Free Printable 7th Grade Integers Worksheets [PDFs] Brighterly - Free Printable

Problem Description:

The task involves solving a series of integer addition problems. The goal is to find the sum of each pair of integers provided in the worksheet.

Solution Approach:

To solve these problems, we need to follow the rules for adding integers:
1. Adding two positive integers: Add their absolute values, and the result is positive.
2. Adding two negative integers: Add their absolute values, and the result is negative.
3. Adding a positive and a negative integer:
- Subtract the smaller absolute value from the larger absolute value.
- The sign of the result will be the same as the integer with the larger absolute value.

Let's solve each problem step by step.

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Problem 1: \( 8 + 20 \)

- Both numbers are positive.
- Add their absolute values: \( 8 + 20 = 28 \).
- Result: \( 28 \).

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Problem 2: \( (-15) + (-3) \)

- Both numbers are negative.
- Add their absolute values: \( 15 + 3 = 18 \).
- The result is negative: \( -18 \).

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Problem 3: \( 17 + (-19) \)

- One number is positive, and the other is negative.
- Subtract the smaller absolute value from the larger: \( 19 - 17 = 2 \).
- The larger absolute value is \( 19 \), which is negative.
- Result: \( -2 \).

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Problem 4: \( (-6) + 20 \)

- One number is negative, and the other is positive.
- Subtract the smaller absolute value from the larger: \( 20 - 6 = 14 \).
- The larger absolute value is \( 20 \), which is positive.
- Result: \( 14 \).

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Problem 5: \( (-11) + 4 \)

- One number is negative, and the other is positive.
- Subtract the smaller absolute value from the larger: \( 11 - 4 = 7 \).
- The larger absolute value is \( 11 \), which is negative.
- Result: \( -7 \).

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Problem 6: \( 18 + (-17) \)

- One number is positive, and the other is negative.
- Subtract the smaller absolute value from the larger: \( 18 - 17 = 1 \).
- The larger absolute value is \( 18 \), which is positive.
- Result: \( 1 \).

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Problem 7: \( (-7) + (-10) \)

- Both numbers are negative.
- Add their absolute values: \( 7 + 10 = 17 \).
- The result is negative: \( -17 \).

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Problem 8: \( 10 + 2 \)

- Both numbers are positive.
- Add their absolute values: \( 10 + 2 = 12 \).
- Result: \( 12 \).

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Problem 9: \( 4 + (-16) \)

- One number is positive, and the other is negative.
- Subtract the smaller absolute value from the larger: \( 16 - 4 = 12 \).
- The larger absolute value is \( 16 \), which is negative.
- Result: \( -12 \).

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Problem 10: \( (-1) + (-14) \)

- Both numbers are negative.
- Add their absolute values: \( 1 + 14 = 15 \).
- The result is negative: \( -15 \).

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Problem 11: \( 15 + 9 \)

- Both numbers are positive.
- Add their absolute values: \( 15 + 9 = 24 \).
- Result: \( 24 \).

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Problem 12: \( (-8) + 16 \)

- One number is negative, and the other is positive.
- Subtract the smaller absolute value from the larger: \( 16 - 8 = 8 \).
- The larger absolute value is \( 16 \), which is positive.
- Result: \( 8 \).

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Problem 13: \( (-12) + 14 \)

- One number is negative, and the other is positive.
- Subtract the smaller absolute value from the larger: \( 14 - 12 = 2 \).
- The larger absolute value is \( 14 \), which is positive.
- Result: \( 2 \).

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Problem 14: \( 13 + (-9) \)

- One number is positive, and the other is negative.
- Subtract the smaller absolute value from the larger: \( 13 - 9 = 4 \).
- The larger absolute value is \( 13 \), which is positive.
- Result: \( 4 \).

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Problem 15: \( (-18) + (-5) \)

- Both numbers are negative.
- Add their absolute values: \( 18 + 5 = 23 \).
- The result is negative: \( -23 \).

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Problem 16: \( (-20) + 11 \)

- One number is negative, and the other is positive.
- Subtract the smaller absolute value from the larger: \( 20 - 11 = 9 \).
- The larger absolute value is \( 20 \), which is negative.
- Result: \( -9 \).

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Final Answers:

\[
\begin{aligned}
1. & \quad 8 + 20 = 28 \\
2. & \quad (-15) + (-3) = -18 \\
3. & \quad 17 + (-19) = -2 \\
4. & \quad (-6) + 20 = 14 \\
5. & \quad (-11) + 4 = -7 \\
6. & \quad 18 + (-17) = 1 \\
7. & \quad (-7) + (-10) = -17 \\
8. & \quad 10 + 2 = 12 \\
9. & \quad 4 + (-16) = -12 \\
10. & \quad (-1) + (-14) = -15 \\
11. & \quad 15 + 9 = 24 \\
12. & \quad (-8) + 16 = 8 \\
13. & \quad (-12) + 14 = 2 \\
14. & \quad 13 + (-9) = 4 \\
15. & \quad (-18) + (-5) = -23 \\
16. & \quad (-20) + 11 = -9 \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
&28, -18, -2, 14, -7, 1, -17, 12, -12, -15, 24, 8, 2, 4, -23, -9
\end{aligned}
}
\]