Problem 35 - Intermediate Algebra

Question

Perform the following operations with real numbers. $$ -17.3+12.5 $$

Step-by-Step Solution

Answer

The result is -4.8.

Step 1: Identify the Numbers

In the given arithmetic operation, we have two real numbers: \(-17.3\) and \(12.5\). The operation to perform is addition.

Step 2: Perform the Addition

To find the result of the operation, you add the two numbers: \(-17.3 + 12.5 = -4.8\). Since one number is negative and the other is positive, subtract the smaller absolute value from the larger absolute value. The sign of the result is the same as the sign of the number with the larger absolute value, which in this case is \(-17.3\).

Key Concepts

Arithmetic Operations

Arithmetic operations are fundamental mathematical processes that include addition, subtraction, multiplication, and division. These operations help us perform calculations and solve various kinds of mathematical problems. In the case of real numbers, these operations follow specific rules that help us determine the outcome accurately. When dealing with real numbers, it is crucial to pay attention to their signs. This impacts the result, especially when engaging in addition or subtraction. Arithmetic operations allow you to combine numbers in meaningful ways, often forming the basis for more advanced math topics.

Addition of Real Numbers

The addition of real numbers involves combining numbers to form a new sum. Real numbers include all rational and irrational numbers. To successfully add them:

• Align the numbers by their decimal point to ensure the proper placement of digits.
• Be aware of the sign of each real number before proceeding with the addition, as the sign will affect the calculation.

In the specific scenario given, \(-17.3 + 12.5\), we notice that one number is negative and the other is positive. To find the sum, consider their absolute values:

• The absolute value of \(-17.3\) is 17.3.
• The absolute value of \(12.5\) is 12.5.

Subtract the smaller absolute value from the larger one \((17.3 - 12.5)\) to get 4.8. Since \(-17.3\) has the larger absolute value and is negative, the result takes the negative sign, making the sum \(-4.8\).

Positive and Negative Numbers

Positive and negative numbers are essential elements of mathematics, especially in the realm of real numbers. Positive numbers are greater than zero and are generally plotted to the right on a number line. Negative numbers are less than zero, represented by a minus sign, and plotted to the left. Understanding these concepts helps in comprehending operations involving such numbers. When adding numbers with different signs, the process involves finding the difference between their absolute values:

• If the numbers have different signs, subtract their absolute values and adopt the sign of the number with the larger absolute value.
• If the numbers have the same sign, add their absolute values and maintain that sign for the result.

This concept is illustrated in the exercise \(-17.3 + 12.5\), where the numbers differ in sign. Following the rule, we find the difference and use the sign of the larger absolute value to determine the result.