Adding positive and negative numbers

​Fundamentals of Addition:

Adding Positive and Negative Numbers

​Scenario:

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You have three dollars. Someone gives you zero dollars. How many dollars do you have now?​

​Scenario:

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You have three dollars. Someone gives you zero dollars. How many dollars do you have now?​

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3 + 3 = 0

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​Additive identity property of addition:

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Any number plus zero equals the original number

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Ex: 3 + 0 = 0​

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​Scenario:

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You have three dollars. Someone gives you two dollars. How many dollars do you have now?

​Scenario:

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You have three dollars. Someone gives you two dollars. How many dollars do you have now?

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3 + 2 = 5​

​Scenario:

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You have two dollars. Someone gives you three dollars. How many dollars do you have now?

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2 + 3 = 5​

​Scenario:

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You have two dollars. Someone gives you three dollars. How many dollars do you have now?

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2 + 3 = 5​

​Scenario: ​

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You have three dollars. Someone gives you two dollars. How many dollars do you have now? ​

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3 + 2 = 5​

​Did you notice you had the same amount of money in both scenarios?

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That's called the commutative property of addition.​

​Commutative Property of Addition:

When we add two or more numbers, the sum is the same no matter what order we add the numbers in.

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Ex:

3 + 2 = 5

2 + 3 = 5​

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Notice - the sum is the same no matter what order you add the numbers in.​

​Scenario:

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You have five dollars. Someone gives you negative five dollars (meaning that you owe someone else five dollars). How much money do you have now?

​Scenario:

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You have five dollars. Someone gives you negative five dollars (meaning that you owe someone else five dollars). How much money do you have now?

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5 + (-5) = 0​

*Notice that I put (-5) in parentheses so we wouldn't get the negative sign confused with a minus sign.​

​Why do -5 and 5 cancel each other out?

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Because -5 and 5 are opposites.

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A fancy word for opposites in addition is "additive inverses."

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​Additive inverses:​

The opposite (or additive inverse) of any positive number is the negative version of that number.

​ Ex: The additive inverse of 5 is -5.​

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The opposite (or additive inverse) of any negative number is the positive version of that number.​

​ Ex: The additive inverse of -5 is 5.​

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When you add two additive inverses, the sum is always zero

Ex: -5 + 5 = 0

5 + (-5) = 0​

​Now, let's practice adding two positive numbers...

Multiple Choice

4 + 1 =

• 1

• 5

• 4

• -1

Multiple Choice

6 + 4 =

• -6

• -10

• 6

• 10

Multiple Choice

Based on what you noticed in the last two questions, fill in the blanks for this statement:

The sum of two positive numbers is always __________.

• positive

• negative

Congrats! We figured out that the sum of two positive numbers is always positive.

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Now, let's see what happens when we add two negative numbers.

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Imagine you owe one person 3 dollars. You owe another person 2 dollars. How many dollars do you have?

Now, let's see what happens when we add two negative numbers.

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Imagine you owe one person 3 dollars. You owe another person 2 dollars. How many dollars do you have?

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-3 + (-2) = -5​

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Multiple Choice

-6 + (-1) =

• -5

• -7

• 7

• 5

Multiple Choice

-2 + (-4) =

• 2

• -6

• -2

• 6

Multiple Choice

Based on what you noticed in the last two problems, the sum of two negative numbers is always...

• positive

• negative

Congrats! We figured out that the sum of two negative numbers is always negative.

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​Adding two numbers with the same sign:

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Add the absolute values and give the answer the same sign.

(In other words, act like both numbers are positive, add them, and then give the answer the same sign of both of the numbers.)

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Ex:

​2 + 4 = 6

-2 + (-4) = -6

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​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-2) = 2

​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-2) = 2

​Scenario: You owe someone three dollars. Someone else gives you six dollars. How many dollars do you have now?

​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-2) = 2

​Scenario: You owe someone three dollars. Someone else gives you six dollars. How many dollars do you have now?

​-3 + 6 = 3

​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-2) = 2

​Scenario: You owe someone three dollars. Someone else gives you six dollars. How many dollars do you have now?

​-3 + 6 = 3

​What do you notice about these two scenarios?

​Scenario: You have four dollars. You owe someone two dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-2) = 2

​Scenario: You owe someone three dollars. Someone else gives you six dollars. How many dollars do you have now?

​-3 + 6 = 3

​What do you notice about these two scenarios?

​When adding two numbers with different signs, if the number with the greater absolute value is positive, the answer is positive.

​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​4 + (-7) = -3

​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​

​

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​4 + (-7) = -3

​Scenario: You owe someone three dollars. Someone else gives you one dollar. How many dollars do you have now?

​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​

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​4 + (-7) = -3

​Scenario: You owe someone three dollars. Someone else gives you one dollar. How many dollars do you have now?

​-3 + 1 = -2

​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​

​

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​4 + (-7) = -3

​Scenario: You owe someone three dollars. Someone else gives you one dollar. How many dollars do you have now?

​-3 + 1 = -2

​What do you notice about these two scenarios?

​Scenario: You have four dollars. You owe someone seven dollars. How many dollars do you have now?

​Adding numbers with different signs:

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​

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​4 + (-7) = -3

​Scenario: You owe someone three dollars. Someone else gives you one dollar. How many dollars do you have now?

​-3 + 1 = -2

​What do you notice about these two scenarios?

​When adding two numbers with different signs, if the number with the greater absolute value is negative, the answer is negative.

​Adding two numbers with different signs:

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Subtract the smaller absolute value from the larger absolute value and give the answer the same sign as the number with the larger absolute value

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Ex:

-3 + 4 = 1

-4 + 3 = 1​

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