Computing with integers is an important skill for higher level algebra work. Here are the ways we have learned to compute with integers in class...

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Adding on a Number Line
Working on a number line makes adding integers visual! Suppose we want to add 5 + –9.
Step 1: Start at zero
Always start at zero when working on a number line.
Step 2: Draw an arrow to represent the first number
Since the first number is a positive 5, we start at zero and move 5 steps in the positive direction. Draw the arrow from zero to the ending point.
Step 3: From there, draw a second arrow to represent the second number
The second number is -9, so we now move 9 steps in the negative direction starting from where we left off. Draw the arrow to the new ending point.
Step 4: Look at the number line for the answer
The place on the number line where you end up is the answer. Since we ended up at –4, we know that 5 + –9 = –4.

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Adding with Integer Chips
Working with integer chips makes adding integers visual, as well as hands-on! Suppose we want to add –6 + 8.
Each red chip represents a negative 1. Each black chip represents a positive 1.
Step 1: Take out enough chips to represent the first number.
In our case, the first number is –6. We need six red chips.
Step 2: Take out enough chips to represent the second number, then combine them.
In our case, the second number is positive 8. We need 8 black chips.
Step 3: Make zero-pairs
We know that one positive and one negative combine to make zero, so we call this a zero-pair (a pair of chips that combine to make zero).
Make as many zero-pairs as you can with your chips. You know you are done when you can't make any more zero pairs - you will either run out of positive chips or negative chips.
Step 4: The chips left over make your answer
Since all of the zero-pairs combine to make zero, count up the chips that are not part of a zero-pair. If the left over chips are negative chips, your answer is negative. If the left over chips are positive, your answer is positive. This is your answer!
In our case, the answer is 2 because there are only 2 positive chips left.

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Subtracting with Integer Chips

Working with integer chips makes adding integers visual, as well as hands-on! Suppose we want to subtract 4 – –3.
Each red chip represents a negative 1. Each black chip represents a positive 1.
Step 1: Take out enough chips to represent the first number
In our case, the first number is positive 4. We need 4 black chips.
Step 2: Add in zero-pairs to the original number
Do we have enough chips to take away the second number? If not, you are going to have to put zero-pairs into the original number so that there are enough chips to take away.
In our case, since we are going to have to eventually take away 3 negative chips, we need 3 negative chips to take away! Add 3 zero-pairs.
Notice how adding zero-pairs doesn't change the value of the original number, it just puts more chips on the board.
Step 3: Take away the second number
Subtraction means to take away, so take away the second number from the chip board.
In our case, we are taking away 3 negative chips.
Step 4: The chips left over make your answer
Since we have 7 positive chips left, our answer is positive 7.


More Examples to Understand
2 – –5 = 7


–4 – 2 = –6


–3 – –7 = 4

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Subtracting on a Number Line

Working on a number line makes subtracting integers visual! Suppose we want to subtract –3 – –6.
Step 1: Start at zero
Always start at zero when working on a number line.
Step 2: Draw an arrow to represent the first number
Since the first number is a negative 3, we start at zero and move 3 steps in the negative direction. Draw the arrow from zero to the ending point.
Step 3: Draw a second arrow to represent the second number but in the OPPOSITE DIRECTION
The second number is –6, so we are going to move 6 steps. But because we are subtracting, we are going to go in the opposite direction that it tells us. Since we have a negative 6, we are going to move 6 steps in the positive directions! Draw the arrow to the new ending point.
Step 4: Look at the number line for the answer
The place on the number line where you end up is the answer. Since we ended up at 3, we know that –3 – –6 = 3.



More Examples to Understand
2 – –5 = 7


–4 – 2 = –6


–3 – –7 = 4