Problem 71 - Algebra 1: Concepts and Skills

Question

Find the sum. $$ 5+16+(-9) $$

Step-by-Step Solution

Answer

The sum of 5+16+(-9) is 12.

Step 1: Addition of Positive Numbers

Firstly, you start off by adding the positive numbers in the sum. Here, \(5 + 16 = 21\)

Step 2: Addition of Negative Numbers

Next, you add the negative number to the sum obtained from the positive numbers. Here, the negative number is -9. So, you have to add -9 to 21. This becomes \(21 + (-9) = 21 - 9 = 12\)

Key Concepts

Addition of Positive Numbers

Adding positive numbers is one of the most straightforward arithmetic operations. When you add two or more positive numbers, you simply combine their values to get a larger number. For instance, consider the numbers 5 and 16. When you add these numbers, you sum their values:

• 5 + 16 = 21

The result is a positive number, and because all operands are positive, the overall sum increases. Always remember that addition of positive numbers results in moving rightward along the number line, indicating an increase.

Addition of Negative Numbers

Adding negative numbers can seem tricky at first, but it's quite simple once you get the hang of it. A negative number is essentially the opposite of a positive number, and it can decrease the overall value when added to a positive number. Think of it as moving leftward on a number line.

• For example, adding -9 to 21 involves adjusting for the negative value: 21 + (-9) = 21 - 9 = 12

The negative sign indicates you should subtract 9 from 21, resulting in a smaller final value. Indeed, combining negative numbers means that you are taking away from the total rather than adding to it. What’s crucial here is recognizing that the negative sign simply indicates a direction opposite to addition.

Basic Arithmetic Operations

Basic arithmetic operations form the foundation of math and include addition, subtraction, multiplication, and division. Addition and subtraction are often dealt with together, as they are inverse operations. When summing integers, adding positive numbers boosts the sum, while adding negative numbers reduces it.

• The order in which you perform addition does not affect the result, a feature termed commutativity. In practice, processing the sum involves straightforward steps. First, add any positive numbers, then incorporate negative values by effectively subtracting them.
• Remember that when you encounter a negative sign, you are instructed to shift left on the number line rather than right, contrasting the addition of positives.

Understanding these basic operations thoroughly makes more complex mathematics accessible and easily manageable. Mastering these basics helps solve problems effortlessly, as demonstrated in the initial exercise.