Operations with Integers

PowerPoint

Created By:

Ms. Cuervo

What is an Integer?

• A whole number that is either greater than 0 (positive) or less than 0

(negative)

• Can be visualized on a number line:

What is a Number Line?

•A line with arrows on both ends that show the 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 numbers

•Zero is the origin and is neither negative nor positive

What are Opposites?

•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

•Example: The opposite of -2 is 2

What is Absolute Value?•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

•Example: |50| = 50 and |-50| = 50

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

Adding Rules – Same Signs

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

•Positive + Positive = Positive Answer

•Negative + Negative = Negative Answer

• Examples: -3 + (-10) = ? ? = -13

• 6 + (8) = ? ? = 14

Adding (Same Signs) - Examples #1. -3 + (-10)

Step 1: 13 Add the #s

Step 2: -13 Keep same sign (Both #s are

negative – Answer is negative!)

#2. 6 + (8)

Step 1: 14 Add the #s

Step 2: 14 Keep same sign (Both #s are positive – Answer is positive!)

Adding Rules – Different Signs

•If the integers have the DIFFERENT signs: SUBTRACT the numbers & use sign of the

BIGGER number!

•Bigger # is Positive = Positive Answer

•Bigger # is Negative = Negative Answer

• Examples: -13 + (7) = ? ? = -6

• 23 + (-8) = ? ? = 15

Adding (Different Signs) - Examples #1. -13 + (7)

Step 1: 6 Subtract the #s

Step 2: -6 Use sign of bigger # (Bigger # is negative - Answer is negative!)

#2. 23 + (-8)

Step 1: 15 Subtract the #s

Step 2: 15 Use sign of bigger # (Bigger # is positive - Answer is positive!)

Subtracting Rules•Put ( ) around second number & its sign

•Change SUBTRACTION sign to an ADDITION sign

•Change sign of 2nd number to its opposite

•Follow the rules for ADDITION:

-SAME signs: Add & keep the same sign -DIFFERENT signs: Subtract &

use sign of bigger # • Examples: -5 – -10 = ? ? = 5• 9 - 23 = ? ? = -14

Subtracting - Examples #1. -5 – -10 #2.9 - 23

Step 1: -5 – (-10) Insert ( ) 9 – (23)

Step 2: -5 + (-10) Change – to + 9 + (23)

Step 3: -5 + (10) Change 2nd sign 9 + (-23)

Step 4: 5 Follow adding rules -14 d

Multiplying Rules• Multiply the numbers like usual

•If the integers have the SAME signs: ANSWER will be POSITIVE

•If the integers have DIFFERENT signs: ANSWER will be NEGATIVE

• Examples: -3 · (-5) = ? ? = 15

• -9 · (-10) = ? ? = 90

• -7 · 7 = ? ? = -49

• 6 · -6 = ? ? = -36

Multiplying - Examples

• #1. -3 · (-5) #2. -9 · (-10)

• 15 Multiply the numbers 90

• 15 Same signs = Positive Answer 90#3. -7 · 7 #4. 6 · -6

49 Multiply the numbers 36

-49 Different signs = Negative Answer -36

Dividing Rules• Divide the numbers like usual

•If the integers have the SAME signs: ANSWER will be POSITIVE

•If the integers have DIFFERENT signs: ANSWER will be NEGATIVE

• Examples: -33 ÷ (-3) = ? ? = 11

• -90 ÷ (-10) = ? ? = 9

• -20 ÷ 2 = ? ? = -10

• 6 ÷ -6 = ? ? = -1

Dividing - Examples

• #1. -33 ÷ (-3) #2. -90 ÷ (-10)

• 11 Divide the numbers 9

• 11 Same signs = Positive Answer 9 #3. -20 ÷ 2 #4. 6

÷ -6

10 Divide the numbers 1

-10 Different signs = Negative Answer -1

Mixed PracticeSolve the following problems:

-9 + - 9

-18

7 · -4

-28

-10 - (-19)

9

-35 ÷-7

5

15 + -25

-10

-23 - 9

-32