Integer Operations Formula
Integer operations are adding, subtracting, multiplying, and dividing integers—numbers that include positive values, negative values, and zero.
The Formula
When to use: Think of a number line with zero in the middle. Positive numbers go right, negative numbers go left. Adding a positive moves right; adding a negative moves left. Multiplying two negatives gives a positive because reversing a reversal brings you back to the original direction.
Quick Example
Notation
What This Formula Means
Adding, subtracting, multiplying, and dividing integers—numbers that include positive values, negative values, and zero.
Think of a number line with zero in the middle. Positive numbers go right, negative numbers go left. Adding a positive moves right; adding a negative moves left. Multiplying two negatives gives a positive because reversing a reversal brings you back to the original direction.
Formal View
Worked Examples
Example 1
easyAnswer
First step
Full solution
- 2 Subtract the smaller absolute value from the larger: .
- 3 Keep the sign of the number with the larger absolute value (): the answer is .
Example 2
mediumExample 3
mediumCommon Mistakes
- Treating subtracting a negative as subtracting - subtracting a negative adds: .
- Making a product of two negatives negative - same signs give a positive product.
- Adding two negatives toward zero - two negatives sum to a more-negative number: .
Why This Formula Matters
It is the first time the sign carries meaning — debt, drop in temperature, distance left — and the rule that two negatives multiply to a positive trips up nearly everyone. Mastering sign tracking is required before expressions, equations, and rational-number work make sense. Recognizing it by "Does a negative number enter the operation so I must track sign as well as size?" — rather than by familiar numbers — is what lets a student tell it apart from operations with rationals and whole-number operations and absolute value in a mixed problem set.
Frequently Asked Questions
What is the Integer Operations formula?
Adding, subtracting, multiplying, and dividing integers—numbers that include positive values, negative values, and zero.
How do you use the Integer Operations formula?
Think of a number line with zero in the middle. Positive numbers go right, negative numbers go left. Adding a positive moves right; adding a negative moves left. Multiplying two negatives gives a positive because reversing a reversal brings you back to the original direction.
What do the symbols mean in the Integer Operations formula?
Negative numbers are written with a leading minus sign: . Parentheses clarify: .
Why is the Integer Operations formula important in Math?
It is the first time the sign carries meaning — debt, drop in temperature, distance left — and the rule that two negatives multiply to a positive trips up nearly everyone. Mastering sign tracking is required before expressions, equations, and rational-number work make sense. Recognizing it by "Does a negative number enter the operation so I must track sign as well as size?" — rather than by familiar numbers — is what lets a student tell it apart from operations with rationals and whole-number operations and absolute value in a mixed problem set.
What do students get wrong about Integer Operations?
The procedure for integer operations is the easy part; the trap is treating subtracting a negative as subtracting. Asking "Does a negative number enter the operation so I must track sign as well as size?" first is what keeps a correct-looking calculation from being attached to the wrong concept.
What should I learn before the Integer Operations formula?
Before studying the Integer Operations formula, you should understand: addition, subtraction, multiplication, division, integers.