Calculating integers in grade 7 involves understanding positive and negative numbers, and how they interact through addition and subtraction.
Understanding Integers
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.
Addition of Integers
- Adding two positive integers: This is straightforward addition as you already know it (e.g., 3 + 5 = 8).
- Adding two negative integers: Add the absolute values of the numbers and keep the negative sign (e.g., -3 + -5 = -8).
- Adding a positive and a negative integer: Think of it as movement on a number line. If the positive number has a larger absolute value, the answer is positive; if the negative number has a larger absolute value, the answer is negative. You are effectively finding the difference between the absolute values and using the sign of the number with the larger absolute value. (e.g., 7 + (-3) = 4, -7 + 3 = -4).
Subtraction of Integers
Subtracting integers can be trickier. A key concept to understand is "subtracting is the same as adding the opposite." This is explained in the provided reference: "[...] minus a positive two all right so what's the opposite of positive two. It's negative two and since we're adding the opposite that minus sign needs to become a plus sign."
- To subtract a positive integer: Change the subtraction sign to an addition sign and change the positive integer to a negative integer. Then, proceed as an addition problem (e.g., 5 - 2 is the same as 5 + (-2), which equals 3).
- To subtract a negative integer: Change the subtraction sign to an addition sign and change the negative integer to a positive integer. Then proceed as an addition problem (e.g., 5 - (-2) is the same as 5 + 2 which equals 7).
Key Concepts Explained
| Operation | Example | Explanation |
|---|---|---|
| Adding positives | 5 + 3 = 8 | Regular addition. |
| Adding negatives | -5 + (-3) = -8 | Add the absolute values, result is negative. |
| Adding different signs | 7 + (-3) = 4 | Difference of absolute values, larger number's sign is the result's. |
| Subtracting positives | 5 - 3 = 2 | Same as adding the opposite: 5 + (-3) = 2 |
| Subtracting negatives | 5 - (-3) = 8 | Same as adding the opposite: 5 + 3 = 8 |
Practical Tips
- Use a number line: Visualizing integers on a number line can help with addition and subtraction.
- "Keep, change, change": When subtracting, keep the first number, change subtraction to addition, and change the sign of the second number.
By mastering these concepts and practicing regularly, Grade 7 students can effectively calculate integers.
