Problem 34 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ 816-1140 $$

Step-by-Step Solution

Answer

The result of the subtraction is -324.

Step 1: Identify the Numbers

Recognize the numbers involved in the subtraction. Here, the numbers are 816 (minuend) and 1140 (subtrahend). Note that the subtrahend (1140) is larger than the minuend (816).

Step 2: Align the Numbers

Align the numbers vertically by place value: \(\begin{array}{c}\ \ 816 \-\ 1140 \\hline\end{array}\)

Step 3: Perform the Subtraction

Since 816 is less than 1140, you will end up with a negative result. Subtract 816 from 1140 to find the difference \(1140 - 816 = 324\). Since the minuend is less, the answer will be negative, resulting in \(-324\).

Step 4: Verify with a Calculator

Use a calculator to perform the subtraction \(816 - 1140\). Confirm that the result is \(-324\). If the calculator displays this result, the subtraction was performed correctly.

Key Concepts

Understanding Negative Numbers

Negative numbers are an essential part of mathematics and they often appear in subtraction problems. When you subtract a larger number from a smaller number, you'll end up with a negative number.
For example, in the operation given as 816 - 1140, since 816 is smaller than 1140, the result will be negative. This can be thought of as moving to the left on a number line, away from zero.
Negative numbers are marked with a minus sign (-) and they are less than zero.

• In our example, subtracting causes us to get -324.
• Think of it like borrowing more money than you have, resulting in debt, which is reflected as a negative balance.

Understanding how negative numbers work is crucial for accurate calculations, especially in more complex math problems.

Using a Calculator Effectively

Calculators are valuable tools that help verify subtraction results, especially when dealing with large numbers or negative results. It's important to use the calculator correctly to ensure you have accurate results.
Here’s a simple guide:

• First, enter the smaller number (minuend) followed by the minus sign.
• Then enter the larger number (subtrahend) followed by the equal sign.

In our example, you would input 816 - 1140, which should display -324.
It's essential to double-check the sign of your result, as a negative result indicates the subtrahend was larger.
Using calculators for these verifications helps to minimize mistakes and ensures that subtraction sequences are correctly performed.

The Importance of Mathematical Verification

Mathematical verification is a critical step in confirming that your calculations are accurate. Without it, you might mistakenly conclude the wrong result, especially with operations involving negatives.
Consider these key steps for thorough verification:

• Recalculate the problem manually to see if you obtain the same result.
• Use the calculator to compare your manual result with the digital one.
• In problems like 816 - 1140, recognizing the negative outcome (-324), consistent between manual and calculator methods, confirms accuracy.

Verification gives confidence in the correctness of your results.
It is a reliable way to spot errors and understand if a subtraction has been executed properly. This process is advantageous, particularly when handling extensive data or more intricate mathematical concepts.