~ 5.5 ~

Representing Subtraction

Learning Targets

  • I can explain the relationship between addition and subtraction of rational numbers.

  • I can use a number line to subtract positive and negative numbers.

Notes

The equation 7 - 5 = ? is equivalent to ? + 5 = 7. The diagram illustrates the second equation.

Notice that the value of 7 + (-5) is 2.

We can solve the equation ? + 5 = 7 by adding -5 to both sides. This shows that 7 - 5 = 7 + (-5). Likewise, 3 - 5 = ? is equivalent to ? + 5 = 3.

Notice that the value of 3 + (-5) is -2.

We can solve the equations ? + 5 = 3 by adding -5 to both sides. This shows that 3 - 5 = 3 + (-5).

In general:

a - b = a + (-b)

If a - b = x, then x + b = a. We can add -b to both sides of this second equations to get that x = a + (-b).

Activities

5.1 Equivalent Equations

For the equations in the second and third columns, write two more equations using the same numbers that express the same relationship in a different way. If you get stuck, consider looking at the examples in the first column.

2 + 3 = 5

3 + 2 = 5

5 - 3 = 2

5 - 2 = 3

9 + (-1) = 8

-11 + x = 7

5.2 Subtraction with Number Lines

  1. Here is an unfinished number line diagram that represents a sum of 8.

    • How long should the other arrow be?

    • For an equation that goes with this diagram, Mai writes 3 + ? = 8. Tyler writes 8 - 3 = ? Do you agree with either of them?

    • What is the unknown number? How do you know?

  2. Here are two more unfinished diagrams that represent sums. For each diagram:

    • What equation would Mai write if she used the same reasoning as before?

    • What equation would Tyler write if he used the same reasoning as before?

    • How long should the other arrow be?

    • What number would complete each equation? Be prepared to explain your reasoning.

3. Draw a number line diagram for (-8) - (-3) = ? What is the unknown number? How do you know?

5.3 We Can Add Instead

Match each diagram to one of these expressions:

  1. Which expressions in the first question have the same value? What do you notice?

2. Complete each of these tables. What do you notice?

Summary

Assignment

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