Grade 9 Integer Review

Review Day 1

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 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

First Remove Double Signs!!

Eg: (-3) + (-4)

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

Adding (Same Signs) - Examples

#1. -3 + (-10)- Change the double sign + (-)

to a (-)- Same signs - add and keep

sign!= -13

#2. 6 + (8)- Same sign so add and keep

sign!= 14

Adding Rules – Different Signs• If the integers have DIFFERENT signs: SUBTRACT

the numbers & use sign of the BIGGER( further from zero) number!

•Bigger # is Positive = Positive Answer

•Bigger # is Negative = Negative Answer

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

- Subtract the numbers- Keep the sign of the number

furthest from zero (bigger number)

= -6

#2. 23 + (-8)

- Subtract the numbers- Keep the sign of the number

furthest from zero (bigger number)

= +15

Subtracting Rules• Make sure to change any double signs

•Follow the rules for ADDITION:

-SAME signs: Add & keep the same sign -

DIFFERENT signs: Subtract & use sign of bigger #

Subtracting - Examples #1. -5 – -12

- Change double signs to a +- Subtract the two numbers and

keep the sign of the number further from zero (bigger number)

= +7

#2. 9 – 23- Subtract the two numbers and

keep the sign of the number further from zero (bigger number)

= -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

Multiplying - Examples• #1. -3 · (-5)

- negative times negative = +

= +15

#2. -9 · (+10)

- Negative times a positive = (-)

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

Dividing - Examples• #1. -33 ÷ (-3)

- Negative divide negative = +

= +11

#2. -90 ÷ (+10)

- Negative divide a positive = (-)

= -9

Mixed PracticeSolve the following problems:

-9 + - 9

-18

7 × -4

-28

-10 - (-19) 9

-35 ÷ -7

5

15 + -25

-10

-23 - 9-32

Review

• Visit the website below for additional information on integers:http://www.math.com/school/subject1/ lessons/S1U1L10GL.html