Problem 80 - Prealgebra and Introductory Algebra

Question

Find the absolute value of the number. $$-7$$

Step-by-Step Solution

Answer

The absolute value of -7 is 7

Step 1: Understanding absolute value

Absolute value is a concept in mathematics that measures 'distance' without taking into account direction. Specifically, absolute value of any number (negative or positive) is the 'distance' of that numerical value from zero on a number line.

Step 2: Applying the concept of absolute value

To find the absolute value of the number -7, simply ignore the negative sign because it does not contribute to 'distance' but signifies 'direction'. For example, -7 and 7 are both 7 units away from 0, therefore, their absolute values are the same.

Key Concepts

Prealgebra Concepts

Prealgebra serves as the foundation for all higher-level math and introduces students to basic arithmetic operations, including addition, subtraction, multiplication, and division. It's crucial for learning how to manipulate numbers and understand their properties. Within prealgebra, one comes across the concept of absolute value which is essential when measuring how far a number is from zero, regardless of direction.

Understanding absolute value is a stepping stone to mastering more complex mathematical concepts such as linear equations and functions. This prealgebra concept helps students develop a clearer view of numbers on the number line, which in turn aids in problem-solving and mathematical reasoning.

Number Line

• Visualizing Numbers: A number line is a visual representation of numbers laid out in a straight line. It helps in comparing and understanding the position of different integers and fractions relative to each other.
• Positive and Negative: Numbers to the right of zero on the line are positive, and those to the left are negative. This visual distinction helps to clarify the concepts of addition and subtraction as moving right or left on the line.
• Zero as a Reference Point: The number zero is the central point on a number line, acting as a reference for evaluating the magnitude of other numbers.

By incorporating a number line into the learning process, students can better grasp numerical relationships and the idea of directional movement, which is significant when delving into the concept of absolute value.

Distance from Zero

The distance from zero on a number line is one way to consider the absolute value of a number. Distance is always non-negative, and this remains true for absolute value as well.

Key Points:

• Always Positive: The absolute value, symbolized as |number|, is always a positive quantity because distance cannot be negative.
• Symmetry About Zero: Numbers such as -7 and 7 demonstrate the symmetrical nature of the number line, as they are equally distant from zero.
• Practical Application: In real life, distance from zero might represent literal distances or signify other concepts such as financial losses or gains in a symmetrical manner.

This foundational understanding makes it clear why the absolute value of -7 is 7, as it measures how far -7 is from zero without considering the direction, which is a critical point often missed in just the procedural computation of absolute value.