Problem 46 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ -373+(-14) $$

Step-by-Step Solution

Answer

The sum is \(-387\).

Step 1: Identify the Numbers

The expression to evaluate is \(-373 + (-14)\). The numbers involved are \(-373\) and \(-14\). Both are negative integers.

Step 2: Apply the Rule for Adding Negative Numbers

When adding two negative numbers, we add their absolute values and assign a negative sign to the result. The absolute value of \(-373\) is 373, and the absolute value of \(-14\) is 14.

Step 3: Calculate the Sum of Absolute Values

Add the absolute values: \(373 + 14 = 387\).

Step 4: Assign the Negative Sign

Since both numbers are negative, the result is \(-387\). The sum of \(-373 + (-14)\) is \(-387\).

Step 5: Verify with a Calculator

Using a calculator, input \(-373 + (-14)\) and confirm that the result is \(-387\).

Key Concepts

Integers

Integers are whole numbers that can be positive, negative, or zero. They do not contain fractions or decimals and are commonly used in mathematical operations. In the context of our exercise, we were dealing with negative integers, specifically -373 and -14.

• Positive Integers: These are numbers greater than zero, like 1, 2, 3, etc.
• Negative Integers: These are numbers less than zero, like -1, -2, -3, etc.
• Zero: This is neither positive nor negative, it's neutral in the realm of integers.

Understanding these is essential when working with operations involving positive and negative numbers. In our exercise, both integers were negative, which means when you calculate the sum, you must keep the negative sign as part of your final answer.

Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering which direction from zero it is. In simple terms, it's the number without its sign.

• The absolute value of a positive number is the number itself.
• The absolute value of a negative number is the number without the negative sign.
• The absolute value of zero is 0.

For example, in our exercise, we found the absolute values of -373 and -14. The absolute value of -373 is 373, and the absolute value of -14 is 14. Absolute values help simplify addition and subtraction problems by allowing you to focus on magnitude rather than sign.

Calculator Verification

Calculator verification is a useful step in any mathematical exercise. It serves as a double-check to ensure that the manual calculation is accurate. When you use a calculator for checking solutions, it can provide confidence in your mathematical skills.
Here’s when and how you should use calculator verification:

• After solving a problem manually, use a calculator to verify the results.
• Input the numbers and operation exactly as you initially calculated.
• If the results match, great! You can be confident in your answer. If they don't, recheck your calculations for any errors.

In our exercise, after manually calculating that -373 + (-14) equals -387, you input the same calculation into a calculator. The result matches the manual calculation, confirming the solution is correct.