Problem 21 - Fundamentals of Mathematics

Question

Use a calculator to find each sum. $$ -1,345.6+(-6,648.1) $$

Step-by-Step Solution

Answer

The sum is \(-7,993.7\).

Step 1: Identify the numbers

We have two numbers to add: 1. \(-1,345.6\)2. \(-6,648.1\). These numbers are both negative.

Step 2: Add the numbers

Since both numbers are negative, we can add their absolute values and then apply the negative sign to the result. Calculate the sum of the absolute values:\[ |1,345.6| + |6,648.1| = 1,345.6 + 6,648.1 = 7,993.7 \].Since both original numbers were negative, the sum is \(-7,993.7\).

Step 3: Verify with a calculator

To ensure the calculation is accurate, use a calculator:1. Enter \(-1,345.6\).2. Add \(-6,648.1\) by keying in the operation as + (-6,648.1) .The result should be \(-7,993.7\).

Key Concepts

Math Calculations

Calculating sums, especially with negative numbers, can sometimes be tricky. It's important to approach math calculations step by step to avoid mistakes and ensure accuracy. When dealing with numbers, the basic operation symbols you need to know include:

• + for addition
• - for subtraction
• × for multiplication
• ÷ for division

When you add two numbers, you are essentially combining their values. In instances where negative numbers are involved, the combining of values can take a different approach due to their properties.
Always ensure that you understand the nature of the numbers you are working with—whether they are positive or negative—before proceeding with the calculation. This understanding helps in applying the rules for math calculations correctly and efficiently.

Absolute Value

The absolute value of a number refers to its distance from zero on the number line, without considering if it's positive or negative. For example, the absolute value of \(-4\) is \(4\), because it is 4 units away from zero. The notation for absolute value is usually two vertical bars around the number, like \(|-4|\).

When performing calculations involving negative numbers, especially when adding them, knowing their absolute value makes it easier to handle their sum. In our exercise, both \(-1,345.6\) and \(-6,648.1\) were negative. To simplify, we first added their absolute values:

• \(1,345.6 + 6,648.1 = 7,993.7\)

Once calculated, it's important to apply the negative sign back, as both numbers were negative initially. Thus, the sum becomes \(-7,993.7\). Understanding and applying absolute values helps in simplifying and solving problems efficiently.

Negative Numbers in Math

Negative numbers represent values below zero, commonly used in various mathematical contexts including debts, temperatures below freezing, and height below sea level. They are indicated by a minus sign (\(-\)).

In math, negative numbers follow specific rules, which are crucial to remember:

• Adding two negative numbers results in a negative sum. For example, adding \(-2\) and \(-3\) gives \(-5\).
• When subtracting a negative number, it becomes an addition. For instance, \(5 - (-3)\) will be \(5 + 3 = 8\).
• Multiplying or dividing two negative numbers yields a positive result.

Understanding how negative numbers operate allows for comprehensive math calculations, whether you're adding, subtracting, multiplying, or dividing. This is particularly helpful when dealing with complex problems where multiple steps and operations are involved.