Problem 49 - Algebra 1: Concepts and Skills

Question

ABSOLUTE VALUE Evaluate the expression. $$ |1.07| $$

Step-by-Step Solution

Answer

The absolute value of 1.07 is 1.07.

Step 1: Determine the Input Value's Sign

Analyze the input value for the absolute value function. In this case, the input is 1.07, which is a positive number.

Step 2: Apply Absolute Value Operation

Since the input number 1.07 is positive, it remains the same after the absolute value operation. Remember, the absolute value operation is defined as the value of a number without regard to its sign, which means positive numbers remain unchanged.

Key Concepts

Positive Numbers

Understanding positive numbers is essential for grasping many mathematical concepts. Positive numbers are those which are greater than zero. They can be whole numbers, fractions, or decimals. In a number line, positive numbers are found to the right of zero. For instance, numbers like 1, 3.5, and 0.25 are all positive.

The concept of positivity in numbers is crucial when dealing with absolute values because absolute value measures the distance a number is from zero. Importantly, this distance is always expressed as a non-negative number. Knowing whether a number is positive helps simplify the calculation of its absolute value, as the number will remain unchanged.

When evaluating expressions that involve absolute values, recognizing positive numbers first can guide the process. It allows you to quickly determine outcomes without additional computation.

Evaluate Expressions

When tasked with evaluating expressions in mathematics, you're essentially finding the value of an equation using given numbers or variables. In the context of absolute values, evaluation involves determining the magnitude of a number, irrespective of its sign.

Here are some steps you might take to evaluate expressions effectively:

• Identify and understand each part of the expression.
• Recognize any operations or functions applied to the numbers, such as absolute values.
• Perform calculations systematically by following order of operations.

For absolute value expressions like \(|1.07|\), the evaluation is straightforward: involve identifying that 1.07 is already positive. Thus, the result of the absolute value is simply 1.07.

This simplicity is why understanding fundamental properties like the sign of numbers makes evaluating such expressions quick and easy.

Mathematical Operations

Mathematical operations are processes or procedures used to solve mathematical problems. Common operations include addition, subtraction, multiplication, and division. In addition to these, functions like the absolute value also fall under mathematical operations.

The absolute value operation is somewhat unique amongst these as it doesn't change the number's magnitude but rather ensures it is non-negative. This specific operation involves analyzing the sign of a number and adjusting accordingly. However, for positive numbers, like in the exercise with \(|1.07|\), the number remains the same after applying the absolute value operation.

Understanding the characteristics and processes involved in different mathematical operations is vital. They help you effectively solve a variety of problems by applying the right methods and simplifying calculations whenever possible. Knowing how to handle absolute value operations can be especially useful in algebra and calculus, where dealing with expressions without regard to sign is often necessary.