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.

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

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

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

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

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

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

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

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

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

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

#### K) \( -15 - (-15) \)
- Subtracting a negative is the same as adding its positive counterpart.
- \( -15 - (-15) = -15 + 15 = 0 \)

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

#### M) \( -12 + 16 \)
- Add -12 and 16.
- Since 16 is positive and has a larger absolute value, the result is positive.
- \( -12 + 16 = 4 \)

#### N) \( 19 + (-5) \)
- Adding a negative is the same as subtracting its positive counterpart.
- \( 19 + (-5) = 19 - 5 = 14 \)

#### O) \( -3 + 9 \)
- Add -3 and 9.
- Since 9 is positive and has a larger absolute value, the result is positive.
- \( -3 + 9 = 6 \)

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

#### Q) \( 28 - (11) \)
- Subtract 11 from 28.
- \( 28 - 11 = 17 \)

#### R) \( -8 - (16) \)
- Subtract 16 from -8.
- Since both numbers are negative, the result is more negative.
- \( -8 - 16 = -24 \)

#### S) \( -25 + (-8) \)
- Adding two negatives results in a negative sum.
- \( -25 + (-8) = -25 - 8 = -33 \)

#### T) \( -3 + (-5) \)
- Adding two negatives results in a negative sum.
- \( -3 + (-5) = -3 - 5 = -8 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{A) } 4 & \text{L) } -11 \\
\text{B) } 7 & \text{M) } 4 \\
\text{C) } 12 & \text{N) } 14 \\
\text{D) } -5 & \text{O) } 6 \\
\text{E) } 12 & \text{P) } 0 \\
\text{F) } 38 & \text{Q) } 17 \\
\text{G) } -8 & \text{R) } -24 \\
\text{H) } -2 & \text{S) } -33 \\
\text{I) } 5 & \text{T) } -8 \\
\text{J) } -10 & \\
\text{K) } 0 & \\
\end{array}
}
\]