Integers (3)

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Operations with

IntegersPowerPoint

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What is an Integer?

A whole number that is eitheror

Can be visualized on a number line:

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What is a Number Line?

A line with arrows on both ends that showthe integers with slash marks

Arrows show the line goes to infinity in

both directions ( + and -)Uses a negative sign (-) with negative

numbers but no positive sign (+)

with positive numbersZero is the origin and is

negative nor positive

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What are Opposites?

Two integers the same distance from theorigin, 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

Example: The opposite of -2 is 2

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What is Absolute Value?

Distance a number is from zero on a numberline (always a positive number)

Indicated by two vertical lines | |

Every number has an absolute value

Opposites have the same absolute valuessince they are the same distance from zero

Example: |-8| = 8 and |8| = 8

Example: |50| = 50 and |-50| = 50

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What Can We Do to Integers?

Integers are numbers, so we can add,subtract, multiply, and divide them

Each operation has different rules to follow

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Adding Rules Same Signs

If the integers have the signs:the numbers & keep the same sign!

Positive + Positive = Positive Answer

Negative + Negative = Negative Answer

Examples: -3 + (-10) = ? ? = -13

6+ (8) = ? ? = 14
http://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppt

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Adding (Same Signs) - Examples

-3 + (-10)13 Add the #s

13 Keep same sign (Both #s arenegative

Answer is negative!)

6 + (8)

14 Add the #s

14 Keep same sign (Both #s arepositiveAnswer is positive!)

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Adding Rules Different Signs

If the integers have the signs:the numbers & use sign of the

number!

Bigger # is Positive = Positive Answer

Bigger # is Negative = Negative Answer

Examples: -13 + (7) = ? ? = -6

23+ (-8) = ? ? = 15

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Adding (Different Signs) - Examples-13 + (7)

6 Subtract the #s

-6 Use sign of bigger # (Bigger # isnegative - Answer isnegative!)

23 + (-8)

15 Subtract the #s

15 Use sign of bigger # (Bigger # ispositive - Answer ispositive!)

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Subtracting RulesPut ( ) around second number & its sign

Change sign to ansign

Change sign of 2nd

number to its

Follow the rules for

- signs:Add & keep the same sign- signs: Subtract & use sign of bigger #

Examples: -5 -10= ? ? = 5 9- 23 = ? ? = -14

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Subtracting - Examples-5 -10 9 - 23

-5 (-10) Insert ( ) 9 (23)

-5 + (-10) Changeto + 9 + (23)

-5 + (10) Change 2ndsign 9 + (-23)

5 Follow adding rules -14

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Multiplying Rules

Multiply the numbers like usualIf the integers have the signs:

will be

If the integers have signs:will be

Examples: -3 (-5) = ? ? = 15

-9 (-10) = ? ? = 90

-7 7 = ? ? = -49

6 -6 = ? ? = -36

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Multiplying - Examples

-5) (-4) ((-1) (-20)

# -4 5 (-1) (4 (-6 ) (-3)

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Find the products of the following.

1. -4 (-6) 9. 2 0 (-5) (-100)

2. 8 (-2) 7 10. (-2) (-1) 3 5

3. -7 4 (-3)

4. 6 3 (-9)

5. (-2 ) (-1) 0

6. 5 (-10) (-1)

7. (-2) 5 (-3) (-5)

8. (-1) (-1) (-1) 7

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Dividing Rules Divide the numbers like usual

If the integers have the signs:will be

If the integers have signs:will be

Examples: -33 (-3) = ? ? = 11

-90 (-10) = ? ? = 9

-20 2 = ? ? = -10

6 -6 = ? ? = -1

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Dividing - Examples

-30 (-3) -9 (-3)

-24 8 36 -6

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Find the quotients of the following.

1. (-40) 5 9. 12 (-2) (-3)

2. (-10) (-2) 10. 7 (-7) 1

3. 45 (-9)4. 60 (-10) 2

5. (-20) (-5) (-1)

6. 4 (-1) (-1)

7. (-144) (-12)

8. 100 (-100) (-1)

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Mixed Practice

:-9 + - 9

-18

7 -4

-28

-10 - (-19)

9

-35 -7

5

15 + -25

-10

-23 - 9

-32

T F l

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True or False?

1.All integers are negative.

2.The absolute value of everyinteger is its opposite.

3.Two integers that areopposites have the same

absolute value.

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True or False?

1.The opposite of an integer isalways negative.

2.The absolute value of apositive integer is the integer

3.The absolute value of an

integer is always greater thanthe integer.

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2.The absolute value of aninteger is always positive.

1.A positive and negativeinteger will always add tozero.

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Point are different points on anumberline. Using the following clues, order theintegers for .

D is the least of the integers

Points A and D are the same distance from 0.

Point C is closer to D than it is to B.

Point C is a positive integer

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Make up a puzzle

same as the one givento you about ordering

of integers. Show onepossible solution.

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Review

Visit the website below for additionalinformation on integers:

http://www.math.com/school/subject1/

lessons/S1U1L10GL.html Click on the signs below to review the

rules for each operation
http://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://localhost/var/www/apps/conversion/current/tmp/scratch11450/Integers.ppthttp://www.math.com/school/subject1/lessons/S1U1L10GL.htmlhttp://www.math.com/school/subject1/lessons/S1U1L10GL.html

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Integers (3)