Adding and subtracting integers can be straightforward once you understand the rules that govern these operations. Here’s how you can do it without using a number line.
Adding Integers
When adding integers, the process differs based on whether the numbers are positive or negative:
- If both integers are positive, simply add the numbers together. For example, 3 + 4 = 7.
- If both integers are negative, add the absolute values and keep the negative sign. For example, (-3) + (-4) = -7.
- If one integer is positive and the other is negative, subtract the smaller absolute value from the larger one. The sign of the result will match the integer with the larger absolute value. For example, 5 + (-3) involves subtracting 3 from 5, resulting in 2 since 5 is larger. Conversely, (-5) + 3 leads to -2.
Subtracting Integers
Subtraction of integers can be transformed into an addition problem. Here’s how:
- To subtract an integer, such as a – b, you can instead add the opposite of the second integer: a + (-b). For example, 5 – 3 can be seen as 5 + (-3) = 2.
- If you’re subtracting a negative integer, remember that it’s the same as adding that integer. For example, 5 – (-3) becomes 5 + 3 = 8.
- If both integers are negative, apply the rule for subtraction. For example, (-5) – (-3) changes to (-5) + 3 = -2.
By understanding these principles, you can manage the addition and subtraction of integers without needing a number line. Practice will help you get comfortable with these rules!