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Integer operations involve basic arithmetic rules applied to whole numbers, which include both positive and negative numbers. The main operations you need to know are addition, subtraction, multiplication, and division. When adding or subtracting integers, pay attention to the signs:

• Adding two positive numbers gives a positive result.
• Adding two negative numbers results in a negative number.
• When adding a positive number to a negative number, subtract their absolute values and keep the sign of the larger absolute value.
• Subtracting a number is like adding its opposite.

Using these rules assures that you handle calculations correctly, even when negative numbers are involved.

Negative numbers represent a value less than zero. They are usually indicated using a minus sign (-). When working with negative numbers in arithmetic:

• Adding a negative number is the same as performing subtraction.
• Subtracting a negative number is the same as adding a positive number.
• Multiplying or dividing two negative numbers results in a positive number.
• Multiplying or dividing a positive number and a negative number results in a negative number.

For example, in the expression 7 + (-5), adding -5 is the same as subtracting 5 from 7. Remember these rules as they will simplify handling different arithmetic problems involving negative numbers.

Solving math problems, especially those involving multiple steps, requires a clear methodology. Here’s how you can approach the problem of adding integers with both positive and negative numbers: First, recognize and list all the numbers involved. This ensures clarity about what you are working with. For the problem 7 + (-5) + (-9), notice there are three numbers: 7, -5, and -9. Next, add the first two numbers. Take 7 and -5: \[ 7 + (-5) = 7 - 5 = 2 \] Finally, take the result and add it to the next number:
2 + (-9): \[ 2 + (-9) = 2 - 9 = -7 \] Simplifying math problems step-by-step prevents errors and aids understanding. Always break down the problem into smaller, manageable parts.