Video and Examples
| We will use hops on a number line to model subtraction of positive and negative numbers. When subtracting a positive number we move to the left on the number line. When subtracting a negative number we move to the right on the number line. Why is this? Read on... |
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Example 1: Simplify 5 – 2 To model this problem we use two hops. The first hop is 5 units to the right. Then hop 2 units to the left. Since we end up on 3, the answer is 3.
5 – 2 = 3 |
Example 5: Simplify (-3) – 2 To model this problem we begin with 3 hops to the left. Subtracting positive 2 means to hops to the left. Since we end up on -5, the answer is -5.
(-3) – 2 = -5 |
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Example 2: Simplify 5 – 8 To model this expression begin by hopping 5 units to the right. Then go 8 units to the left, landing at -3.
5 – 8 = (-3) |
Example 6: Simplify (-3) – 8 This expression is model by a hop 3 units to the left, followed by another hop to the left of 8 units.
(-3) – 8 = -11 |
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Example 3: Simplify 5 – (-2) If subtracting a positive means a move to the left on a number line, then subtracting a negative means a move towards the right. To model this problem, we hop 5 units to the right. The second hop is 2 units to the right (please see note below). Since we end up on 7, the answer is 7.
5 – (-2) = 7 |
Example 7: Simplify (-3) – (-2) Just as in Example 3 above, subtracting -2 means moving to the right. So the number line with show two hops: the first is a hop 3 spaces to the left and the second hop 2 spaces to the right. The result is -1.
(-3) – (-2) = -1 |
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Example 4: Simplify 5 – (-8) To model this problem, go 5 units to the right, and then 8 more units to the right. Since we end up at 13, the answer is 13.
5 – (-8) = 13 |
Example 8: Simplify (-3) – (-8) This expression is modeled by hopping 3 units to the left and then 8 units to the right. This lands at 5.
(-3) – (-8) = +5 |
In the example 5 – (-2) we saw that it was modeled with a 5 unit-hop to the right and then a 2 unit-hop to the right. How can we be certain that subtracting (-2) represents a hop to the right?
Let's look at this table of problems and look for a pattern.
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5 – 3 = 2 |
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As the second number goes down, the difference gets larger. The pattern verifies that 5 – (-2) is equal to 7. This means subtracting (-2) is accurately represented by a hop to the right. |
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5 – 2 = 3 |
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5 – 1 = 4 |
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5 – 0 = 5 |
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5 – (-1) = 6 |
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5 – (-2) = 7 |
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5 +– (-3) = 8 |
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Important understandings |
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Self-Check
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Question 1 Simplify: (7) – (10)
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[show answer] |
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Question 2 Simplify: (-4) – (-9)
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[show answer] |
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Question 3 Simplify: (-3) – (5)
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[show answer] |