A DDING AND SUBTRACTING INTEGERS Mrs. Landon. G OAL : ADD INTEGERS WITH THE SAME SIGN How do you add...

ADDING AND SUBTRACTING INTEGERSMrs. Landon

GOAL: ADD INTEGERS WITH THE SAME SIGN

How do you add integers with the same sign?

When in real life do you use integers?

Integer: Any whole number that is positive, negative, or zero

LESSON 1.1 ADDING AND SUBTRACTING INTEGERS

Integer: Any whole number that is positive, negative, or zero

Non-integers consist of fractions that can be written as terminating or repeating decimals. A terminating decimal comes to a complete stop. A repeating decimal continues the same digit

or block of digits forever.

Rational Number: any number that can be written as ratio in the form of a / b where a and b are both integers and b is NOT zero.

In order to be a rational number, the decimal form of the number either terminates or has a repeating pattern. (Define: terminates and repeats)

LET’S EXPLORE

With your partner go through page 7 and answer the few questions you are presented with.

Raise your hand when you are finished.

Then complete page 8!

ADDING INTEGERS WITH LIKE SIGNS

STEP 1: Find the absolute value of each number Absolute value: a distance of the number from

zero on the number line. Written as ||

Practice |8|=

|-8| =

|-2| =

|4| =

STEP 1: Find the absolute value of each number Absolute value: a distance of the number from

zero on the number line. Written as ||

STEP 2: Find the sum of the absolute values 7 + 6 = 13 -7 + (-6) = -13

STEP 3: Use the sign of the integers to write the sum. 5 + 4 = 9 -5 + (-4) = -9

COMMUTATIVE PROPERTY OF ADDITION

Does this property apply when adding two negative integers?

Definition of Commutative Property of Addition: The Commutative Property of Addition states that changing the order of addends does not change the sum, i.e. if a and b are two real numbers, then a + b = b + a.

So does -5 + (-4) = -4 + -5 ?

CRITICAL THINKING

Choose any two negative integers.

Is the sum of the integers less than or greater than the value of either of the integers?

Will this be true no matter which two negative integers?

USING A NUMBER LINE

-2 + -1 =

1 + 4 =

YOUR TURN

1. -8 + (-6) =

2. 102 + 18 =

3. -42 + (-16) =

4. -8 + (-8) =

5. 12 + 19 =

YOUR TURN

Page 9 # 7-14

1-2 GOAL: ADDING INTEGERS WITH DIFFERENT SIGNS

How do you add integers with different signs?

Example: At the school fundraiser for the band, your class raised $300, but you spent $28 on supplies to raise the money.

How can you express the actual amount you earned as the SUM of two integers with DIFFERENT signs?

ADDING ON A NUMBER LINE

Example: 4 + (-3)

Start at 4. Move 3 units to the left (in the negative

direction)

4 + (-3) = _________

Let’s Try

-4 + 2 Start at -4 Move to the right 2 spaces

-4 + 2 = _______

Page 13 practice

MODELING SUMS OF INTEGERS WITH DIFFERENT SIGNS Each yellow represents a positive integer and each red

represents a negative integer.

4 + (-1) Start with 4 positive counters

Add 1 negative counter

Form zero pairs (add a negative and a positive to get a zero)

What is left when you remove the zero pairs is the sum.

3 positive counters are left so 4 + (-1) = 3

Page 14 practice

NUMERICAL

Step 1: Find the absolute value of each addend.

Step 2: Subtract the lesser absolute value from the greater absolute value.

Step 3:Use the sign of the integer with the greater absolute value for the sum

Practice – 11 + 6

ADDING INTEGERS

Adding Integers Example

Same signs Add the absolute value of the integers. Use the common sign for the sum

3 + 5 =8

-2 + (-7) = -9

Different signs Subtract the lesser absolute value from the greater absolute value. Use the sign of the integer with the greater absolute value for the sum

-3 + 5 = 2

-10 + 1 = -9

A number and its opposite

The sum is 0. The opposite of any numbers is called its additive inverse

4 + (-4) = 0

-11 + 11 = 0

CHOOSE YOUR METHOD

1. - 37 + 37 =

2. 12 + (-4) =

3. 10 + (-15) =

4. -23 + 4 =

5. -4 + (-6) =

ANSWER

1. - 37 + 37 = 0

2. 12 + (-4) = 8

3. 10 + (-15) = -5

4. -23 + 4 = -19

5. -4 + (-6) = -10

YOUR TURN

Page 15 # 3-10

Individual practice page 16 ODD 1, 3, 5, 7, 9, 11, 13 (CHECK)

Homework: EVENS

1.3 SUBTRACTING INTEGERS

Goal: How do you subtract integers?

Consider the following: you have $10 but you want to buy something that costs $15, so you borrow $5 and have a $5 debt. You can write this as 10-15 = -5. How would you subtract a great number from a lesser number?

MODELING SUBTRACTION

You can use counters to find the difference of two integers

Model -3 – (-2)

Start with 3 negative counters to represent -3

Take two negative counters away to represent subtracting -2

What is left? 1 negative counter

So -3 – (-2) = -1

YOUR TURN

-5 – (-3) Start with 5 negative counters to represent -5

Take three negative counters away to represent subtracting -3

What is left? 2 negative counter

So -5 – (-3)= -2

SUBTRACT USING MODEL METHOD

Model 6- (-3) =

Start with 6 positive counters to represent 6

You need to take away 3 negative counters, so add 3 zero pairs.

What is left? 9 positive counters

So 6 – (-3) = 9

YOUR TURN: 4 – (-2) =

Model 4 – (-2) =

Start with 4 positive counters to represent 4

You need to take away 2 negative counters, so add 2 zero pairs.

What is left? 6 positive counters

So 4 – (-2) = 6

YOUR TURN

1. -2 – (-4) = -2 – (-4) = 2

2. -5 – (-4) = -5 – (-4) = -1

3. 6 – (-4) = 6 – (-4) = 10

4. 7 – (-2) = 7 – (-2) = 9

SUBTRACTING ON A NUMBER LINE

To model the difference of 5-3 , you start at 5 and move 3 units to the left.

NOTICE: 5 - 3 = 5 + (-3) . Subtracting 3 is the same as adding its opposite, -3

You can use the fact that subtracting a number is the same as adding its opposite to find the difference of two integers.

NUMBER LINE: -1 – 5

Rewrite subtraction as addition of the opposite -1 – 5 = -1 + (-5)

Practice 1. -4 – 6 =

-4 + (-6)

2. -6 – 2 = -6 + (-2)

3. -7 – (-3) = -7 + 3 =

4. -6 – (-2) = -6 + 2 =

TO GRAPH ON A NUMBER LINE

Example: -1 – 4 Rewrite subtraction as addition of the opposite -1

+ 4

Start at -1 and move 4 units to the left.

The difference is 3

PRACTICE

-5 – (-2) Rewrite subtraction as addition of the opposite - 5 – (-2) = -5 + 2

Start at _____ and move _____ units to the _________.

The difference is _________

YOUR TURN

Complete page 19, 20 and the top of page 21 to practice modeling integer subtraction and subtracting on a number line

SUBTRACTING INTEGERS BY ADDING THE OPPOSITES

Step 1: Write the subtraction expression Step 2: find the difference by adding the opposite.

The temperature on Monday was -5 °Celsius. By Tuesday the temperature rose to -2 °Celsius. Find the change in temperature.

Final temperature – Monday’s temperature = change in the temperature.

-2 °C – (-5 ° C) = the change

-2 + 5 = 3 ° C

Complete page 21 and the top of page 22

GET IT CHECKED

Complete page 22