Adding and Subtracting Integers
using algebra tiles
Representation
Zero Pair
Addition: Show 3 + (-5) = - 2
The process of addition is the combining of the two quantities.
Pair up opposites:
Zero Pair
Represent the situation
=
Answer
=
Addition:
Show 5 + (-8) = - 3
The process of addition is the
combining of the two quantities.
Addition:
Show -7 + (+9) = 2
The process of addition is the
combining of the two quantities.
Addition:
Show -11 + (6) = -5
The process of addition is the
combining of the two quantities.
Subtraction: Show 5 - (-2) = 7
The process of subtraction is the removal of -2 (or two red
chips).
Remove
Represent the first value
-
Introduce zero pair
=
Answer
Subtraction: Show 9 - (-5) = 14
•The process of subtraction is the removal
of -5 (or five red chips).
Subtraction: Show 6 - (-9) = 15
Subtraction: Show 7 - (-8) = 15
Understanding the Subtraction RULE:
This manner of viewing the process of subtracting integers,
shown above is justification of "WHY" we use the "Rule" for
subtracting signed numbers.
RULE:
"To subtract signed numbers,
change the sign of the number being subtracted
and then follow the rules for addition."
Evaluate : (-4) + (+3)
Solution :
Start with four negative counters to represent -4 and three positive counters to
represent +3.
•Evaluate : (-8) + (+2)
•Evaluate : (9) - (-6) =
•Evaluate : (-12) + 8 =
Evaluate : (-4) + (+3)
Mark the zero pairs.
Answer
In the above figure, if you remove the three zero pairs, the result will be one
negative counter.
So, the answer is -1.
Evaluate : (+5) - (+2)
Solution:
Start with five positive counters to represent +5 and two negative counters to
represent -2.
Evaluate : (+5) - (+2)
Mark the zero pair.
Answer
In the above figure, if you remove two zero pairs, the result will be three positive
counters.
So, the answer is +3.
Exercise
Find the sum of +4 and -7.
Evaluate:
(-7) + (+5)
Evaluate:
(-9) + (+4)
Use counters to subtract –3 − (–2).
Use counters to subtract 1 − (–3).
Use counters to add –3 + (–1).