Adding and Subtracting Negative Numbers - Free Printable

Problem: Solving Negative Number Addition and Subtraction

The task involves solving a series of problems involving addition and subtraction with negative numbers. Let's solve each section step by step.

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Section A

#### 1) \( 2 - 7 \)
- Subtracting a positive number is the same as adding its negative.
- \( 2 - 7 = 2 + (-7) = -5 \)

#### 2) \( -4 + 8 \)
- Adding a positive number to a negative number.
- \( -4 + 8 = 4 \)

#### 3) \( -2 + 12 \)
- Adding a positive number to a negative number.
- \( -2 + 12 = 10 \)

#### 4) \( -7 - 4 \)
- Subtracting a positive number from a negative number.
- \( -7 - 4 = -7 + (-4) = -11 \)

#### 5) \( 9 - 10 \)
- Subtracting a larger positive number from a smaller one.
- \( 9 - 10 = -1 \)

#### 6) \( -7 + 4 \)
- Adding a positive number to a negative number.
- \( -7 + 4 = -3 \)

#### 7) \( -8 - 11 \)
- Subtracting a positive number from a negative number.
- \( -8 - 11 = -8 + (-11) = -19 \)

#### 8) \( -15 + 1 \)
- Adding a small positive number to a negative number.
- \( -15 + 1 = -14 \)

#### 9) \( -12 + 14 \)
- Adding a positive number to a negative number.
- \( -12 + 14 = 2 \)

#### 10) \( -10 + 23 \)
- Adding a positive number to a negative number.
- \( -10 + 23 = 13 \)

#### 11) \( -6 - 11 \)
- Subtracting a positive number from a negative number.
- \( -6 - 11 = -6 + (-11) = -17 \)

#### 12) \( -12 - 17 \)
- Subtracting a positive number from a negative number.
- \( -12 - 17 = -12 + (-17) = -29 \)

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Section B

#### 1) \( 2 + -6 \)
- Adding a negative number is the same as subtracting its positive counterpart.
- \( 2 + -6 = 2 - 6 = -4 \)

#### 2) \( -9 - +9 \)
- Subtracting a positive number from a negative number.
- \( -9 - +9 = -9 - 9 = -18 \)

#### 3) \( 4 + -3 \)
- Adding a negative number.
- \( 4 + -3 = 4 - 3 = 1 \)

#### 4) \( 3 - +8 \)
- Subtracting a positive number.
- \( 3 - +8 = 3 - 8 = -5 \)

#### 5) \( -2 + -4 \)
- Adding two negative numbers.
- \( -2 + -4 = -2 - 4 = -6 \)

#### 6) \( -5 - +5 \)
- Subtracting a positive number from a negative number.
- \( -5 - +5 = -5 - 5 = -10 \)

#### 7) \( 3 --4 \)
- Subtracting a negative number is the same as adding its positive counterpart.
- \( 3 --4 = 3 + 4 = 7 \)

#### 8) \( 8 --5 \)
- Subtracting a negative number.
- \( 8 --5 = 8 + 5 = 13 \)

#### 9) \( 10 - -6 \)
- Subtracting a negative number.
- \( 10 - -6 = 10 + 6 = 16 \)

#### 10) \( -7 - -3 \)
- Subtracting a negative number.
- \( -7 - -3 = -7 + 3 = -4 \)

#### 11) \( -1 - -3 \)
- Subtracting a negative number.
- \( -1 - -3 = -1 + 3 = 2 \)

#### 12) \( -6 - -2 \)
- Subtracting a negative number.
- \( -6 - -2 = -6 + 2 = -4 \)

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Section C

#### 1) \( -8 --12 \)
- Subtracting a negative number.
- \( -8 --12 = -8 + 12 = 4 \)

#### 2) \( -8 + -10 \)
- Adding two negative numbers.
- \( -8 + -10 = -8 - 10 = -18 \)

#### 3) \( -16 --7 \)
- Subtracting a negative number.
- \( -16 --7 = -16 + 7 = -9 \)

#### 4) \( 27 + -5 \)
- Adding a negative number.
- \( 27 + -5 = 27 - 5 = 22 \)

#### 5) \( -17 --3 \)
- Subtracting a negative number.
- \( -17 --3 = -17 + 3 = -14 \)

#### 6) \( -3 --14 \)
- Subtracting a negative number.
- \( -3 --14 = -3 + 14 = 11 \)

#### 7) \( -17 + -9 \)
- Adding two negative numbers.
- \( -17 + -9 = -17 - 9 = -26 \)

#### 8) \( -8 - +19 \)
- Subtracting a positive number from a negative number.
- \( -8 - +19 = -8 - 19 = -27 \)

#### 9) \( -54 - +24 \)
- Subtracting a positive number from a negative number.
- \( -54 - +24 = -54 - 24 = -78 \)

#### 10) \( -10 - -8 \)
- Subtracting a negative number.
- \( -10 - -8 = -10 + 8 = -2 \)

#### 11) \( 9 - +20 \)
- Subtracting a positive number.
- \( 9 - +20 = 9 - 20 = -11 \)

#### 12) \( -18 - -33 \)
- Subtracting a negative number.
- \( -18 - -33 = -18 + 33 = 15 \)

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Section D

#### 1) \( 7 - +2 - -4 \)
- Simplify step by step:
- \( 7 - +2 = 7 - 2 = 5 \)
- \( 5 - -4 = 5 + 4 = 9 \)
- Final answer: \( 9 \)

#### 2) \( -5 - -4 + -2 \)
- Simplify step by step:
- \( -5 - -4 = -5 + 4 = -1 \)
- \( -1 + -2 = -1 - 2 = -3 \)
- Final answer: \( -3 \)

#### 3) \( 4 + -6 - -7 \)
- Simplify step by step:
- \( 4 + -6 = 4 - 6 = -2 \)
- \( -2 - -7 = -2 + 7 = 5 \)
- Final answer: \( 5 \)

#### 4) \( -3 - -9 + -9 \)
- Simplify step by step:
- \( -3 - -9 = -3 + 9 = 6 \)
- \( 6 + -9 = 6 - 9 = -3 \)
- Final answer: \( -3 \)

#### 5) \( 18 + -3 - -4 \)
- Simplify step by step:
- \( 18 + -3 = 18 - 3 = 15 \)
- \( 15 - -4 = 15 + 4 = 19 \)
- Final answer: \( 19 \)

#### 6) \( 2 + (5 - -3) \)
- Simplify inside the parentheses first:
- \( 5 - -3 = 5 + 3 = 8 \)
- \( 2 + 8 = 10 \)
- Final answer: \( 10 \)

#### 7) \( -11 + (-8 - -2) \)
- Simplify inside the parentheses first:
- \( -8 - -2 = -8 + 2 = -6 \)
- \( -11 + (-6) = -11 - 6 = -17 \)
- Final answer: \( -17 \)

#### 8) \( 7 - (-2 + -6) \)
- Simplify inside the parentheses first:
- \( -2 + -6 = -2 - 6 = -8 \)
- \( 7 - (-8) = 7 + 8 = 15 \)
- Final answer: \( 15 \)

#### 9) \( (-4 + -2) + (4 - -9) \)
- Simplify each part separately:
- \( -4 + -2 = -4 - 2 = -6 \)
- \( 4 - -9 = 4 + 9 = 13 \)
- \( -6 + 13 = 7 \)
- Final answer: \( 7 \)

#### 10) \( 3 - ((-1 + -5) - 12) \)
- Simplify inside the innermost parentheses first:
- \( -1 + -5 = -1 - 5 = -6 \)
- \( -6 - 12 = -18 \)
- \( 3 - (-18) = 3 + 18 = 21 \)
- Final answer: \( 21 \)

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Final Answers

Section A:
1) \(-5\)
2) \(4\)
3) \(10\)
4) \(-11\)
5) \(-1\)
6) \(-3\)
7) \(-19\)
8) \(-14\)
9) \(2\)
10) \(13\)
11) \(-17\)
12) \(-29\)

Section B:
1) \(-4\)
2) \(-18\)
3) \(1\)
4) \(-5\)
5) \(-6\)
6) \(-10\)
7) \(7\)
8) \(13\)
9) \(16\)
10) \(-4\)
11) \(2\)
12) \(-4\)

Section C:
1) \(4\)
2) \(-18\)
3) \(-9\)
4) \(22\)
5) \(-14\)
6) \(11\)
7) \(-26\)
8) \(-27\)
9) \(-78\)
10) \(-2\)
11) \(-11\)
12) \(15\)

Section D:
1) \(9\)
2) \(-3\)
3) \(5\)
4) \(-3\)
5) \(19\)
6) \(10\)
7) \(-17\)
8) \(15\)
9) \(7\)
10) \(21\)

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Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Section A: } -5, 4, 10, -11, -1, -3, -19, -14, 2, 13, -17, -29 \\
\text{Section B: } -4, -18, 1, -5, -6, -10, 7, 13, 16, -4, 2, -4 \\
\text{Section C: } 4, -18, -9, 22, -14, 11, -26, -27, -78, -2, -11, 15 \\
\text{Section D: } 9, -3, 5, -3, 19, 10, -17, 15, 7, 21
\end{array}
}
\]