Adding with negative numbers - Number and Place Value for Year 6 ... - Free Printable

Problem Description:

The task involves solving a series of addition problems that include negative numbers. The goal is to compute the sum of each pair of numbers and fill in the blanks.

Solution Approach:

To solve these problems, we need to follow the rules for adding integers, especially when dealing with negative numbers:
1. Adding two positive numbers: Add them as usual.
2. Adding two negative numbers: Add their absolute values and keep the negative sign.
3. Adding a positive and a negative number: Subtract the smaller absolute value from the larger one, and the result takes the sign of the number with the larger absolute value.

Let's solve each problem step by step.

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Problem 1: $-3 + 2$

- $-3$ is negative, and $2$ is positive.
- Subtract the smaller absolute value ($2$) from the larger absolute value ($3$): $3 - 2 = 1$.
- Since $-3$ has the larger absolute value, the result is negative: $-1$.
Answer: $-1$

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Problem 2: $-9 + 6$

- $-9$ is negative, and $6$ is positive.
- Subtract the smaller absolute value ($6$) from the larger absolute value ($9$): $9 - 6 = 3$.
- Since $-9$ has the larger absolute value, the result is negative: $-3$.
Answer: $-3$

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Problem 3: $-4 + 2$

- $-4$ is negative, and $2$ is positive.
- Subtract the smaller absolute value ($2$) from the larger absolute value ($4$): $4 - 2 = 2$.
- Since $-4$ has the larger absolute value, the result is negative: $-2$.
Answer: $-2$

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Problem 4: $-7 + 4$

- $-7$ is negative, and $4$ is positive.
- Subtract the smaller absolute value ($4$) from the larger absolute value ($7$): $7 - 4 = 3$.
- Since $-7$ has the larger absolute value, the result is negative: $-3$.
Answer: $-3$

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Problem 5: $-9 + (-3)$

- Both numbers are negative.
- Add their absolute values: $9 + 3 = 12$.
- The result is negative: $-12$.
Answer: $-12$

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Problem 6: $-6 + 4$

- $-6$ is negative, and $4$ is positive.
- Subtract the smaller absolute value ($4$) from the larger absolute value ($6$): $6 - 4 = 2$.
- Since $-6$ has the larger absolute value, the result is negative: $-2$.
Answer: $-2$

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Problem 7: $-8 + (-8)$

- Both numbers are negative.
- Add their absolute values: $8 + 8 = 16$.
- The result is negative: $-16$.
Answer: $-16$

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Problem 8: $-7 + 6$

- $-7$ is negative, and $6$ is positive.
- Subtract the smaller absolute value ($6$) from the larger absolute value ($7$): $7 - 6 = 1$.
- Since $-7$ has the larger absolute value, the result is negative: $-1$.
Answer: $-1$

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Problem 9: $-5 + (-2)$

- Both numbers are negative.
- Add their absolute values: $5 + 2 = 7$.
- The result is negative: $-7$.
Answer: $-7$

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Problem 10: $-2 + 1$

- $-2$ is negative, and $1$ is positive.
- Subtract the smaller absolute value ($1$) from the larger absolute value ($2$): $2 - 1 = 1$.
- Since $-2$ has the larger absolute value, the result is negative: $-1$.
Answer: $-1$

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Problem 11: $-9 + (-2)$

- Both numbers are negative.
- Add their absolute values: $9 + 2 = 11$.
- The result is negative: $-11$.
Answer: $-11$

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Problem 12: $-9 + 2$

- $-9$ is negative, and $2$ is positive.
- Subtract the smaller absolute value ($2$) from the larger absolute value ($9$): $9 - 2 = 7$.
- Since $-9$ has the larger absolute value, the result is negative: $-7$.
Answer: $-7$

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Problem 13: $-6 + (-4)$

- Both numbers are negative.
- Add their absolute values: $6 + 4 = 10$.
- The result is negative: $-10$.
Answer: $-10$

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Problem 14: $-8 + 5$

- $-8$ is negative, and $5$ is positive.
- Subtract the smaller absolute value ($5$) from the larger absolute value ($8$): $8 - 5 = 3$.
- Since $-8$ has the larger absolute value, the result is negative: $-3$.
Answer: $-3$

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Problem 15: $-3 + 5$

- $-3$ is negative, and $5$ is positive.
- Subtract the smaller absolute value ($3$) from the larger absolute value ($5$): $5 - 3 = 2$.
- Since $5$ has the larger absolute value, the result is positive: $2$.
Answer: $2$

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Problem 16: $-4 + (-4)$

- Both numbers are negative.
- Add their absolute values: $4 + 4 = 8$.
- The result is negative: $-8$.
Answer: $-8$

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Final Answers:

1. $-1$
2. $-3$
3. $-2$
4. $-3$
5. $-12$
6. $-2$
7. $-16$
8. $-1$
9. $-7$
10. $-1$
11. $-11$
12. $-7$
13. $-10$
14. $-3$
15. $2$
16. $-8$

Boxed Final Answer:

\[
\boxed{-1, -3, -2, -3, -12, -2, -16, -1, -7, -1, -11, -7, -10, -3, 2, -8}
\]