INTEGERS What is an Integer An integer is

INTEGERS

What is an Integer?

• An integer is a positive or negative whole number, including 0. …-3, -2, -1, 0, 1, 2, 3…

There are “ 4” Integer Operations

4 Integer Operations • Addition • Subtraction • Multiplication • Division + x ÷

Rule #1 for Adding Integers (+) • The sum of two positive integers is always positive. 5 + 1 = 6

Rule #2 for Adding Integers (+) • The sum of two negative integers is always negative. -5 + (-1) = -6

Rule #3 for Adding Integers (+) • The sum of a positive and a negative integer could be positive, negative, or zero.

Rule #3 for Adding Integers Continued • When you add a positive and negative integer, you are really subtracting. Then, you give the answer the sign of the greater absolute value. 5 + (-1) = +4 -5 + 1 = -4 -5 + (+5) = 0

Let’s Practice “Addition” 1) 2) 3) 4) 5) 5+6= -3 + (-2) = -6 + 5 = 8 + (-7) = -9 + 9 =

ü Let’s Check 1) 2) 3) 4) 5) 5+6= -3 + (-2) = -6 + 5 = 8 + (-7) = -9 + 9 = 11 -5 -1 1 0

Subtracting Integers

Rules for Subtracting Integers (-) • To subtract an integer, add its opposite. • You will need to correctly change all subtraction problems into addition problems!

How do you change a subtraction problem into an addition problem?

We ADD the OPPOSITE • Eg: • 14 - (-3)

OR… there are three steps: 1. Keep the first integer the same. (Keep) 2. Flip the subtraction sign into an addition sign. (Flip) 3. Take the opposite of the number that immediately follows the newly placed addition sign. (Change)

Think … Keep, Flip, Change Examples: Ø 5 – (-2) = 5+2 = Ø -5 – 2 = -5 + (-2) = 7 -7

Let’s Practice “Subtraction” 1) 5 – 2 = 2) -3 – 4 = 3) -1 – (-2) = 4) -5 – (-3) = 5) 7 – (-6) =

Multi-Step Questions: 1) -8 + 5 – (-2)

Multiplying & Dividing Integers

Did you know that the rules for multiplication and division are the same?

Guess what…. They are!

Rules for Multiplying or Dividing Integers • The product (or quotient) of two integers with the same signs is POSITIVE. • The product (or quotient) of two integers with different signs is NEGATIVE.

Rules Summary for Multiplication (& Division) + - x x + - = = + + + - x x + = = -

When there are more than 2 integers… • The product of an even number of negative integers is positive. • Ex: (-1)(-2)(-4) = ______ • The product of an odd number of negative integers is negative. • Ex: (-1)(-4)(-3) = ______

Let’s Practice “Multiplication” 1) 6 x (-3) = 2) 3 x -3 = 3) -4 x 5 x (-2) = 4) -6 x (-2) = 5) -7 x (-8) = 6) Will the answer be positive or negative? (-2) x (-3) x (-4) x (-5) x (-6)

ü Let’s Check 1) 6 x (-3) = 2) 3 x -3 = 3) -4 x 5 x -2 = 4) -6 x (-2) = 5) -7 x (-8) = -18 -27 +40 12 56

Let’s Practice “Division” 1) 18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) =

ü Let’s Check 1) 18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) = -9 8 -3 8 -6

The rules for division are exactly the same as those for multiplication. If we were to take the rules for multiplication and change the multiplication signs to division signs, we would have an accurate set of rules for division.

Rules for Dividing Integers (÷) • The quotient of two integers with the same signs is POSITIVE. • The quotient of two integers with different signs is NEGATIVE.

Rules Summary for Division • Positive ÷ Positive = Positive • Negative ÷ Negative = Positive • Positive ÷ Negative= Negative • Negative ÷ Positive = Negative

Let’s Practice “Division” 1) 18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) =

ü Let’s Check 1) 18 ÷ (-2) = 2) -48 ÷ (-6) = 3) -27 ÷ 9 = 4) 64 ÷ 8 = 5) 30 ÷ (-5) = -9 8 -3 8 -6

Order of Operations • • • Brackets Exponents Division Multiplication Addition Subtraction

Examples: • 1) 2 + 42

Let’s Review…

What is an integer?

ANSWER • An integer is a positive or negative whole number, including 0.

Can you give an example of an integer?

ANSWER • …-3, -2, -1, 0, 1, 2, 3…

What are the four operations?

ANSWER • The four operations are: addition, subtraction, multiplication, and division.

How do you add integers?

ANSWER • The sum of two positive integers is always positive. • The sum of two negative integers is always negative. • When you add a positive and negative integer, you are really subtracting. Then, you give the answer the sign of the greater absolute value.

How do you subtract integers?

ANSWER • To subtract an integer, add its opposite. • Same, Change

How do you multiply integers?

ANSWER • If the signs are the same, your answer is always positive. • If the signs are different, your answer is always negative.

How do you divide integers?

ANSWER • If the signs are the same, your answer is always positive. • If the signs are different, your answer is always negative. *Multiplication and Division Rules are the same!