1TH/vwo §11.1 Addition and subtraction

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

Ch 11 Calculating with variables

Today we do:

§ 11.1 Addition and subtraction,

so:   +   and    -

By the way: we do more than 2 exercises from §11.1 now, in this LessonUp.

Pay attention well and you don't have to make them on paper any more!

You can shorten a formula .....

By adding " Like terms" together

or by subtracting " Like terms" from each other

But what are like terms?

They are the terms that have the same variables.

By the way, 'just numbers', so without any variables, are also like terms:

8 + 9 = 17  Here 8 and 9 are like terms that you can add together.

Examples

h = 4r + 2r  there are 2 terms both with variable r

so adding them gives h = 6r

b = 2a + 7a -10 here there are 3 terms but only 2a and 7a are like terms

so we get      b = 9a -10

p = 4 + 6 + 2s

p = 10 + 2s ( we cannot add 10 to 2s)

A few tasks for you ...

Shorten:
k = -4 + 6k -6

1. k = 10 + 6k
2. k = 6k - 10
3. k = -10 + 6k
4. k = 16k

Solution:

k = -4 + 6k -6         The like terms are the terms we like.

                                    The like terms here are -4 and -6.

k = -10 + 6k    or  also:    k = 6k - 10           

 Attention: in 'Ch8 Negative numbers' you                                                                             learned that -4 -6 = -10

                                     however:      -4 x -6 = 24 (so: positive!)

t = -5k - 5 + 3k + 7
Shorten again!

1. t = 2k + 2
2. t = -2k + 2
3. t = -2k - 2
4. t = -4k

Solution:

t = -5k - 5 + 3k + 7              Taking the like terms together gives:

t = -2k + 2                              

  Finally: -2k and 2 are not like terms,

                                                    so you cannot add them together.

Open your Notebook and get a pen, for the following task!

Answer this question 

in your Notebook!

A possible solution:

Make  1b in your Notebook:

Answer in the next slide.

Also give your answer in the next slide.

SHORTEN:
P = 20 + b+ b + 20 + b + b + 20 + b + b + 20 + b + b

Solution:

High time ...

for a Joke.

Think about question 5b!

Choose in next slide.

1. 1st
2. 2nd

We do an exercise together now, which saves you some homework.

It isn't an easy one (and that is why we do it together!).

So participate and learn.

Let's read this task together first!

1st  Open your Notebook and get a pen or pencil.

2nd Make this TASK in your Notebook. 

My final answer is...

SOLUTION a:

Make the Task above in your Notebook! A key word is: TOTAL.

Also answer this question in the next slide.

The formula for Rose and Cindy together is:

1. s = 8m + 12.50
2. s = 20.50m
3. s = 12.50m + 8
4. s = 20.50

Solution b:

FOTOVRAAG!                          

MAKE THE TASK BELOW in your NOTEBOOK.

WORK OUT, SOLVING AN EQUATION, AS YOU LEARNED IN CH9!

A little help:

A little help on your way:

Solve this EQUATION:

12.50m + 8 = 95.50

95.50 euros both have saved.
After how many months?

                                                                               the Formula:

                                                                               s = 12.50m + 8

After how many months did they save 87.50 euros?

SOLUTION c:

Homework:

H/V :        2, 3, 4, 6,  S4       So we skip 1, 5 and 7

VWO:       2, 3, 4, 6, 7, C1       So we skip 1 and 5