7.U2.L5.6-Adding and Subtracting Integers

• 7th Grade

Unit 2: Lesson 5-7 

Adding and Subtracting Integers

Scuba Diving 

Imagine a scuba diver dives to a depth of 65 feet. Then she rises 15 feet back up toward the surface, where she stops to photograph some coral. What is the diver’s depth when she stops to take a photograph?

Why would the scuba diver need to know the depth?

The Rule for Adding Integers with the Same Sign

To combine integers with the same sign, add their absolute values. Then give their sum the same sign as the addends.  

       

            8 + 15 =                         -8 +-15 =

23

7

-7

-23

The Rule for Adding Integers with the Opposite Sign

       To combine integers with different signs, find their absolute values. Then subtract the lesser absolute value from the greater one. assign the sum the same sign as the number with the greater absolute value.

          

-8 + 15 =                   8 +-15 =

23

7

-7

-23

Scuba Diving 

Imagine a scuba diver dives to a depth of 65 feet. Then she rises 15 feet back up toward the surface, where she stops to photograph some coral. What is the diver’s depth when she stops to take a photograph?

The coldest temperature

The average winter temperature in Antarctica is −30°F.  The coldest temperature ever recorded was -129 degrees F. What is the difference between the 2 temperatures?

Why would we need to know the difference?

How can we subtract
2 negative numbers?

Subtraction is the inverse of addition. What does that mean? How is it different from the opposite?

The Rule for Subtracting Integers

When solving a subtraction problem with negative numbers, turn it into an addition problem by adding its opposite 

Example 1: -1-(-6)

Example 3: 6-(-1)

Example 2: -2-5

To Summarize 

• When adding negative numbers, add the absolute values of the numbers, then apply the sign in the problem
• When adding a negative and a positive number, subtract the absolute values of the numbers and apply the sign of the number with greatest absolute value 
• When subtracting negative numbers turn the problem into an addition problem by adding the opposite of the negative number