NUMERICAL SYSTEM BASIC OPERATIONS TYPES OF NUMBERS MEASUREMENT NEW TECHNOLOGIES APPLIED TO...

NUMERICAL SYSTEM

BASIC OPERATIONS

TYPES OF NUMBERS

MEASUREMENT

NEW TECHNOLOGIES APPLIED TO MATHEMATICS

DIDACTICS MATERIALS FOR ADULTS

CREDITS

Project financiated by

The European Comission (Minerva Programm)

CREDITS

CREA – University of Barcelona (Spain) Co-ordinator

VOCB – Flemish Support and Development Centre for Adult Basic Education (Belgium)

DIE – Deutsches Institut für Erwachsenenbildung (Germany)

ACADEMUS (Portugal)

University of West from Timisoara

(Romania)

Some pictures from this materials are propierty of Microsoft.

BACK

NUMERICAL SYSTEM

A) Brief history of the numerical system

The current concept of numbers arose from the practical need to count objects. These were counted with the help of available resources: fingers, stones, feet, twigs.

¿How many fingers are there?11

5 10

20

Click on the correct answer

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NUMERICAL SYSTEM

¿How many pyramides are there?

We get out current sexagesimal system from the Mayan civilization. This was the first civilization to count in units of sixty. The way we measure time today is based on the sexagesimal system.

224

6

3


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NUMERICAL SYSTEM

¿How many coins are there?


16

3

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NUMERICAL SYSTEM

b) Explanation of basic numbers

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NUMERICAL SYSTEM

Read and click the correct answer:Read and click the correct answer:

0zero

two1

zero

one2

four

two

3two

three4

four

nine5

five

one6

zero

six

7zero

seven8

eight

five9

four

nine

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NUMERICAL SYSTEM

¿How many cars are there?

11

2233

66Click on the correct answer

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NUMERICAL SYSTEM

¿How many keys are there?

1122

33

66


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NUMERICAL SYSTEM

1122

33

66

¿How many houses are there?


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NUMERICAL SYSTEM

¿How many cigarettes are there?

1122

33

66


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NUMERICAL SYSTEM

C) Combinations of numbers: Counting by units of 10

Look at this pictures

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NUMERICAL SYSTEM

10,02 € 10,03 €

0,02 €

1,02 €

Choose the correct answer

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NUMERICAL SYSTEM

Fill in the missing numbers

Click here for open this activity

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NUMERICAL SYSTEM

How many numbers are missing from the series: 4, 2, 7, 6, 9, 8?

Write all the numbers:

a) bigger than 3 and smaller than 10;

b) bigger than 8 and smaller than 10;

c) bigger than 2 and smaller than 4.

Write the following numbers is an increasing order, using the sign “”:

a) 9, 1, 3, 5, 7.

b) 2, 0, 8, 4, 6.

c) 7, 6, 8, 5, 9.

Write in your notebook the following activities:

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NUMERICAL SYSTEM

Write the following numbers in a decreasing order, using the sign “<“:

a) 1, 2, 4, 8, 9

b) 0. 3, 6, 9, 10

c) 1, 9, 8 3 , 5

Write number 7 as being a sum of:

a) two numbers;

b) three numbers;

c) seven numbers;

Cross out the futile zeroes from the written numbers:

0 035 607, 101 202, 042 032 022, 0 610 002 000, 200 505 040

The number of consonants from the word Numbers is bigger, smaller or equal with the numbers of the letters of this word?

Make the next activities in your notebook:

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NUMERICAL SYSTEM


You should obtain a 3 figures number. The first figure of this number is the number you have chosen (the number of times you wanted to eat out). The last two figures are you age. This is the only year 2002 when this game is correct so, have fun while you can!

- Read these numbers.

-Write the following natural numbers

•seventeen milion five hundred and seven thousand four hundred and four

•eight milion

•ten milion five hundred and four

•fifty four thousand seven hundred

•thirty six thousand eight hundred ninety nine.

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NUMERICAL SYSTEM

D) Roman numerals

This is a numerical system that uses capital letters to wich numerical values have been asigned

They are maily used:

•For numbers of chapters and volumes of a literacy work.

•For the acts and scenes of a play.

•For the names of popes, kings and emperors.

•For the designation of conferences, olympic-games, assembleis, contexts and so on.

•Centuries.

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NUMERICAL SYSTEM

Rules: Roman numbers use seven capital letters, to wich the following values correspond:

Letters I V X L C D MValues 1 5 10 50 100 500 1000

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NUMERICAL SYSTEM

The following are the rules for how to write them:

I before V or before X is in the 1 unit. Example: V = 5 and IV = 4 and IX = 9.

X before L or before M is in the 10 units. Example: xxx = 30 and XL = 40. C = 100 and XC = 90.

C before D or before M is in the 100 units. Examples: CCC = 300 and CD = 400, M = 1000 and XC = 90.

In summary: You write the roman numerals like you say them.

If to the right of a letter one of the same value or less is written, then the value of the first one will be increased by the value of the second one. You get the value of the numeral by adding the value of the letters it is composed of.Example: LXI = 50 + 10 + 1You can repeat the letters I, X and C as much as three consecutives times. When it comes to the following number you go to the next number of subtract the unit before it.

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NUMERICAL SYSTEM

Some roman numerals...

From which year to which year there are the following centuries:

V, XI, XIV, XVII, XVIII, XIX

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BASIC OPERATIONS

A) ADDITION.

1

3 5

46

2


Click here for open the next activity

An other activity more...

Think about and solve this problem I ate 5 pieces of toast bread for breakfast and 3 for afternoon snack. How many pieces of toast did I eat?

6

7

8


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BASIC OPERATIONS

+ 1 3 4

2

4

3 5

8

8

Complete the following adding table in your notebook

Calculate

879009 + 174532 + 216593 =

475680 + 1399457 + 887456 =

125643 + 769032 + 1147321 =

4357687 + 1594321 + 7643332 =

2332471 + 5678900 + 432345 =

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BASIC OPERATIONS

B) SUBTRACTION.

Click here for open the activity

Example: Look at the following pictures.

An other activity more...

And finally...

My son has 8 euros and spends 2 euros. How many does he have left?

7 6

8Click on the correct answer...

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BASIC OPERATIONS

Which natural number has the sum of its neighbours equal to 10?

Every figure we see below stands for a number. Find these numbers

a) + = 8 b) - = 3

7 - = + = 7

+ = - = 1


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BASIC OPERATIONS

Complete with the numbers missing from these rows:

a) a) 9, 8, ..., ..., ..., ..., 3

b) b) 2, 4, ..., ..., 10.

c) c) 1, 3, ..., 7, ...

d) d) 8, ..., 4, 2, ...

The sum of three natural numbers is 10. What are these numbers if the first is too more bigger than number two and the others are equal.

Calculate

25+14+7+2+6+3+18+5=

23+19+4+11+17+16=

17+35+22+13+15+18=

35+13+15+17=

29+14+12+25+16+11+18=

22+31+9+18+15+5

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Which are the natural numbers of two figures, if the figure’s sum: 1, 2, 3, 4, 18?

Write all the numbers between 30 and 100 that can be formed with the figures below:

a) {2, 5};

b) {2, 3, 5};

c) {0, 2, 4};

d) {0, 1, 3, 5};

BASIC OPERATIONS home

BASIC OPERATIONS

Calculate mentally by using the properties of addition and subtraction

a) 27+30+33=

b) 157+99=

c) 203-59=

d) 15+25+12+28+11+29+7+13=

e) 22+33+44+55+66-18-29-40-51-62=

Show that:

16+17+18+19+20=21+22+23+24

25+26+27+28+29+30=31+32+33+34+35

Can you make up other exercises of this kind by using consecutive numbers.

Cornel is 3 years old, and his father is nine times older, his mother is 4 yers younger than his father. How old was his mother when she gave birth to Cornel?

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BASIC OPERATIONS

C) MULTIPLICATION.

Look at the square bellow. You will find the multiplication table

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BASIC OPERATIONS

Do the following multiplication problems:

Connect each multiplication problem with the corresponding answer

1 x 2 =

3 x 1 =

5 x 1 =

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BASIC OPERATIONS

Do the following multiplication problems:

Connect the following addition problems with the corresponding multiplication problems.





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BASIC OPERATIONS

Think about and solve this problem...

During the spring, a beehive can produce 15 kilos of honey per month. How many kilos are produced in three months?

45

35

25

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BASIC OPERATIONS

D) DIVISION

Connect the following problems with the corresponding answer.

:

:

:

=

=

=

1

2

2

4

2

3

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BASIC OPERATIONS

Calculate:

3 8 : 6 30 : 6 7

40 : 5 8 54 : 6 0

45 : 9 5 54 : 9 7

28 : 7 6 4 8 : 6

The 1st of June1995 will “be” a Thursday. What day of the week will be 2nd of August 1996?

In 8 bottles there are 24 liters of paint. How many liters of paint did Mihae need, if he bought 2 bottles?

Verify if the equality is true:

(40 x 2 ) + (34 x 2 ) – 140= (194 x 2) – (375 + 1) 3

Write in your notebook:

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BASIC OPERATIONS

Find out the last two figures of this number:

A = 19453 x 86372 + 8544 x 17344

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BASIC OPERATIONS

Paul and Marcus want to go to the cinema. A cinema ticket costs €5.50.

They each have €10 to spend on the visit to the cinema and want to spend

the rest on a drink, popcorn and an ice cream. The following things are on

sale at the cinema:

1 Beer €2.00

2 Lemonade €1.50

3 Popcorn (small) €1.20

4 Popcorn (medium)€1.80

5 Popcorn (large) €2.00

6 Fruit ice-lolly €1.20

7 Nut ice-lolly €1.30

a) How much money can they spend?

b) Paul and Marcus don´t buy the same things.

What are the two different ways in wich they can spend all their money.

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BASIC OPERATIONS

To buy a house

Purchase house € 106 495

Notary fees € 17 505

Prime € 4 000

Calculate the total price by head or on a piece of paper

You can use a calculator

Note the total price in the space beelow

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TYPES OF NUMBERS

A) Introduction to the different types of numbers

Whole numbers

Whole numbers are positive (1, 2, 3, 4,....) or negative ( -1, -2, -3,...)

Do the subtraction

- =+ 1

- 1

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Rationals

Rational numbers are fractions

Examples of rational numbers (1/2, 1/3, 3/4, 11/5, 2535/3)

TYPES OF NUMBERS

A) Introduction to the different types of numbers

Irrationals

Are decimals numbers(with comas), that are infinitive(they never finish)

Examples: (1, 144442321.......or 3, 14169.......)

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TYPES OF NUMBERS

Calculate

2/8 + 3/8 + 1/8 =

2/3 + 1/6 + 2/6 =

1 – 1/7 – 4/7 =

Costel drinks the equivalent of 7/23 from what is in a 1,5 liter Coca-Cola Bottle. What quantity is left in the bottle?

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MEASUREMENT

3800

6800

2800

How many people can sit here?

Count only the red seats.

Count practical and try to estimate!

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MEASUREMENT

Which forms do I need to make this figure? Click on A or B

A

B

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MEASUREMENT

Introduction to the metric decimal system. Decimals: 0,1 ; 0,01; 0,001.

The metric decimal system is a system or measurement used all over the world. The units of measurement are based on the meter, wich is the basic unit. The following table shows the metrical decimal units .

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MEASUREMENT

Indicate wich units must be used to describe the following longitudes:

Click here for open the question



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MEASUREMENT

Do the following operations in your notebook

a)27 Km + 3.5 m f) 1 m - 9.5 mmb) 2.4 Dam + 0.48 m g) 6.32 m x 3c) 2 m + 105 cm h) 8.43 m x 6d) 143 dm - 0.47 m i) 4.03 m x 5 cme) 1 m - 3 dm - 8 cm j) 16.13 m x (2 Dam - 5 cm)

B) Complete the next table in your notebook

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MEASUREMENT

Find the numbers from the empty squares:

18 m + 21 dam + 1 km = m

20 hm + 18000 m + 3 km = km

7 km – (300 m + 70 dam) = m

1 h + 30 min + h = 150 min

8 h şi 15 min – 6 h şi 35 min = min

Find the smallest natural number of five figures, wich stands to these conditions:

a) has no repeating figures;

b) is bigger than 20000;

c) the sum of it’s figures is bigger than 19.

What is the lenght of the broken line formed by

AB = 3 cm BC = 4 cm, CD = 5 cm

DE = 6 cm. We can say AE= 3 + 4 + 5 + 6 = 18 cm

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MEASUREMENT

Calculate:

a)½ kg + 0, 255 kg + 85 g

b)0,02 kg + 22 g ¾ hg

c)1995 g + 995 dag + 9,5 kg

d)0,05 m + 2 cm + 0.9 dam

e)1,51 m + 0, 02 hm + 0, 21 dam

Hello, mister. I want to buy 3 light bulbs of 100 W and 2 light bulbs of 60 W.

- It will cost you 2550 lei.

- Oh, please excuse me, I made a mistake. I want 3 light bulbs of 60 W

and 2 light bulbs of 100 W.

- No problem, I’ll give you back 100 lei.

How much does an 100 W light bulbs costs?

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MEASUREMENT

Taxi

Two taxi agencies offer the following costs:

- 3000 lei departure plus 580 lei/km

- 100 lei departure plus 630 lei/km

Up to what distance the second cost is more profitable?

A problem with the calendar

Don’t read the lines below until you have solved the problem:

1. Pick the number of week-days in wich you wanted to eat out or to go the cinema?

2. Multiply this number by 2.

3. Add 5.

4. Multiply the result by 50.

5. Add. 3.

6. If you have already celebrated your birthday, this year, add 1749, if not, add 1748.

7. The last step. From the numbers obtained subtract the 4 figures year in which you

were born.

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MEASUREMENT

Tom has borrowed three films from the video shop. Each film costs €1.60 per day. He has one film for one day longer, one film two days longer and the third film three days longer.

a) How much extra does he have to pay?

b) How much money does he get back if he pays with a €10 note?

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Now we will practice basic addition, subtraction, multiplication, and division problems using the calculator and the Excel programme available in your computer.

To use your calculator, first go to start, then to programmes an lastly to calculator.

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Now do the following operations with the calculator

A)Addition

1333 + 2527 =

2476 + 7378 =

3762 + 5296 =

B) Subtraction

48 - 24 =

148 - 74 =

296 - 8 =

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C) Multiplication

12 x 12 =

7 x 3 =

4 x 224 =

D) Division

122 : 2 =

14 : 3 =

48 : 4 =

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Now we are going to do basic operations using the EXCEL calculus programme. At the computer go to Start, then to Proggrammes, and lastly to Microsoft Excel. Now you will use this programme. First insert the equal sign(=) in the square A1. Afterwards, introduce the number you want, then the symbol of the basic operation you want to use (+, -, x, :) and lastly another number. You will find the answer to the operation that you have done in the top left-hand window with the equal sign. Do the following basic addition, subtraction, multiplication, division problems.

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A) Addition

1526 + 7834 =

7623 + 8214 =

7654 + 21 =

1222 - 8 =

6474 – 2228 =

406 - 12 =

C) Multiplication

23 x 73 =

24 x 20 =

14 x 120 =

D) Division

120 : 10 =

121 : 2 =

250 : 50 =

B) Subtraction

Click here for enter to EXCEL program

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Paul and Marcus want to go to the cinema. A cinema ticket costs €5.50.

They each have €10 to spend on the visit to the cinema and want to spend the

rest on a drink, popcorn and an ice cream. The following things are on sale at the

cinema:

1 Beer €2.00

2 Lemonade €1.50

3 Popcorn (small) €1.20

4 Popcorn (medium)€1.80

5 Popcorn (large) €2.00

6 Fruit ice-lolly €1.20

7 Nut ice-lolly €1.30

a) How much money can they spend?

b) Paul and Marcus don´t buy the same things. What are the two

different ways in wich they can spend all their money.

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Tom has borrowed three films from the video shop. Each film costs €1.60 per day.

He has one film for one day longer, one film two days longer and the third film

three days longer.

a) How much extra does he have to pay?

b) How much money does he get back if he pays with a €10 note?

Three people put their money together for a birthday present for a friend.

They want to buy Madonna’s new CD which costs €15.90. How much does each of them have to pay?

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Peter wants to buy a new car. He doesn´t have enough money for

a new car and looks at several used cars. He wants the used car dealer to

take his old car in part exchange. Three dealers make him different offers for three

equally. Good used cars and for what they will give him for his old car. Peter wants

to work out wich new used car he would pay the least for.

Which dealer does he choose?

Prices for used cars Offer for Peter´s car

Dealer A 4, 200 euros 1, 800 euros

Dealer B 4, 000 euros 900 euros

Dealer C 3,800 euros 600 euros

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Kate owes Mary €15. They meet to go a disco together. Kate pays €4

for Mary to get into the disco. Then she pays the bill for two beers and two

glasses of water which comes to €9. How much does she owe Mary now?

You are your friends are planning a party for twenty people. You agree to buy

the drinks and snacks beforehand and then share the costs. You write a shopping list.

6 1 1/2 litre bottles of Coke at €1.40 each

3 crates of beer at €14,50 each

1 crate of mineral water at €5.50

1 bottle of Caipirinha at €9.50

25 limes a €0.40 each

1 packet of brown sugar at €1.60

1 packet of coffee at €4.50

Snacks altogether €15.00

How much will you need to get from each gest to cover the costs

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You work for a television repair service. Your boss has asked you to get a shelf

for the eight staff toolboxes. Each toolbox is 40 cm wide. How long must the

shelf be if you want to leave 10 cm between the toolboxes.

During a walking tour you arrive at a ski chalet at 6 p.m. and see with horror

that you only have 10 cigarettes left. You will only get to the next cigarette machine

at 12 noon the next day. You want to go to bed at 11 p.m. and to get up at 7 a.m.

The friend who is with you, who is also a smoker, doesn’t have any cigarettes and

so you decide to share yours with him. How much time should you leave between

two cigarettes in theory?

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You have rented a small plot of land with a weekend cottage on it. The fence

around the plot is broken and so you decide to buy a new fence. You see from

the plans that the plot of land is 15 metres wide and 18 metres long. The back

of the house is 5 metres long and the house is at the edge of the plot so that no

fence is necessary there. The gate in the fence is 1.50 wide.

a)Draw a sketch of the plot of land.

b)How many metres of fence do you have to buy?

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You lent €1,000 to a friend on April 1st. You arrange that he will pay you half of

the money back two months later on June 1st and them €100 each month after that.

a) When will he pay the last instalment?

b) After one month your friend rings you up and asks you to change the way he

pays you back. He would like to pay back a quarter of the money he has lent every

two months. You want to have your money back as soon as possible. Do you agree

to his suggestion or not?

You lend your car to a friend and a arrange that he will give you the money for

the petrol he uses. What information do you need to work out how much

he has to pay you.

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It´s winter and outside the temperarture is –15º. You want to go on a winter

walking tour with a friend, but your sleepeng bag is only suitable for temperatures

of –7º or higher. You hear on the weather forecast that the temperature is going to

rise each day by 1ºC. How long should you wait before setting off on your walk?.

One issue of a weekly magazine with radio and television programmes in it

costs €1.30. A subscription for one year costs €60. How much money do you

save? (A year has 52 weeks)

According to the producer, a 1 ½ kilo packet of washing powder should last for

35 washes. A packet twice as heavy (3 kilos) of a different brand of washing powder

should last for 80 washes. Which packet will last longer?

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You are playing a board game with dice with a few people. You have one

more throw of the dice and need 8 points to win. How many different ways are

there of getting this number of points?

Four flatmates arrange that they will all take turns to wash up. At least how often

does each person have to wash up in a month (30 days)?

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You are standing in a queue at the ticket counter in the station. You look at the

clock and see that each customer is dealt with in three minutes. Your train leaves in

22 minutes and there are 6 people in front of you in the queue. You it will take you

two minutes to get to the platform. Will you catch your train

The bill for your mobile phone comes to €100. Half of your bill is for the

calls you make to your girlfriend who almost never rings you up. You tell her that

you would her to ring you as often as you ring her. How much money would you

save by doing this?

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At half-time in a basketball match your favourite team is losing 45 to 51.

How many points must your team get in the second half to win, assuming the

other team gets 51 points again?

You want to build a doll’s house for your daughter which is open at one side.

It will have a pointed roof, and consist of a ground floor, a first floor and an attic.

How many boards will you need to build it as simply as possible?

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These are the profits on three companies. Which company makes the most profit?

• UOCO

• DOMO

• HONDA

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DOMO realised a profit of € 419 003. Look good at digit 1 in this number:

It is:

• Thousand

• Hundred thousand

• Ten

• Ten thousand

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I want to save some money. I put 4 euro in a money box every day.

How much will I save in 5 years?

You can use a calculator

Do the sum in your head or on a piece of paper.

DIDACTICS MATERIALS FOR ADULTS home


This archive will be moved. All books will be putted in boxes. There are 514 books. Is it possible to divide up these books exactely in boxes of 4?

• YES

• NO

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The damage on this floor should be repaired. You also have to break out the half tiles. How many tiles in total do you need to repair the floor?

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Three quarters = 3/4

%

Experessess three quarters in a percentage:

%

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In this class 3/4 of the 24 students are male.

In this class 2/3 of the 24 students are male.

• In class A

• In class B

In which class are there most male students ?

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Grafic with following information

Glass:18kg

Paper, carton:33kg

Metal:6kg

Synthetic:2kg

Gft:15kg

Kga:1.5kg

Greengarbage:39kg

Drink cartons:0.3kg

Building garbage:46kg

Wheels:0.2kg

Other:5.3kg

In 1995, each flernish inhabitant selectively collectively collected 166kg garbage. How many of that is paper, carton and greengarbage

18

33

62

15

1,5

39

0,3

46

0,2

5,3

0

5

10

15

20

25

30

35

40

45

50

1

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These old roofing tiles should be brought down. There are 950 roofing tiles. I can carry 10 tiles at once. In how many times can I buing all the tiles down?

in times

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How many right angles do you see here?

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Read this thermometer

It is about 17 degrees celcius

It is about 60 degrees celcius

173 degrees celcius

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This picture shows a grassland:

Length: 505 cm

Width: 476 cm

We would like to fence off this grassland with a thread. About how many meters of thread should we need? Please round off!

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How many minutes takes the film “Rush Hour”?

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Mono Lake is a lake in Amerika, California. It’s a unique lake where thousands of peculiar birds are brooding. The lake is at a height of 1945 metres.

Scale 1/400000

1 cm = 9 km

How width is this lake at widthest point?

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By a train ticket. I pay with a bill of € 100. How many change do I get?

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I pay with a bill of € 50. How much change will I get back?

• € 32,46

• € 31,56

• € 31,46

• € 30,46

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Advertisement:

“Kitchen in woodcolor. Sink included.

Try to estimate how much this kitchen will cost.

• Between 400 and 500 euro




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Place the mouse on the “Bloemdalestraat”.

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How many cubes do you count here?

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Straight line a and straight line b...

• cut

• Are vertical

• Are perpendicular

• Are parallel

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Symbolize!

Right line a and right line b...

Which symbol is correct?

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Numerical System

Guess who I am! I am a whole number; I am comprised between 10 and 30; my figure for unities is 5; I am closer to 30 than to 10.

Basic Operations

Pedro went shopping for his mother. He bought 2,5 kg of apples, 1,2 kg of oranges, 300g of almonds and 250 of butter. What was the total weight of his shopping bag?

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In the 200 metres race organised in the neighbourhood, it took the 2nd classified 25 seconds and 19 hundredths of second. The winner was 39 hundredths of second faster. What was the time spent by the winner of the 200 metres’ race?

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DIDACTIC MATERIAL FOR ADULTS

Types of numbers

Point out the relative number that you would use to express each of the following situations:

a) win 7 marbles ………………………………………… b) fatten 3 kg………………………………………………c) lose 12 euros…………………………………………..d) go up 4 steps…………………………………………..e) go back 1,5 metres……………………………………. f) be born in the year 1984 A.D…………………………

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DIDACTIC MATERIALS FOR ADULTS

Consider the following whole

A = - 4; -1,2; -1; 0, 2/3; 2,6; 7

Of the elements in A, point out which are

a) natural numbers = b) negative whole numbers = c) positive rational relative whole numbers = d) non positive rational numbers =

e) rational numbers =

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Measurement

Introduction to the metric decimal system

x 10 100 1000 0.1 0.01 0.001

4025

0.25

30.2

0.1

2000

60.04

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Using your calculator, fill in the coloured lines in the table.

From the results, try to find a rule to multiply a number by 10, 100, 1000...and by 0.1;0.01; 0.001....

Fill in the other lines in the table, without the calculator, just by applying the rule.

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The giant wheel is, no doubt, one of the favourite attractions in popular parties.

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Imagine there are 8 chairs, equally spaced, and that the wheel´s radium is 10 metresLong.

· The passengers who is farther away and the one who is closer;

· The passerngers who is 20 metres away;

· The passangers who travel at the same distance from the centre of the wheel;

· The passangers who travel at the same distance from the chosen passenger;

· The breadth of each of the angles defined by the spokes of the wheel.

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NUMERICAL SYSTEM BASIC OPERATIONS TYPES OF NUMBERS MEASUREMENT NEW TECHNOLOGIES APPLIED TO...

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