and

6 and 3 are like terms

so you can write 

like

f=4h+3

2p + 4 + 3p + 6 =

1. 6p + 24
2. 15
3. 15p
4. 5p + 10

Solution:

2p + 4 + 3p + 6 = 

2p + 3p + 4 + 6 =

5p + 10

4c - 5 - 6c + 3 =

1. -2c -2
2. -2c + 2
3. 10c + 8
4. -4c

Solution:

4c - 5 - 6c + 3 =

4c - 6c - 5 + 3 =

-2c - 2

Note : You do not need to write the number 1

shorten as much as possible:
4d - 3d + 5t - 6t =

1. 7d + 11t
2. d - t
3. 1d - 1t
4. d + t

Solution:

4d - 3d + 5t - 6t =

1d + - 1t =

d - t

The word AREA (= oppervlakte) you will

probably know.

However, do you know the English word for 

'OMTREK' ? (In exercise 15 this comes up.)

See the next slides for an explanation and some illustrations!   

First the AREA comes up.

AREA     -    PERIMETER

The English word for 

'OMTREK'  is:   PERIMETER ! 

For an illustration, see the next slide. 

The Perimeter here consists

of all the blue and red lengths:

15 cm + 15 cm + 15 cm + 15 cm

+ b + b + b + b

TASK:

SHORTEN this expression (=uitdrukking) above.

1. 60 cm + b
2. 64 b
3. 60 cm + 4b

Solution:

15 cm + 15 cm + 15 cm + 15cm = 60 cm

b + b + b + b = 4b,         so:

the total result is:

P = 60 + 4b

Homework

Paragraph 9.2

You may all skip exercise 8 (we did this in the Lessonup.)

Havo and H/V: choose between the Support path and the Standard path

Vwo: do the challenge path, so : skip 12 and 13 

but do:    C3 and C4!