📚 Topic Summary
Subtracting integers can be simplified by using the principle of 'adding the opposite'. Instead of subtracting a number, you add its additive inverse (the opposite). For example, $a - b$ is the same as $a + (-b)$. This method converts subtraction problems into addition problems, which are often easier to solve. Remember that the opposite of a positive number is negative, and the opposite of a negative number is positive. This technique is crucial for working with negative numbers and ensuring accurate calculations.
When subtracting integers, visualize a number line. Moving to the right represents addition, and moving to the left represents subtraction. When you 'add the opposite,' you're essentially changing the direction you move on the number line. This method works for all integers, whether they are positive, negative, or zero. By consistently applying this rule, you can avoid common mistakes and confidently solve any integer subtraction problem.
🧠 Part A: Vocabulary
Instructions: Match the term with its correct definition.
| Term |
Definition |
| 1. Integer |
A. The distance of a number from zero on the number line. |
| 2. Additive Inverse |
B. A whole number (not a fraction) that can be positive, negative, or zero. |
| 3. Opposite |
C. The result of subtraction. |
| 4. Difference |
D. Another term for additive inverse. |
| 5. Absolute Value |
E. Two numbers that are the same distance from zero on a number line, but on opposite sides. |
✍️ Part B: Fill in the Blanks
Instructions: Fill in the missing words in the paragraph below.
Subtracting an integer is the same as __________ its __________. To do this, change the subtraction sign to an __________ sign and change the sign of the second number to its __________. Then, simply perform the __________ operation.
🤔 Part C: Critical Thinking
Instructions: Answer the following question in a few sentences.
Explain why 'adding the opposite' works when subtracting integers. Use a real-world example to illustrate your explanation.