Grade 6 integers addition worksheet with 18 problems to find the sum of three integers.

Problem Description:

The task is to solve the addition of three integers for each problem listed in the worksheet. The problems involve adding positive and negative integers, which requires understanding how to handle signs during addition.

Solution Approach:

1. Understand Integer Addition Rules:
- Adding two positive integers results in a positive sum.
- Adding two negative integers results in a negative sum (add their absolute values and keep the negative sign).
- Adding a positive and a negative integer involves subtracting their absolute values and keeping the sign of the larger absolute value.

2. Solve Each Problem Step-by-Step:
- Break down each problem into steps.
- Perform the addition carefully, paying attention to the signs.

Detailed Solutions:

#### Problem 1: \( 6 + (-12) + 2 \)
- First, add \( 6 + (-12) \):
\[
6 + (-12) = 6 - 12 = -6
\]
- Next, add \( -6 + 2 \):
\[
-6 + 2 = -4
\]
- Answer: \(-4\)

#### Problem 2: \( 11 + 14 + (-2) \)
- First, add \( 11 + 14 \):
\[
11 + 14 = 25
\]
- Next, add \( 25 + (-2) \):
\[
25 + (-2) = 25 - 2 = 23
\]
- Answer: \(23\)

#### Problem 3: \( -12 + (-5) + (-10) \)
- First, add \( -12 + (-5) \):
\[
-12 + (-5) = -12 - 5 = -17
\]
- Next, add \( -17 + (-10) \):
\[
-17 + (-10) = -17 - 10 = -27
\]
- Answer: \(-27\)

#### Problem 4: \( 5 + 13 + 6 \)
- First, add \( 5 + 13 \):
\[
5 + 13 = 18
\]
- Next, add \( 18 + 6 \):
\[
18 + 6 = 24
\]
- Answer: \(24\)

#### Problem 5: \( 1 + (-13) + 14 \)
- First, add \( 1 + (-13) \):
\[
1 + (-13) = 1 - 13 = -12
\]
- Next, add \( -12 + 14 \):
\[
-12 + 14 = 2
\]
- Answer: \(2\)

#### Problem 6: \( 1 + 14 + 17 \)
- First, add \( 1 + 14 \):
\[
1 + 14 = 15
\]
- Next, add \( 15 + 17 \):
\[
15 + 17 = 32
\]
- Answer: \(32\)

#### Problem 7: \( 6 + 20 + 15 \)
- First, add \( 6 + 20 \):
\[
6 + 20 = 26
\]
- Next, add \( 26 + 15 \):
\[
26 + 15 = 41
\]
- Answer: \(41\)

#### Problem 8: \( 0 + (-8) + (-7) \)
- First, add \( 0 + (-8) \):
\[
0 + (-8) = -8
\]
- Next, add \( -8 + (-7) \):
\[
-8 + (-7) = -8 - 7 = -15
\]
- Answer: \(-15\)

#### Problem 9: \( 3 + 10 + (-15) \)
- First, add \( 3 + 10 \):
\[
3 + 10 = 13
\]
- Next, add \( 13 + (-15) \):
\[
13 + (-15) = 13 - 15 = -2
\]
- Answer: \(-2\)

#### Problem 10: \( 3 + (-16) + (-16) \)
- First, add \( 3 + (-16) \):
\[
3 + (-16) = 3 - 16 = -13
\]
- Next, add \( -13 + (-16) \):
\[
-13 + (-16) = -13 - 16 = -29
\]
- Answer: \(-29\)

#### Problem 11: \( -18 + (-5) + 3 \)
- First, add \( -18 + (-5) \):
\[
-18 + (-5) = -18 - 5 = -23
\]
- Next, add \( -23 + 3 \):
\[
-23 + 3 = -20
\]
- Answer: \(-20\)

#### Problem 12: \( 18 + 15 + 14 \)
- First, add \( 18 + 15 \):
\[
18 + 15 = 33
\]
- Next, add \( 33 + 14 \):
\[
33 + 14 = 47
\]
- Answer: \(47\)

#### Problem 13: \( -14 + 4 + 5 \)
- First, add \( -14 + 4 \):
\[
-14 + 4 = -10
\]
- Next, add \( -10 + 5 \):
\[
-10 + 5 = -5
\]
- Answer: \(-5\)

#### Problem 14: \( -5 + 17 + (-15) \)
- First, add \( -5 + 17 \):
\[
-5 + 17 = 12
\]
- Next, add \( 12 + (-15) \):
\[
12 + (-15) = 12 - 15 = -3
\]
- Answer: \(-3\)

#### Problem 15: \( 5 + (-16) + 15 \)
- First, add \( 5 + (-16) \):
\[
5 + (-16) = 5 - 16 = -11
\]
- Next, add \( -11 + 15 \):
\[
-11 + 15 = 4
\]
- Answer: \(4\)

#### Problem 16: \( 3 + (-6) + 17 \)
- First, add \( 3 + (-6) \):
\[
3 + (-6) = 3 - 6 = -3
\]
- Next, add \( -3 + 17 \):
\[
-3 + 17 = 14
\]
- Answer: \(14\)

#### Problem 17: \( -19 + (-8) + (-15) \)
- First, add \( -19 + (-8) \):
\[
-19 + (-8) = -19 - 8 = -27
\]
- Next, add \( -27 + (-15) \):
\[
-27 + (-15) = -27 - 15 = -42
\]
- Answer: \(-42\)

#### Problem 18: \( -9 + 4 + 15 \)
- First, add \( -9 + 4 \):
\[
-9 + 4 = -5
\]
- Next, add \( -5 + 15 \):
\[
-5 + 15 = 10
\]
- Answer: \(10\)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & -4 \\
2. & 23 \\
3. & -27 \\
4. & 24 \\
5. & 2 \\
6. & 32 \\
7. & 41 \\
8. & -15 \\
9. & -2 \\
10. & -29 \\
11. & -20 \\
12. & 47 \\
13. & -5 \\
14. & -3 \\
15. & 4 \\
16. & 14 \\
17. & -42 \\
18. & 10 \\
\end{array}
}
\]