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# 2-hour CLIL module. OPERATIONS WITH NATURAL NUMBERS

Now that we know what a natural number is, let's go with the operations.

Now, you are supposed to be able to do a multi-digit addition of natural numbers.

Do you know what is the name of the terms of an addition?

OK, they are called addends (a and b), and the result is the sum (c). a + b = c

1. Commutative: The order of the addends does not change the addition.

a + b = b + a

2 + 5 = 5 + 2

7 = 7

2. Associative: It doesn't matter the way in which the addends are grouped, because the result does not change.

(a + b) + c = a + (b + c)

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

5 + 5 = 2 + 8

10 = 10

3. Closure: The sum of two natural numbers is also a natural number.

a + b

4. Additive identity: The 0 is the identity element of the addition because every number added with it gives the same number.

a + 0 = a

3 + 0 = 3

You can click on SUPPORT 1 button, where you will find a pdf file with an addition table of the numbers from 1 to 9.

Now it's the time for the subtraction. First of all, please watch the VIDEO 2, by clicking on its button.

In this case, the terms of a subtraction are called: the minuend, a, and the subtrahend, b, and the result, c, is called the difference. a - b = c

And the properties of the subtraction are:

1. No closure: The result of subtracting two natural numbers is not always another natural number.

2 − 5

2. No commutative: The order in which you make the subtraction change it.

a - b ≠ b - a

5 − 2 ≠ 2 − 5

And now we are ready to do also a multi-digit subtraction of natural numbers.

Do you want to check it? Let's do TASK 1, with some multi-digit additions and subtractions.

We know how to do an addition and how to do a subtraction, and now we are going to learn how to multiply and divide.

First of all, it is the multiplication turn.

And now,  follow the next steps:

1. Once in the website click on “Skip intro”

2. Click on “Lesson” at the left bottom.

3. Click on the lesson called “Multiplication of whole numbers”.

4. Watch all the video, by clicking on the play button always that it is required. Sometimes the video asks the user to do some tasks.

And now, it is the division turn.

Again, you have to click on the button LINK 1 and follow the next steps:

1. Once in the website click on “Skip intro”

2. Click on “Lesson” at the left bottom.

3. Click on the lesson called “Division of whole numbers”

4. Watch all the video, by clicking on the play button always that it is required. Sometimes the video asks the user to do some tasks.

5. When you have finished watching the two videos, please click on TASK 1 and do the tasks that are proposed. When you finished give them to me in order to correct them.

To finish this lesson we have to talk about the properties of the multiplication and the division.

Talking about multiplication, we have to say that to multiply two natural numbers is the same as saying, to add one factor to itself many times as indicated by the other factor. a · b = c

The terms a and b are called factors and the result, c, is the product

And the properties of the multiplication are:

1. Closure: The result of multiplying two natural numbers is another natural number.

a · b

2. Associative: The way in which the factors are grouped does not change the result.

(a · b) · c = a · (b · c)

(2 · 3) · 5 = 2 · (3 · 5)

6 · 5 = 2 · 15

30 = 30

3. Commutative: The order of the factors does not change the product.

a · b = b · a

2 · 5 = 5 · 2

10 = 10

4. Multiplicative Identity: The 1 is the neutral element of the multiplication because any number multiplied by it gives the same number.

a · 1 = a

3 · 1 = 3

5. Distributive: The multiplication of a natural number and a sum is equal to the sum of the multiplication of the natural number for each of the addends.

a · (b + c) = a · b + a · c

2 · (3 + 5) = 2 · 3 + 2 · 5

2 · 8 = 6 + 10

16 = 16

Talking about division, the terms involved in a division are called, D, the dividend and, d, the divisor. The result, c, is the quotient. D : d = c

A division can be an exact division when the remainder is zero (D = d · c), or a no exact division when the remainder is not zero (D = d · c + r).

And the properties of the division are:

1. No closure

1. No closure: The result of dividing two natural numbers is not always another natural number.

2 : 6

2. No commutative:

a : b ≠ b : a

6:2 ≠ 2:6

3. Zero divided by a number equals zero.

0 : a = 0

0 : 5 = 0

4. Division by 0 is undefined.

Short url:   http://multidict.net/cs/4256