Problem 36 - Fundamentals of Mathematics

Question

For the following 18 problems, perform each subtraction. Use a calcula tor to cherk each result. $$ -550-(-121) $$

Step-by-Step Solution

Answer

The result is \(-429\).

Step 1: Understand the Problem

We need to perform the subtraction \(-550 - (-121)\). This involves subtracting a negative number, which essentially means adding the positive version of the number.

Step 2: Convert Subtraction of a Negative to Addition

Instead of subtracting \(-121\), we can rewrite the expression as an addition of \(121\). Thus, \(-550 - (-121)\) becomes \(-550 + 121\).

Step 3: Perform the Addition

Calculate \(-550 + 121\). This can be done by finding out how much \(-550\) increases when \(121\) is added to it. Since you are essentially adding \(121\), you move from \(-550\) towards zero: \(-550 + 121 = -429\).

Step 4: Verification Using a Calculator

Use a calculator to input \(-550 + 121\) to verify the result. The calculator should confirm that the result of the operation is \(-429\).

Key Concepts

Subtraction of Negative Numbers

Subtraction of negative numbers can often be a bit tricky because it is not as intuitive as other operations. When you subtract a negative number, it's similar to moving in the opposite direction on a number line. To subtract a negative number, you simply turn it into the addition of a positive.
For example, consider the expression \[ -550 - (-121) \]. Instead of thinking of this as taking away, you should switch to thinking of it as adding, like flipping a card from its dark side to its light side! So you would rewrite this as \[ -550 + 121 \]. Now, you just perform the regular addition to find the result. This makes the entire process simpler because handling negative signs can be confusing. Remember, subtracting a negative equals adding its positive counterpart.
Here is how you can remember it:

• Two negatives make a positive.
• Think of "minus minus" as a plus sign!

Addition and Subtraction Strategies

When dealing with these kinds of problems, having a reliable strategy for addition and subtraction can be a game changer. Let's focus on making number manipulation easier.
Imagine you're on a number line for \[ -550 + 121 \]. You start at -550 and need to add 121. Think of it as moving forward 121 steps from -550. Here's how you can do it:

• Break down the 121 into parts for easier addition, such as 100 and 21.
• First, add 100 to -550, which gets you to -450.
• Next, add the remaining 21, moving you to -429.

This way, you don't drown in numbers; you swim right through them! By splitting numbers into manageable pieces, computations become less error-prone and more straightforward.

Calculator Verification

Verifying your answer with a calculator is a great way to ensure accuracy in your math calculations. Calculators provide an instant and error-free way to confirm your results.
Here's how you would verify the example expression:- Enter the converted expression \[ -550 + 121 \] into the calculator.- If the calculator returns \[ -429 \], you can be confident that your manual calculation is indeed correct.
Make sure you input the correct symbols and numbers into the calculator to avoid any mishaps. Using a calculator is especially helpful in confirming results after performing manual arithmetic, as it helps to reinforce your understanding and ensure accuracy.
Remember:

• Double-check every entry.
• Use the calculator's memory function for repetitive calculations.