Math worksheet answer key for adding and subtracting integers, displaying correct sums and differences.

Problem Overview:

The task involves solving a series of addition and subtraction problems with integers. The goal is to find the sum or difference for each given expression.

Key Concepts:

1. Addition of Integers:
- Adding two positive integers results in a positive integer.
- Adding two negative integers results in a negative integer.
- Adding a positive and a negative integer involves subtracting their absolute values and using the sign of the larger absolute value.

2. Subtraction of Integers:
- Subtracting a positive integer is the same as adding its negative.
- Subtracting a negative integer is the same as adding its positive counterpart.

3. Rules for Signs:
- When adding integers with the same sign, add their absolute values and keep the common sign.
- When adding integers with different signs, subtract their absolute values and use the sign of the integer with the larger absolute value.
- When subtracting integers, change the operation to addition and change the sign of the second number.

Solution Explanation:

Let's go through a few examples from the worksheet to illustrate the process:

#### Example 1: \( (-7) - (-5) \)
- Subtracting a negative is the same as adding its positive counterpart.
- So, \( (-7) - (-5) = (-7) + (+5) \).
- Now, add the integers:
- Absolute values: \( |7| = 7 \) and \( |5| = 5 \).
- Since \( 7 > 5 \), the result will be negative.
- Subtract the smaller absolute value from the larger: \( 7 - 5 = 2 \).
- Result: \( -2 \).

#### Example 2: \( (+4) + (+8) \)
- Both numbers are positive, so add their absolute values.
- \( 4 + 8 = 12 \).
- Result: \( +12 \).

#### Example 3: \( (+5) + (0) \)
- Adding zero to any number does not change the number.
- Result: \( +5 \).

#### Example 4: \( (+7) + (-9) \)
- One number is positive, and the other is negative.
- Subtract their absolute values: \( |7| = 7 \) and \( |9| = 9 \).
- Since \( 9 > 7 \), the result will be negative.
- Subtract the smaller absolute value from the larger: \( 9 - 7 = 2 \).
- Result: \( -2 \).

#### Example 5: \( (+8) + (-2) \)
- One number is positive, and the other is negative.
- Subtract their absolute values: \( |8| = 8 \) and \( |2| = 2 \).
- Since \( 8 > 2 \), the result will be positive.
- Subtract the smaller absolute value from the larger: \( 8 - 2 = 6 \).
- Result: \( +6 \).

Full Worksheet Solutions:

Here are the solutions for all the problems in the worksheet, following the same reasoning:

1. \( (-7) - (-5) = (-7) + (+5) = -2 \)
2. \( (-4) + (+8) = +4 \)
3. \( (-8) + (+6) = -2 \)
4. \( (+5) + (0) = +5 \)
5. \( (+5) - (+2) = +3 \)
6. \( (+1) + (+1) = +2 \)
7. \( (+7) + (-9) = -2 \)
8. \( (+3) + (-2) = +1 \)
9. \( (-7) + (-4) = -11 \)
10. \( (+7) + (-7) = 0 \)
11. \( (+3) + (-3) = 0 \)
12. \( (+8) + (+2) = +10 \)
13. \( (+8) + (-1) = +7 \)
14. \( (-1) + (+9) = +8 \)
15. \( (+3) - (-6) = (+3) + (+6) = +9 \)
16. \( (+17) - (+8) = +9 \)
17. \( (+1) + (+6) = +7 \)
18. \( (-1) - (-4) = (-1) + (+4) = +3 \)
19. \( (-4) + (-1) = -5 \)
20. \( (-8) + (-3) = -11 \)
21. \( (-9) + (+7) = -2 \)
22. \( (+1) - (-1) = (+1) + (+1) = +2 \)
23. \( (-16) - (-9) = (-16) + (+9) = -7 \)
24. \( (-7) + (+6) = -1 \)
25. \( (+14) - (+5) = +9 \)
26. \( (+6) - (+5) = +1 \)
27. \( (+7) + (+3) = +10 \)
28. \( (-17) - (-8) = (-17) + (+8) = -9 \)
29. \( (+14) - (+7) = +7 \)
30. \( (-8) - (-2) = (-8) + (+2) = -6 \)

Final Answer:

\[
\boxed{
\begin{array}{ccc}
(-7) - (-5) = (-2) & (-4) + (+8) = (+4) & (-8) + (+6) = (-2) \\
(+5) + (0) = (+5) & (+5) - (+2) = (+3) & (+1) + (+1) = (+2) \\
(+7) + (-9) = (-2) & (+3) + (-2) = (+1) & (-7) + (-4) = (-11) \\
(+7) + (-7) = (0) & (+3) + (-3) = (0) & (+8) + (+2) = (+10) \\
(+8) + (-1) = (+7) & (-1) + (+9) = (+8) & (+3) - (-6) = (+9) \\
(+17) - (+8) = (+9) & (+1) + (+6) = (+7) & (-1) - (-4) = (+3) \\
(-4) + (-1) = (-5) & (-8) + (-3) = (-11) & (-9) + (+7) = (-2) \\
(+1) - (-1) = (+2) & (-16) - (-9) = (-7) & (-7) + (+6) = (-1) \\
(+14) - (+5) = (+9) & (+6) - (+5) = (+1) & (+7) + (+3) = (+10) \\
(-17) - (-8) = (-9) & (+14) - (+7) = (+7) & (-8) - (-2) = (-6) \\
\end{array}
}
\]