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Understanding how to add integers is crucial for solving many mathematical problems. Integers include all whole numbers and their negative opposites. When adding integers, it's important to follow the rules for combining positive and negative numbers.
To add two positive numbers, simply add their absolute values. For example, in the problem above, we added 11 and 3 to get 14. This is straightforward because both numbers are positive.
However, when you encounter a negative number, the process changes slightly. You need to pay attention to the sign of each number. If you're adding a negative number to a positive one, you'll actually be doing a subtraction. For example, in the second step of our exercise, we added -15 to 14, which is the same as subtracting 15 from 14, giving us -1.
Mastering this concept will help you solve a variety of math problems more easily.

Combining positive and negative numbers might seem tricky at first, but it becomes simple with practice. When you add a positive number to a negative number, you are essentially performing a subtraction. The larger number's sign determines the result's sign.
For instance, in our given exercise, we had to combine 14 and -15 in the final step. We look at the numbers: 14 is positive, and -15 is negative. The negative number has the greater absolute value. Therefore, our result is negative. We subtract 14 from 15, leading us to -1.
Here are some useful tips to keep in mind:

• When adding two positive numbers, simply add their values.
• When adding two negative numbers, add their absolute values, and remember the result is also negative.
• When adding a positive number and a negative number, subtract the smaller number from the larger, and the sign of the result will match the larger number's sign.

These guidelines will help you handle combining any positive or negative numbers confidently.

Prealgebra is the foundation for all future algebra courses. It covers basic arithmetic operations and introduces students to the fundamental concepts of algebra. Simplifying expressions, like the one we solved above, is a key component of prealgebra.
In prealgebra, you will encounter various expressions that involve combining integers, understanding the order of operations, and simplifying complex expressions. The exercises you practice now lay the groundwork for more advanced mathematical concepts.
For example, the step-by-step solution provided for 11 + (-15) + 3 shows how to approach a problem methodically:

• First, focus on the order of operations. Combine similar terms—in this case, the positive integers: 11 and 3.
• Next, handle the negative number by combining it with the result. This shows how addition and subtraction intertwine when different signs are involved.

Practicing these prealgebra skills will make your transition to algebra smoother and your problem-solving abilities sharper.