Problem 43 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ 452+(-124) $$

Step-by-Step Solution

Answer

The sum of 452 and -124 is 328.

Step 1: Identify the Type of Operation

In this exercise, we need to find the sum of two numbers: 452 and -124. Notice that we are adding a positive number and a negative number.

Step 2: Understand the Addition of a Negative Number

When adding a negative number, it's equivalent to subtracting the positive version of that number. Therefore, adding -124 is the same as subtracting 124 from 452.

Step 3: Perform the Subtraction Operation

Subtract 124 from 452:\[452 - 124 = 328\]

Step 4: Verify with a Calculator

Use a calculator to verify the manual computation. Enter 452 + (-124) and check the result, which should confirm our manual calculation of 328.

Key Concepts

Negative Numbers

The concept of negative numbers can be tricky at first, but they are an essential part of mathematics. Negative numbers are numbers less than zero and are usually represented with a minus sign (-). They are the counterparts to positive numbers.
In real life, you might encounter negative numbers in situations involving debts or temperatures below freezing. For instance:

• Owing $20 is the same as having a negative $20.
• A temperature of -5°C is 5 degrees below zero.

When working with negative numbers in addition or subtraction, it's important to get comfortable with switching between positive and negative values. In many cases, adding a negative number means you're actually performing subtraction. We'll explore this next in more detail.

Subtraction as Addition

Understanding that subtraction can be expressed as the addition of a negative number opens a door to simplifying many mathematical operations. This concept can transform how we approach problems and make calculation processes clearer.
Imagine you have the expression 452 + (-124). Initially, it might seem complicated because we're combining both positive and negative numbers. However, if you realize that adding a negative is the same as subtracting its positive counterpart, the equation becomes 452 - 124.
This approach simplifies the problem, making it easier to compute. By turning addition of negative numbers into a subtraction task, it ensures our calculations are straightforward and logical. Try applying this method to other similar problems to boost your math skills!

Calculator Verification

Once you've manually solved a problem involving integer addition with negative numbers, it's wise to use a calculator to double-check your answer. This is a good practice not just for students but for anyone working with numbers.
To verify your result using a calculator:

• Enter the numbers as given in the original problem. For example, type 452 + (-124).
• Press the equals button to see the result.

If the calculator's answer matches your manual computation, you've done it correctly. In our exercise, entering 452 + (-124) should yield 328, confirming our hand-calculated result. Calculators can quickly alert us to any errors, ensuring that we have solved the problem accurately and confidently. Check your work this way whenever you can!