The rules for adding integers can be confusing for some students. Focusing on the actual meanings of the words we use when we talk about integers can help students toward understanding integers and how to add them.
Before we go to the three rules for adding integers, we need to review the terms opposite of a number and absolute value of a number. Many of the students I tutor do not understand absolute value. They usually get the terms "opposite of a number" and "absolute value of a number" mixed up.
OPPOSITE OF A NUMBER:
The opposite of a number are numbers that are in opposite positions on the number line, such as −6 and +6 or −150 and +150. When we add opposite numbers we get 0. The opposite of a number is also known as the additive inverse.Example:
ABSOLUTE VALUE:
The absolute value of a number represents the distance between 0 and the number on the number line. Remember the absolute value of x is written as | x |. To find the absolute value, count the number of jumps from the number to zero.
Example:
a. |4| b. |-4|
The answer to both is positive four because the distance between 4 and 0 and 0 and -4 is 4.
IMPORTANT: The absolute value of a number is always positive because it represents a distance.
We are ready to get to the nitty gritty of adding integers with different signs.
The rules for adding integers:
1. Find the absolute value of each integer.
2. Subtract the larger absolute value minus the smaller absolute value.
3. Take the sign of the larger absolute value.
For example -8 + 2
Find the absolute value of each integer.
|-8| = 8 |2| = 2
Rule 2: Subtract the larger absolute value minus the smaller absolute value.
8 – 2 = 6
Rule 3: Find the Sign: Is it positive or negative? The sign is negative because we take the sign of the larger absolute value. In this example the larger absolute value is 8, therefore the sign is negative.
-8 + 2 = -6
Visualizing the example on a number line can be very helpful when you are beginning to learn integer operations.
Visual Method:
When using a number line, start at 0, go to the left 8 jumps. We go to the left because the number is negative. Negative numbers are to the left of 0. At -8, go to the right 2 jumps because the 2 positive and we go to the right when we add positive integers
Next example 4 + (-9)
Find the absolute value of each integer.
|4| = 4 |-9| = 9
Subtract: Larger absolute value – Smaller absolute value
9 - 4 = 5
Find the sign. Take the sign of the larger absolute value which is 9 so the sign is negative.
4 + -9 = -5
Visual Method:
When using a number line, start at 0, go to the right 8 jumps. We go to the righ because the number is positive. Positive numbers are to the right of 0. At 4, go to the left 9 jumps because the 9 is negative and we go to the left when we add negative numbers. The solution is -5.
The rules for adding integers:
1. Find the absolute value of each integer.
2. Subtract: Larger absolute value – Smaller absolute value.
3. Take the sign of the larger absolute value.
Now it’s your turn. Try out these problems. Check your answers.
1. -5 + 4 =
2. -8 + 3 =
3. 4 + (-3) =
4. 11 + (-17) =
5. 13 + (-4) =
Solutions
1. -1
2. -5
3. 1
4. -6
5. 9
The best way to get better at any math skill is to practice. It takes someone between 15 and 30 repetitions, to master a skill. I have given you a couple of examples and practice problems. Some students need a lot of practice to grasp integer operations. For more review on adding integers and all the skills that you need for Algebra 1, watch the videos in my bio or go to my website, maryiverstine.com and schedule a free consultation.
I can help you get ready for Algebra!!!
Comments