INTEGER NUMBERS€¦ · INTEGER NUMBERS Integer numbers : Positive numbers, negative numbers and zero. We use the number line to represent numbers Z N 0, 1, 2, 3, -1, -2, -3,

INTEGER NUMBERS

Almudena Casares Fernández www.matematicasalmudena.com

INTEGERS IN THE REAL WORLD

VIDEO https://www.youtube.com/watch?v=NX3mNjSfERo


https://www.youtube.com/watch?v=NX3mNjSfERo

POSITIVE AND NEGATIVE NUMBERS

Positive numbers: These numbers are greater than zero.

Sometime, positive numbers have a plus sign in front of them.

Negative numbers: These numbers are lower than zero.

Negative numbers have a minus sign in front of them.

Where are they used?

- Altitudes below sea level

- Winter temperatures (below freezing point)

- …

Zero is neither positive nor negative.

3

3


INTEGER NUMBERS

Integer numbers : Positive numbers, negative

numbers and zero.

We use the number line to represent numbers

Z N

0, 1, 2, 3, ...

-1, -2, -3, ...

Venn Diagram


ABSOLUTE VALUE

The absolute value is the number without its sign.

Absolute value represents the distance from zero in the

number line.

3 3 3 3


OPPOSITE NUMBERS

The opposite number is obtained by changing its sign.

They have the same absolute value.

Op 3 3 Op 3 3


ORDERING NUMBERS

Ordering numbers: The number line also shows the

order of numbers. For negative numbers you count

backwards from zero on the number line.


ADDING AND SUBTRACTING

We can add and subtract negative numbers using the

number line to help us.

When adding, move to the right.

When subtracting, move to the left.

6 4 2

5 8 3

+1 5 4Almudena Casares Fernández www.matematicasalmudena.com

ADDING AND SUBTRACTING. RULE

a) If integers have the same sign before them,

add their absolute values and give the result

with the same sign as the integers.

b) If integers have different sign before them,

find the difference between their absolute

values and give the result with the same sign

as the integer with the greater absolute

value.


RULE OF SIGNS TOGETHER

+ + = +

+ - = -

- + = -

- - = +

5 6 5 6 11


REMOVING BRACKETS

1st) Remove all the brackets.

2nd) Joint similar numbers (with the same sing in front of them).

3rd) Do the operations with the similar numbers.

4th) End up the operation.

5 6 2 4 3 1

5 2 3 6 4 1

10 11

10 1 11

5 6 2 4 3 1


ADDING AND SUBTRACTING. BRACKETS

Brackets inside out. Removing brakets.

5 4 10

5 6

5 6

11

5 4 10

5 4 10

5 10 4

5

11

1 4


BRACKETS. RULE

+ Nothing changes - Change all the

signs

5 4 10

5 4 10

9 10

1

5 4 10

5 4 10

5 10 4

15 4

11


MULTIPLYING AND DIVIDING

Use the rule of the signs:

+ + = +

+ - = -

- + = -

- - = +

+ : + = +

+ : - = -

- : + = -

- : - = +


OPERATIONS REVIEW

PLAY AND LEARN

www.math-play.com/Integers-Jeopardy/Integers-

Jeopardy.html


http://www.math-play.com/Integers-Jeopardy/Integers-Jeopardy.html







POWERS OF INTEGER NUMBERS

Rule:

If the base is positive then the result is always

positive.

If the base is negative then we look at the index.

If the index is an even number then the result is

positive.

If the index is an odd number then the result is

negative.

n times)

· ·na aaa a a



Rule:

( )

( )

positive

posit

negativ

i

e

ve

n odd

n

n even

a

a

a



Rule:

( )

( )

positive

posit

negativ

i

e

ve

n odd

n

n even

a

a

a

3

2

3

3 3 · 3 · 3 27

4 4 · 4 16

5 5 · 5 · 5 125


POWERS. PROPERTIES

0

·

1) 1

2) ·

3) :

4)

5) · ·

6) : :

n m n m

n m n m

mn n m

nn n

nn n

a

a a a

a a a

a a

a b ab

a b a b


ROOTS OF INTEGER NUMBERS

Negative numbers don’t have square root.

9 3

Non-exis n9 te t


ORDER OF OPERATIONS

1st) Parentheses

2nd) Powers and roots

3rd) Multiplications and divisions

4th) Additions and subtractions


EXAMPLES

Example 1

Example 2

5 · 2 2 · 3 1· 7

10 6 7

10 13 3

14 : 7 2· 3 5

14 : 7 2· 8

2 16 14Almudena Casares Fernández www.matematicasalmudena.com

Documents

INTEGER NUMBERS€¦ · INTEGER NUMBERS Integer numbers : Positive numbers, negative numbers and zero. We use the number line to represent numbers Z N 0, 1, 2, 3, -1, -2, -3,