Subtracting Integers Using Number Lines | Worksheet - Free Printable

Problem Description:

The task involves solving subtraction problems using number lines. The key concept is to convert subtraction into addition by adding the opposite (or additive inverse) of the number being subtracted. This method simplifies the process and allows us to use the number line effectively.

Steps to Solve:

1. Understand the Concept:
- Subtraction can be thought of as adding the opposite. For example, \( a - b \) is equivalent to \( a + (-b) \).
- Use the number line to visualize this process:
- Start at the first number (the minuend).
- Move left if you are subtracting a positive number (or adding a negative number).
- Move right if you are adding a positive number (or subtracting a negative number).

2. Solve Each Problem:
Let's solve each problem step by step:

#### Problem 1: \(-1 - 7\)
- Convert to addition: \(-1 - 7 = -1 + (-7)\).
- Start at \(-1\) on the number line.
- Move 7 units to the left (since you are adding \(-7\)).
- You end up at \(-8\).
- Answer: \(-8\)

#### Problem 2: \(2 - 8\)
- Convert to addition: \(2 - 8 = 2 + (-8)\).
- Start at \(2\) on the number line.
- Move 8 units to the left (since you are adding \(-8\)).
- You end up at \(-6\).
- Answer: \(-6\)

#### Problem 3: \(6 - (-3)\)
- Convert to addition: \(6 - (-3) = 6 + 3\).
- Start at \(6\) on the number line.
- Move 3 units to the right (since you are adding \(3\)).
- You end up at \(9\).
- Answer: \(9\)

#### Problem 4: \(-5 - (-4)\)
- Convert to addition: \(-5 - (-4) = -5 + 4\).
- Start at \(-5\) on the number line.
- Move 4 units to the right (since you are adding \(4\)).
- You end up at \(-1\).
- Answer: \(-1\)

#### Problem 5: \(0 - 9\)
- Convert to addition: \(0 - 9 = 0 + (-9)\).
- Start at \(0\) on the number line.
- Move 9 units to the left (since you are adding \(-9\)).
- You end up at \(-9\).
- Answer: \(-9\)

#### Problem 6: \(-2 - (-9)\)
- Convert to addition: \(-2 - (-9) = -2 + 9\).
- Start at \(-2\) on the number line.
- Move 9 units to the right (since you are adding \(9\)).
- You end up at \(7\).
- Answer: \(7\)

Final Answers:

\[
\boxed{-8, -6, 9, -1, -9, 7}
\]

Explanation:

- Each problem was solved by converting the subtraction into addition using the opposite of the number being subtracted.
- The number line was used to visualize the movement (left for negative numbers, right for positive numbers).
- This method ensures accuracy and helps in understanding the relationship between addition and subtraction of integers.