Adding Positive and Subtracting Integers | Integer Worksheets - Free Printable

Problem Overview:

The task involves solving a series of addition and subtraction problems with integers. The key is to carefully follow the rules for adding and subtracting integers, paying close attention to the signs (+ or -).

Rules for Adding and Subtracting Integers:

1. Adding Integers:
- If both numbers have the same sign, add their absolute values and keep the common sign.
- If the numbers have different signs, subtract the smaller absolute value from the larger one, and the result takes the sign of the number with the larger absolute value.

2. Subtracting Integers:
- To subtract an integer, add its opposite. For example, \( a - b = a + (-b) \).

Solution:

We will solve each problem step by step.

---

#### A) \( 8 - 4 = \)
- Subtract 4 from 8.
- \( 8 - 4 = 4 \)

Answer: \( 4 \)

#### B) \( 5 + 2 = \)
- Add 5 and 2.
- \( 5 + 2 = 7 \)

Answer: \( 7 \)

#### C) \( 9 - (-3) = \)
- Subtracting a negative is the same as adding the positive.
- \( 9 - (-3) = 9 + 3 = 12 \)

Answer: \( 12 \)

#### D) \( 6 - 11 = \)
- Subtract 11 from 6.
- Since 11 is larger than 6, the result is negative.
- \( 6 - 11 = -5 \)

Answer: \( -5 \)

#### E) \( 7 + 5 = \)
- Add 7 and 5.
- \( 7 + 5 = 12 \)

Answer: \( 12 \)

#### F) \( 8 - (-30) = \)
- Subtracting a negative is the same as adding the positive.
- \( 8 - (-30) = 8 + 30 = 38 \)

Answer: \( 38 \)

#### G) \( -12 + 4 = \)
- Add -12 and 4.
- Since the absolute value of -12 (12) is larger than 4, the result is negative.
- \( -12 + 4 = -8 \)

Answer: \( -8 \)

#### H) \( -5 + 3 = \)
- Add -5 and 3.
- Since the absolute value of -5 (5) is larger than 3, the result is negative.
- \( -5 + 3 = -2 \)

Answer: \( -2 \)

#### I) \( 10 + (-5) = \)
- Adding a negative is the same as subtracting the positive.
- \( 10 + (-5) = 10 - 5 = 5 \)

Answer: \( 5 \)

#### J) \( -7 - 3 = \)
- Subtract 3 from -7.
- Since both numbers are negative, the result is more negative.
- \( -7 - 3 = -10 \)

Answer: \( -10 \)

#### K) \( -8 - (-16) = \)
- Subtracting a negative is the same as adding the positive.
- \( -8 - (-16) = -8 + 16 = 8 \)

Answer: \( 8 \)

#### L) \( -17 + 6 = \)
- Add -17 and 6.
- Since the absolute value of -17 (17) is larger than 6, the result is negative.
- \( -17 + 6 = -11 \)

Answer: \( -11 \)

#### M) \( 12 - 16 = \)
- Subtract 16 from 12.
- Since 16 is larger than 12, the result is negative.
- \( 12 - 16 = -4 \)

Answer: \( -4 \)

#### N) \( 9 + (-5) = \)
- Adding a negative is the same as subtracting the positive.
- \( 9 + (-5) = 9 - 5 = 4 \)

Answer: \( 4 \)

#### O) \( 13 - 9 = \)
- Subtract 9 from 13.
- \( 13 - 9 = 4 \)

Answer: \( 4 \)

#### P) \( -20 + 20 = \)
- Add -20 and 20.
- The result is zero because they are additive inverses.
- \( -20 + 20 = 0 \)

Answer: \( 0 \)

#### Q) \( 28 - (-11) = \)
- Subtracting a negative is the same as adding the positive.
- \( 28 - (-11) = 28 + 11 = 39 \)

Answer: \( 39 \)

#### R) \( -25 + (-8) = \)
- Add -25 and -8.
- Both numbers are negative, so the result is more negative.
- \( -25 + (-8) = -33 \)

Answer: \( -33 \)

#### S) \( -3 + (-5) = \)
- Add -3 and -5.
- Both numbers are negative, so the result is more negative.
- \( -3 + (-5) = -8 \)

Answer: \( -8 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
A) & 4 \\
B) & 7 \\
C) & 12 \\
D) & -5 \\
E) & 12 \\
F) & 38 \\
G) & -8 \\
H) & -2 \\
I) & 5 \\
J) & -10 \\
K) & 8 \\
L) & -11 \\
M) & -4 \\
N) & 4 \\
O) & 4 \\
P) & 0 \\
Q) & 39 \\
R) & -33 \\
S) & -8 \\
\end{array}
}
\]