Group Work Sheet Answer Sheet
(Subtracting Integers & Sum of Opposites)
Names:
Review:
What is the absolute value of a number? The distance a number is from zero
If a climber descends in a cave 15 feet what is the distance the climber is from the top? 15 feet
You deposit 55 dollars to open a checking account and there are no other transactions, what is the balance
of your account? $55
Explain how to add integers or rational numbers with the same signs using absolute value?
Find the absolute values of the integers add them and keep the common sign
Explain how to add integers or rational numbers with different signs using absolute value?
Find the absolute value of each integer find their differences and take the sign of the number with
the larger absolute value
1. Subtracting Integers with the Same Signs: (Positive – Positive)
Subtraction Expression: 4 - 2
How far will the answer be from 4? 2 spaces
How do you know? Because the distance between terms in an addition expression/equation is
always the absolute value of the second term away from the first term.
Re-write the subtraction equation as an addition equation using the additive inverse.
Addition Equation: 4 + (-2) = 2
Use the number line below to model your additive inverse equation.
-2
-5
-4
-3
-2
-1
0
1
2
3
4
5
2. Subtracting Integers with the Different Signs: (Negative – Positive)
Subtraction Expression: -3 - 2
How far will the answer be from 4? 2 spaces
How do you know? Because the distance between terms in an addition expression/equation is
always the absolute value of the second term away from the first term.
Re-write the subtraction equation as an addition equation using the additive inverse.
Additive Inverse (addition equation): -3 + (-2) = (-5)
Use the number line below to model your additive inverse equation.
-2
-3
-5
-4
-3
-2
-1
0
1
2
3
4
5
3. Subtracting Integers with the Same Signs: (Negative - Negative)
You borrowed money from a friend, and now you have a debt of $3. Later, your friend wiped out
$2 of your debt. What is your current financial status with your friend?
Write a subtraction expression to represent this scenario: -3 – (-2)
How far will the answer be from 4? 2 spaces
How do you know? Because the distance between terms in an addition expression/equation is
always the absolute value of the second term away from the first term.
Re-write the subtraction equation as an addition equation using the additive inverse.
Additive Inverse (addition equation): -3 + (+2) = (-1)
Use the number line below to model your additive inverse equation.
+2
-3
-5
-4
-3
-2
-1
0
1
2
3
4
5
4. Subtracting Integers with the Different Signs: (Positive – Negative)
Working as a group, create your own subtraction equation where the first number is positive and
the second number is negative.
Original Subtraction Equation: Answers will vary
Re-write the subtraction equation as an addition equation using the additive inverse.
Addition Equation: Answers will vary
Use the number line below to model your additive inverse equation. Answers will vary
-5
-4
-3
-2
-1
0
1
2
3
4
5
Real World Application Using Rational Numbers:
Morgan is making a cake she has
3
1
cup of sugar left in her container. She used
cup of the sugar to
4
2
make her famous butter cream icing. How much sugar did she have left?
Write a Subtraction Equation for this problem:
How far will the answer be from
3 1
- =s
4 2
3 1
?
4 2
How do you know? Because the distance between terms in an addition expression/equation is
always the absolute value of the second term away from the first term.
Re-write the subtraction equation as an addition equation using the additive inverse.
3
1
+ (- ) = s
2
Addition Equation: 4
3
2
1
+ (- ) =
4
4 4
The Sum of Opposite Integers:
What is the sum of a number and its opposite? _their sum is zero_
Write and model an equation to prove sum of opposite integers
Equation: Answers will vary - 3 + (-3) = 0
Use the number line below for your model Answers will vary
-3
3
-5
-4
-3
-2
-1
0
1
2
3
4
5
Summary
Reflecting back on your work above describe the strategy for modeling and solving subtraction
problems, especially those involving negative integers.
Answers may vary, but must include the following points for full credit:


Always change subtraction equations to addition equations using the additive inverse of the
second term.
When modeling on the number line, the second value should “start” at the location of the first
value, not at zero.
What will always be the sum when an integer is added to the same integer with the opposite sign?
The sum of opposite integers will always be zero.