Problem 23 - Elementary Algebra

Question

For the following exercises, perform the indicated operations. $$ 4-11 $$

Step-by-Step Solution

Answer

Answer: The result of the subtraction operation 4 - 11 is -7.

Step 1: Identify the numbers being subtracted

In this problem, we are given two numbers, 4 and 11, and we need to find the difference between them. So we will subtract 11 from 4.

Step 2: Perform the subtraction operation

To perform the subtraction, we subtract 11 from 4: $$ 4 - 11 = -7 $$

Step 3: Write down the answer

After performing the subtraction operation, we got -7 as a result. So the answer to the problem is: $$ 4 - 11 = -7 $$

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They appear on a number line to the left of zero and are often used to represent values below a defined level. In the subtraction operation presented in the exercise, we see negative numbers in action.

When you subtract a larger number from a smaller one, like 4 - 11, it gives a negative result. This is because you are essentially moving leftward on the number line, passing zero and heading into the territory of negative numbers.

Consider negative numbers like a debt. If you have 4 dollars and you owe 11 dollars, you would have -7 dollars after settling, representing a debt of 7 dollars. This concept is crucial in both everyday calculations and in more advanced mathematics. Understanding how to work with negative numbers prepares you for topics like algebra.

Basic Arithmetic

Basic arithmetic involves simple operations such as addition, subtraction, multiplication, and division. These operations are the foundation of all mathematical calculations. Subtraction, as demonstrated in the exercise, is one of these fundamental actions.

Subtraction is essentially the process of taking one quantity away from another. The goal is to find what remains. To solve a subtraction problem effectively, it's important to think about the two numbers involved and what happens as you take one away from the other. In our example, subtracting 11 from 4, we find that the result is -7.

Practicing arithmetic operations without a calculator helps strengthen your mental math skills.

• Remember to ensure the numbers are correctly aligned, especially when dealing with decimals or larger numbers.
• Keep track of any negatives in the problem to avoid mistakes.

Number Operations

Number operations encompass all the different ways you can work with numbers to calculate a result. These include addition, subtraction, multiplication, and division. In subtraction operations, like the one in our exercise 4 - 11, comprehension of the process is key.

Here's how you break down a subtraction operation:

• Identify the numbers involved: Start by pinpointing which numbers you need to subtract.
• Determine the roles: Know which number is being subtracted from (minuend) and which number is doing the subtracting (subtrahend).
• Calculate the result: Subtract the subtrahend from the minuend. If the subtrahend is larger, the result will be a negative.

For 4 - 11, we identified that 4 is the minuend and 11 is the subtrahend. Since 11 is larger than 4, the result is -7. This operation helps you understand how numbers interact in different operations, setting the groundwork for more complex problems.