Problem 13 - Elementary Algebra

Question

Simplify the following problems. $$ 3-(-14) $$

Step-by-Step Solution

Answer

Question: Simplify the expression: 3 - (-14) Answer: 17

Step 1: Understand the expression

The given expression is \(3-(-14)\). Here, we need to simplify it by subtracting a negative number.

Step 2: Convert subtraction to addition

Since we are subtracting a negative number, we will convert it to addition. According to arithmetic rules, subtracting a negative number is the same as adding its positive counterpart. So, the expression becomes: \(3 - (-14) = 3 + 14\)

Step 3: Perform the addition

Now, we will simply add the numbers: \(3 + 14 = 17\)

Step 4: Write the final simplified expression

The simplified expression is: \(3-(-14) = 17\)

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They are the opposite of positive numbers and appear on the left side of zero on the number line. Working with negative numbers can be tricky at first, but they follow clear and simple rules. A negative number can be seen as a debt or a below-zero temperature, which makes it easier to visualize. Understanding how negative numbers interact in an expression is important. In arithmetic operations involving negative numbers, remembering that two negatives make a positive is key.
For instance, subtracting a negative number means you are actually adding its positive counterpart. This is because "minus a negative" flips the direction on the number line in a positive direction. Knowing these basics helps in simplifying expressions efficiently.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They are the foundational processes used to manipulate numbers, whether they are positive or negative. When working with these operations, certain rules apply to ensure numbers are combined or separated accurately.
In subtraction, if you encounter an expression like "3 - (-14)", you're dealing with the operation of taking away a negative number. According to arithmetic rules, this can be transformed by changing the subtraction of a negative into addition. This is because subtracting a negative is equivalent to adding a positive, leading to the transformation \(3 - (-14) = 3 + 14 \). Understanding these principles can simplify solving problems with various arithmetic operations.
Additionally, practicing how to switch between operations can improve accuracy and speed in math calculations. Hence, learning these fundamentals thoroughly makes advanced math problems more manageable.

Addition of Integers

Addition of integers involves combining numbers that can be positive, negative, or zero. When adding integers, the sign (positive or negative) of each number must be considered. Positive numbers generally add to the sum, while negative numbers subtract from it.
This process can be visualized using a number line, enabling a clear idea of how numbers shift through addition. For example, in an operation such as \(3 + 14 \), both numbers are positive, and they move further to the right on the number line, resulting in \(17\). When dealing with negative numbers, the same principles apply, and it’s always crucial to observe the signs involved.
Understanding the addition of integers is essential because it frequently appears in various math problems. It is a foundational skill that supports solving more complex equations and expressions. Practicing with various combinations enhances the ability to intuitively solve arithmetic problems with ease.