Problem 56 - Fundamentals of Mathematics

Question

Perform each operation. $$ 8-12 $$

Step-by-Step Solution

Answer

The answer is -4.

Step 1: Identify the Operation

The problem requires us to subtract 12 from 8. This operation is subtraction.

Step 2: Write the Expression

Express the operation as a mathematical expression: \(8 - 12\).

Step 3: Perform the Subtraction

Since we are subtracting a larger number from a smaller number, we will have a negative result. Subtract 12 from 8 to get \(-4\).

Step 4: Verify the Solution

Check the calculation: Add the result \(-4\) to 12 to see if it equals 8. Since \(-4 + 12 = 8\), the solution is correct.

Key Concepts

Understanding Negative Numbers

Negative numbers can seem confusing at first, but they are straightforward once you understand their role. Imagine the number line, which runs left to right, where numbers to the right are positive and numbers to the left are negative. When we move left from zero, we encounter negative numbers like

• -1
• -2
• -3

Negative numbers are essentially the opposite of positive numbers. They show a decrease or loss. For instance, when you subtract a larger number from a smaller one, the result is negative. In the problem we solved, subtracting 12 from 8 gives us \(-4\). This result is a negative number because the starting number (8) is less than what we subtracted (12). Whenever the subtrahend (the number being subtracted) is bigger than the minuend (the number from which another number is subtracted), the result will be negative.

Crafting a Mathematical Expression

A mathematical expression is a way to symbolize a math operation using numbers and symbols. In subtraction, the symbol is \(-\). In our given operation, 8 is the minuend, 12 is the subtrahend, and \(-\) is the subtraction symbol. Together, they form the expression \(8 - 12\).This expression tells us exactly what to do: subtract 12 from 8. Writing it out helps to understand and visualize the math problem, especially for more complex calculations. By breaking down the operation into a clear, symbolic form, it becomes easier to solve. Properly writing mathematical expressions also enhances communication and reduces errors, as it provides a universal language in mathematics to represent problems clearly.

Verification of Results

Verification involves double-checking your work to ensure the solution is correct. In math, it's a crucial step that provides confidence in your answers. Here's how to verify subtraction:

• Add the result back to the subtrahend to see if you get the starting number (minuend). If it checks out, the result is verified.

For instance, we found \(-4\) as the result of our subtraction \(8 - 12\). To verify, take \(-4\) and add 12:\(-4 + 12 = 8\). Since this sum equals our original minuend, 8, our result is indeed correct.
This process ensures that no arithmetic errors occurred during calculation. Verification not only helps solidify your understanding but also boosts your confidence in problem-solving!