1 / 48

# Everything about Integers - PowerPoint PPT Presentation

Everything about Integers. Interesting Integers!. We can represent integers using red and yellow counters. Red tiles will represent negative integers, and yellow tiles will represent positive integers. Positive integer. Negative integer. Definition.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

• We can represent integers using red and yellow counters.

• Red tiles will represent negative integers, and yellow tiles will represent positive integers.

Positive integer

Negative integer

• Positive number – a number greater than zero.

0

1

2

3

4

5

6

• Negative number – a number less than zero.

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

• Opposite Numbers – numbers that are the same distance from zero in the opposite direction

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

-7

opposite

Definition

• Integers – Integers are all the whole numbers, their opposites and zero.

• Two integers the same distance from the origin, but on different sides of zero

• Every positive integer has a negative integer an equal distance from the origin

• Example: The opposite of 6 is -6

• The opposite of -2 is 2

• If there are the same number of red tiles as yellow tiles, what number is represented?

zero pair

• It represents 0.

• Absolute Value – The distance a number is from zero.

• Distance is always positive therefore, absolute value is always positive.

The absolute value of

9 or of –9 is 9.

• Distance a number is from zero on a number line (always a positive number)

• Indicated by two vertical lines | |

• Every number has an absolute value

• Opposites have the same absolute values since they are the same distance from zero

• Example: |-8| = 8 and |8| = 8

• |50| = 50 and |-50| = 50

7 =

7

10 =

10

-100 =

100

 - 8 =

8

y

 y =

w

 - w =

• -9

• -5

• 5

• 9

• -1

• 1

• 7

• Purple

• Any number that is to right of another

• number on the number line.

6

Six is greater than negative one because six is at the right of negative one on the number line

>

-1

6

5

4

3

2

1

0

-1

-2

• Any number that is to the left of another

• number on the number line.

Negative two is less than one because negative two is at the left of one on the number line

1

<

-2

6

5

4

3

2

1

0

-1

-2

Place the symbol(<,>,=) to make

the sentence true:

-9____8

-3____-3

0____-1

-12____12

-5____-7

<

=

>

<

>

30

20

10

0

-10

-20

-30

-40

-50

Let’s say your parents bought a car but

had to get a loan from the bank for \$5,000.

When counting all their money they add

in -\$5.000 to show they still owe the bank.

• If you don’t see a negative or positive sign in front of a number it is positive.

9

+

• We can model integer addition with tiles.

• Represent -2 with the fewest number of tiles

• Represent +5 with the fewest number of tiles.

• What number is represented by combining the 2 groups of tiles?

• Write the number sentence that is illustrated.

-2 + +5 = +3

+3

• Use your red and yellow tiles to find each sum.

-2 + -3 = ?

= -5

+

-2 + -3 = -5

-6 + +2 = ?

+

- 4

=

-6 + +2 = -4

-3 + +4 = ?

+1

=

+

-3 + +4 = +1

Solve the Problems

-8

• -3 + -5 =

• 4 + 7 =

• (+3) + (+4) =

• -6 + -7 =

• 5 + 9 =

• -9 + -9 =

11

7

-13

14

-18

Solve These Problems

-2

• 3 + -5 =

• -4 + 7 =

• (+3) + (-4) =

• -6 + 7 =

• 5 + -9 =

• -9 + 9 =

3

-1

1

-4

0

Number line

T-Method

using the number line

- 3 + 2 =

-1

Negative three means

move 3 places to the left

Positive two means

move 2 places to the right

1

2

0

-3

-2

-1

-1

using the number line

8 - 3 =

5

Positive eight means

move 8 places to the right

Negative three means

move 3 places to the left

4

5

6

3

1

7

8

2

8

0

7

5

6

1

2

3

5

T- Method

T-Method

2 + 5 = ?

-

+

2

+

=

5

7

T-Method

-2 + (-5) = ?

-

+

2

+

=

5

7

T-Method

2 + (-5) = ?

+

-

5

2

2

+

=

3

T-Method

-2 + 5 = ?

-

+

2

2

5

+

=

3

T-Method

Subtracting Integers and

T- Method

T-Method

• We often think of subtraction as a “take away” operation.

• Which diagram could be used to compute

+3 - +5 = ?

+3

+3

• This diagram also represents +3, and we can take away +5.

• When we take 5 yellow tiles away, we have 2 red tiles left.

We can’t take away 5 yellow tiles from this diagram. There is not enough tiles to take away!!

• Use your red and yellow tiles to model each subtraction problem.

-2 - -4 = ?

Now you can take away 4 red tiles.

2 yellow tiles are left, so the answer is…

This representation of -2 doesn’t have enough tiles to take away -4.

Now if you add 2 more reds tiles and 2 more yellow tiles (adding zero) you would have a total of 4 red tiles and the tiles still represent -2.

-2 - -4 = +2

Work this problem.

+3 - -5 = ?

• Add enough red and yellow pairs so you can take away 5 red tiles.

• Take away 5 red tiles, you have 8 yellow tiles left.

+3 - -5 = +8

Work this problem.

-3 - +2 = ?

• Add two pairs of red and yellow tiles so you can take away 2 yellow tiles.

• Take away 2 yellow tiles, you have 5 red tiles left.

-3 - +2 = -5

• -3 – ( -5) =

• 4 - 7 =

• (+3) - (+4) =

• -6 – (-7) =

• 5 - 9 =

• -9 – (-9) =

2

-3

-1

1

-4

0

• 3 – (-5) =

• -4 - 7 =

• (+3) - (-4) =

• -6 - 7 =

• 5 – (-9)=

• -9 - 9 =

8

-11

7

13

14

-18

In order to subtract two integers, you would need to re-write the problem as an addition problem.

Keep in mind that subtract means add the opposite.

-

-

2

2

(-5)

-5

=

=

5

+

T-Method

SUBTRACTING INTEGERS re-write the problem as an addition problem.

• -8 – ( -2) =

• 5- 4 =

• (+7) - (+2) =

• -8 – (-7) =

• 8- 5 =

• -10 – (-2) =

6

1

5

-1

3

-8