Operations with integers can be a confusing concept to many middle school students. Shortcuts such as “subtract to add” usually only add to the confusion. A solid foundation grounded in concrete visual models will help students make sense of this new concept.
So far in math, adding always results in a sum that is greater than the numbers being added. Suddenly with integers, adding can result in a sum that is less than the starting number. Opposite numbers and zero-sum pairs help students make sense of this new possibility.
How To Add Integers
Why opposites matter
Every number has its opposite. Opposite numbers are each the same distance from zero.
When opposites are added, the result is always zero. If we move 3 units to the right (positive 3) and then 3 units to the left (negative 3) we will end up at 0.
Zero Sum Pairs
One red counter and one black counter basically cancel each other out because -1+1=0. This is called a zero-sum pair. Adding 0 to any number does not change the value of that number, so these pairs of integers can be eliminated.
Using Counters
Counters allow students to visualize the expression and then remove zero-sum pairs. Starting out with this concrete strategy will eventually help students make sense of the general rules for adding integers.
The expression 4+(-2) has two zero-sum pairs.
Each combination of one red counter and one black counter is equal to zero. Since adding zero to any number does not change the value, the zero-sum pairs can be eliminated.
The counters that remain are the sum of the expression.
You may also like to read: 40 Fun Math Questions with Answers
Frequently Asked Questions On How To Add Integers:
What does the addition of integers mean?
The addition of integers refers to a mathematical operation that helps find the total sum of two or more integers. This final sum is the addition of the two integers.
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What do zero-sum pairs mean?
In simple words, zero-sum pairs in integers refer to a sum of integers when added equals zero.
What are the rules for the addition of integers?
The simple rules for the addition of integers are:
1. Start by adding the absolute values of the integers.
2. If one of the integers is negative, subtract the integers.
3. If both the integers are positive, add the integers.
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