5.2.8 Rules for Negatives

As you first learn how to work with negative numbers and develop your skills, a number line will be very helpful—but it can sometimes be tedious. Let’s create a few rules that can help us perform addition and subtraction when negative numbers are involved. Remember that you can always use a number line if you find it useful or if you’re unsure of your answer!

Rule 1:

If you are adding two numbers that have the same sign, like four minus plus open three minus close, momentarily ignore the signs, and add the numbers together. Then, place the sign in front of the sum.

We think of four minus plus open three minus close as four plus three, which equals 7. Since both numbers were negative, we place a negative sign in front of the answer. Thus, equation left hand side four minus plus open three minus close equals right hand side seven minus. You can verify this using a number line.

Rule 2:

If you are adding two numbers that have different signs, such as eight minus plus two, momentarily ignore the signs. Then SUBTRACT the numbers and place the sign of the “larger” number (we are ignoring signs!) in front of the difference.

We ignore the signs in eight minus plus two and subtract: eight minus two, which equals 6. Since the “larger number” is 8, and it has a negative sign in front of it, the overall answer is also negative: equation left hand side eight minus plus two equals right hand side six minus.

Rule 3:

If you are subtracting a positive number, like five minus minus three, then rewrite it as addition of the negative number and then use the rules for addition.

So, equation sequence five minus minus three equals five minus plus open three minus close equals eight minus. For help visualizing this example, look at the number line below.

Rule 4:

If you are subtracting a negative number, such as six minus en dash open three minus close, then rewrite it as addition of the positive number and then use the rules for addition.

So, equation sequence six minus minus open three minus close equals six minus plus three equals three minus. Check out the number line below to see the addition.

Of course if you feel comfortable adding and subtracting negative without these rule there is no need to use them.

Activity symbol Activity: Adding and Subtracting Negative Numbers Using the Four Strategies

Try these questions again using the four strategies above. 

(a) 20 plus open five minus close

Hint symbol

Discussion

Look at rule 2.

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Answer

(a) We are adding two numbers with different signs. Ignore the signs and subtract the numbers  20 – 5 and use the sign from the larger number in the answer. So 20 plus open five minus close equals 15

(b) two minus times zero plus open five minus close

Hint symbol

Discussion

Look at rule 1.

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Answer

Solution symbol

(b) We are adding two numbers with the same sign. Ignore the signs and add the numbers, 20 + 5 and put back the sign from the numbers. So equation left hand side two minus times zero plus open five minus close equals right hand side two minus times five

(c) 20 minus open five minus close

Hint symbol

Discussion

Look at rule 4.

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Answer

(c) Re-write as addition of a positive number, 20 + 520 minus open five minus close equals 25

(d) two minus times zero minus open five minus close

Solution symbol

Answer

(d) Re-write as addition of a positive number, -20 + 5. Then follow rule 2. Ignore the signs and subtract the numbers 20 – 5 and use the sign from the larger number in the answer. equation left hand side two minus times zero minus open five minus close equals right hand side minus times 15

Videoclip symbol If you’d like a little more explanation on subtracting negative numbers, you can check out this video:

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5.2.7 Adding and Subtracting Negative Numbers

5.2.9 Calculator Exploration—Negative Numbers