Addition and Subtraction of Integers

8/3/2019 Addition and Subtraction of Integers

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Created by: Mohd Said Tegoh


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ADDING WITH NEGATIVE NUMBERS

ADDING WITH NEGATIVE NUMBERS

The first thing to know is that x and its additive inverse, -x,add up to zero. So:

-1 + 1 = 0

-99 + 99 =

12+ = 0-12

0

+ = 0

Once you know this, its easy to add any two integers using

imaginary tiles.

3

1

3

1


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Forexample, suppose you want to add 5 + (-2). Let green tiles

stand forpositive ones, and let red tiles stand fornegative ones.

+

Group the two negative tiles with two positive tiles.

+

Since 2 + (-2) = 0, these tiles disappear.

We are left with 3 positive tiles.

3

So, 5 + (-2) = 3


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When one number is negative and the other number is

positive, example : -5 + 2, use tiles as below:

Group the two positive tiles with two negative tiles.

+

-3

Since 2 + (-2) = 0, these tiles disappear.

We are left with 3 negative tiles.

So, -5 + 2 = -3


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Subtract the smaller absolute value from the greater absolutevalue. Then, give youranswer the same sign as the number

with greaterabsolute value.

Without using tiles;

Forexample: -5 + 2

The absolute value of -5 is 5, and absolute value of 2 is 2.

So, subtract: 5 2 = 3

Since -5 had the greaterabsolute value, the answer is negative.

-5 + 2 = -3

Note: -5 + 2 = -(5-2) = -3


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Anotherexamples:

15 + (-17) =

-35 + 25 =

70 + (-100) =

-2

-10

-30

-370 + 90 = -280

578 + (-736) = -158


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Without using tiles;

Example: -2 + 5

The absolute value of -2 is 2, and absolute value of 5 is 5.

So, subtract: 5 2 = 3

Since 5 had the greaterabsolute value, the answer is positive.

-2+ 5 = 3

Note: -2 + 5 = +(5-2) = 3


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Anotherexamples:

16 + (-14) =

-45 + 85 =

100 + (-70) =

2

40

30

-90 + 270 = 280

978 + (-736) = 242


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When both numbers are negative, we have only negative tiles,

so the answeralso negative. Forexample:

-5 + (-2) =

+

-7-7

Anotherexamples:

-6 + (-14) =

-25 + (-45) =

-100 + (-200) =

-20

-70

-300


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SUBTRACTING WITH NEGATIVE NUMBERS

You can use imaginary tiles to help you here, too.

Example: -5 (-2)

Start with 5 red tiles.

Then,rem

ove 2

of them.

You a

re left with 3 negative tiles

-3

So, -5 (-2) = -3

Note: -5 (-2) = -5 + 2 = -3


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For other problems, you may need to add zero pairs

Example: 5 8

Start with 5 positive tiles

We need to subtract 8 positive tiles, so we add 3 zero pairs

Afterremoving the 8 positive tiles, we are left with 3 negative

tiles.

So, 5 8 = -3

Note: 5 8 = 5 + (-8) = -8 + 5 = -3

-3

Then, remove 8 positive tiles .


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Example: -2 3

Start with 2 negative tiles

We need to subtract 3 positive tiles, so we add 3 zero pairs

Afterremoving the 3 positive tiles, we are left with 5 negativetiles.

So, -2 3 = -5

Note: -2 + (-3) = -5

-5

Then, remove 3 positive tiles.


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Example: 2 (-5)

Start with 2 positive tiles

We need to subtract 5 negative tiles, so we add 5 zero pairs

Afte

rrem

oving the 5 negative tiles, we a

re left with 7 p

ositivetiles.

So, 2 (-5) = 7

Note: 2 (-5) = 2 + 5 = 7

7

Then, remove 5 negative tiles.


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Example: -2 (-5)

Start with 2 negative tiles

We need to subtract 5 negative tiles, so we add 3 zero pairs

Afterremoving the 5 negative tiles, we are left with 3 positive

tiles.

So, -2 (-5) = 3

Note: -2 (-5) = -2 + 5 = 3

3

Then, remove 5 negative tiles.


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Anotherexamples:

6 -14 =

-14 - (-23) =

-100 - (-70) =

-8

9

-30

90 (-180) = 270

-123 17 = -150


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CONCLUSION

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

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

=

2 - 5 =

-5 + (-2) = -2 + (-5) -(5 + 2) = -7= -5 - 2 =

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

5 8 = 5 + (-8) = -(8 5) = -3-2 3 = -2 + (-3) -(2 + 3) = -5=

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Addition and Subtraction of Integers