Add and Subtract Integers Learning Objective: We will add and subtract positive and negative...

Add and Subtract Integers

Learning Objective: We will add and subtract positive and negative integers.

Math NS 1.3

What do we already know?

• Positive integers are on the right side of zero. 4

• Negative integers are on the left side of zero. -4

• This means that they are opposites. -3 + 3 = 0

PositiveNegative

5 + -2 =3

5

-2

You know how to plot an expression on the number line and find the sum.

Step 1: Plot the first integer on the number line.Step 2: Plot the second integer on the number line beginning where the last number left off.

You know how to plot an expression on the number line and find the difference.

5 + -2=

5

-2

3

Step 1: Plot the first integer on the number line.Step 2: Plot the second integer on the number line beginning where the last number left off.

You know how to plot an expression on the number line and find each sum.

-3 + -1 =- 4

-1 -3

Step 1: Plot the first integer on the number line.Step 2: Plot the second integer on the number line beginning where the last number left off.

You already learned that subtracting a negative integer

gives the same solution as adding its opposite.

Vocabulary

• Define integers: a positive or negative number.

• Define a positive integer: whole numbers to the left of zero.

• Define a negative integer: whole numbers to the right of zero.

positivenegative

Vocabulary

Define absolute value: the distance from zero.

Plot each of the integers below on a number line and then tell the absolute value of

each. -1 2 -5

QuickTime™ and a decompressor

are needed to see this picture.

(1) (2) (5)

-1

2-5

You already learned that subtracting a negative integer

gives the same solution as adding its opposite.

To help predict whether the sum of two integers will be positive or

negative, you can use these rules.

1st Variation

Is the sum of 2 and 7 positive or negative?Rule: The sum of two positive integers is positive.

2+7=

Solution: The sum of 2 and 7 is positive.

2 7

9Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

2nd Variation

Is the sum of -2 and -7 positive or negative?Rule: the sum of two negative integers is negative.

-2 + -7=

Solution: The sum of -2 and -7 is negative.

-2-7

-9Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

3rd VariationIs the sum of -2 and 7 positive or negative?

Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value.

-2 + 7=

Solution: The sum of -2 and 7 is positive.

QuickTime™ and a decompressor

are needed to see this picture.

-2

7

5

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Why is this important?

If the temperature was 10 ｰ F at lunch time and dropped to -5 ｰ F in the evening. What is the difference between these temperatures?

10 - -5= 15 degrees

Mauricio were at the corner store. Mauricio forgot his money and needs $10 to pay for his treats. IfOmar let Mauricio borrow $10, Mauricio now has$10. - $10 + $10 = 0

Guided Practice - I Do It

Rule: The sum of two positive integers is positive. 1 + 4=

1 4

5

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of 1 and 4 is positive.

Guided Practice - We Do It

Rule: The sum of two positive integers is positive. 5 + 3=

5 3

8

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of 5 and 3 is positive.

Guided Practice - You Do It

Rule: The sum of two positive integers is positive. 7 + 3=

7 3

10

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of 7 and 3 is positive.

Guided Practice - I Do It

Rule: the sum of two negative integers is negative.

-2 + -3=

-2-3

-5 Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of -2 and -3 is negative.

Guided Practice - We Do It

Rule: the sum of two negative integers is negative.

-1 + -4=

-1-4

-5Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of -1 and -4 is negative.

Guided Practice - You Do It

Rule: the sum of two negative integers is negative.

-4 + -6=

-4-6

-10Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The sum of -6 and- 4 is negative.

Guided Practice - I Do It

Rule: the sum of a positive integer and a negative integer willhave the same sign as the integer with the greater absolute value. 4 - -2= 4 + 2=

6

4 2

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The difference of 4 and -2 is positive.

Guided Practice - We Do It

Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. 4 - -6=

4 + 6=

4 6

10Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The difference of 4 and -6 is positive.

Guided Practice - You Do It

Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. 3 - -7=

3 + 7 =

3 7

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.

Solution: The difference of 3 and -7 is positive.

10

Closure• What is a whole number to the right of zero? • It is a positive integer.

• What is a whole number to the left of zero?• It is a negative integer

• What is the distance from zero?• It is the absolute value.

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Negative Positive

Closure

Decide if the sum or difference is positive or negative.

Explain how you decided.

Solve the expression.

-10 + -6 = 8 - -6=

Share with your partner one thing that you learned today.

QuickTime™ and a decompressor

are needed to see this picture.

Step 1: Change the expression to an addition by using the absolute value.Step 2: Plot the first integer on the number line.Step 3: Plot the second integer on the number line beginning where the last number left off.