Mathagogy: adding and subtracting negative numbers | mathagogy - Free Printable

Let's solve each of the 24 arithmetic problems listed, and then explain how to approach them. The problems involve adding and subtracting integers (positive and negative numbers). We'll go step by step.

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Rules for Adding and Subtracting Integers:

1. Adding two positive numbers: Add normally.
2. Adding two negative numbers: Add their absolute values, result is negative.
3. Adding a positive and a negative number: Subtract the smaller absolute value from the larger one. The sign of the result matches the number with the larger absolute value.
4. Subtracting a number: Change the sign of the number being subtracted and add.

For example:
- $ a - b = a + (-b) $

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Now, let’s solve each problem:

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1) $-4 + 3$
= $-(4 - 3) = -1$

✔ Answer: -1

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2) $-6 + 4$
= $-(6 - 4) = -2$

✔ Answer: -2

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3) $-8 + 5$
= $-(8 - 5) = -3$

✔ Answer: -3

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4) $-3 + 7$
= $7 - 3 = 4$

✔ Answer: 4

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5) $-10 + 15$
= $15 - 10 = 5$

✔ Answer: 5

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6) $-12 + 18$
= $18 - 12 = 6$

✔ Answer: 6

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7) $1 - 7$
= $-(7 - 1) = -6$

✔ Answer: -6

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8) $3 - 8$
= $-(8 - 3) = -5$

✔ Answer: -5

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9) $5 - 9$
= $-(9 - 5) = -4$

✔ Answer: -4

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10) $12 - 15$
= $-(15 - 12) = -3$

✔ Answer: -3

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11) $16 - 18$
= $-(18 - 16) = -2$

✔ Answer: -2

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12) $82 - 83$
= $-(83 - 82) = -1$

✔ Answer: -1

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13) $-4 - 3$
= $-4 + (-3) = -7$

✔ Answer: -7

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14) $-6 - 4$
= $-6 + (-4) = -10$

✔ Answer: -10

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15) $-8 - 5$
= $-8 + (-5) = -13$

✔ Answer: -13

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16) $-3 - 14$
= $-3 + (-14) = -17$

✔ Answer: -17

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17) $-10 - 10$
= $-10 + (-10) = -20$

✔ Answer: -20

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18) $-12 - 11$
= $-12 + (-11) = -23$

✔ Answer: -23

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19) $-7 + 10$
= $10 - 7 = 3$

✔ Answer: 3

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20) $-26 + 20$
= $-(26 - 20) = -6$

✔ Answer: -6

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21) $-10 + 19$
= $19 - 10 = 9$

✔ Answer: 9

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22) $-12 + 24$
= $24 - 12 = 12$

✔ Answer: 12

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23) $-33 + 18$
= $-(33 - 18) = -15$

✔ Answer: -15

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24) $-42 + 24$
= $-(42 - 24) = -18$

✔ Answer: -18

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | -1 |
| 2) | -2 |
| 3) | -3 |
| 4) | 4 |
| 5) | 5 |
| 6) | 6 |
| 7) | -6 |
| 8) | -5 |
| 9) | -4 |
| 10) | -3 |
| 11) | -2 |
| 12) | -1 |
| 13) | -7 |
| 14) | -10 |
| 15) | -13 |
| 16) | -17 |
| 17) | -20 |
| 18) | -23 |
| 19) | 3 |
| 20) | -6 |
| 21) | 9 |
| 22) | 12 |
| 23) | -15 |
| 24) | -18 |

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🔍 Explanation Summary:

- When you add a negative and a positive number, think of it as moving left or right on a number line.
- Subtraction is the same as adding the opposite.
- Always consider the signs and absolute values.
- The larger absolute value determines the sign in mixed addition.

Let me know if you'd like this turned into a chart or visualized on a number line!