Integers are all about Positives and Negatives.
Each passing day is full of Positive and Negative situations.
We can work out an overall score for our day by combining the negative scores with the positive scores.
We then cancel out each individual positive, with an individual negative to obtain an overall score.
Here is another example of cancelling out scores to obtain an overall value.
In this post we will show how to do adding Integers using the “Zero Pairs” Method.
This method involves cancelling out positive and negative pairs, and then seeing what is left over.
Adding Integers by Cancelling Zero Pairs
Let’s first look at the example of +6 + -2
We have lined up each positive with a negative, and now we can cancel out to get our answer.
-5 + 4 = ?
In this example we can see that there are five negatives, and four positives.
There are more negatives than positives, and so we should suspect that the answer should turn out to be a negative number.
We now group the zero pairs (eg. each group of -1 + 1 = 0), and determine the final result.
-4 + -3 = ?
In this example there are no positives to form zero pairs with, and so the overall result should be negative.
+3 + +2 = ?
In this example there are no negatives to form zero pairs with, and so the overall result should be positive.
25 + -15 = ?
In this sum we have too many items to draw individually.
However, it should be fairly obvious that there are more positives (25 of them), compared to negatives (only 15 negatives).
Therefore the answer should be a positive number.
The final answer is the number of extra positives that we have left over at the end.
Passy World Video of Cancelling Zeroes Method
This You Tube Video gives a narrated version of PowerPoint slides which covers the same material as in this blog post about the Cancelling Zero Pairs method.
You Tube Video About Zero Pairs Method
This You Tube Video is about Adding and Subtracting Integers using the Cancelling Zero Pairs method. It shows how to cancel out negatives with positives and then see what is left over to from the final answer.
Blues Song About Zero Pairs Method
This You Tube blues song is about Adding and Subtracting Integers and uses the Cancelling Zero Pairs method. The quality is not very high resolution, and you may need to watch it a couple of times to get all the parts. It shows how to cancel out negatives with positives and then see what is left over to from the final answer.
Adding Integers Using Shortcut Rules
We can work out the sign of the final answer by identifying the larger amount of negatives or positives in the sum.
For 8 + -5, we have 8 positives, but only 5 negatives, and so the answer will be Positive.
When we cancel all of the five negatives with five of the positives, there are three positives left over.
The positives are in excess by 3, and so the answer is +3 or just 3.
For -10 + 3 we have more negatives than positives, and so the answer will be negative.
When we cancel all of the three positives with three of the negatives, there are seven negatives left over.
The negatives are in excess by 7, and so the answer is -7.
The following video shows these shortcut rules for adding Integers.
These rules are very useful for when we get experienced at adding directed numbers.
Adding Integers Game – Spider Match
This is a fun game that helps us learn how to add Integers.
Click on a pair of numbered flies that add up to the required value in the center of the web and your spider should then eat them and give you a score. Keep clicking more pairs of numbers to get more points.
Click on the image below, or the text link which follows, to play this game.
Introduction to Integers
Arranging Integers in Order
Adding Integers Using Number Lines
Integers Order of Operations
Directed Number Integers Games
Integers in the Real World
Integers in Drag Racing
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