Question

Simplify. $$|-200|$$

Short answer

Answer: The simplified expression of the absolute value of -200 is 200.

Step-by-step solution

Identify the absolute value expression

We are given an expression: $$|-200|$$

Apply the absolute value definition

The absolute value of a number is the distance from that number to 0 on the number line. Therefore, we have: $$|-200| = 200$$ The simplified expression is 200.

Key concepts

Prealgebra

Prealgebra is the foundation of mathematics where we start learning about operations with numbers and basic algebraic concepts. One of the key skills in prealgebra is understanding how to manipulate numbers using basic arithmetic operations like addition, subtraction, multiplication, and division.

It also introduces concepts like absolute values, where we emphasize the value of a number without considering its sign. Understanding prealgebra is vital because it sets the stage for more advanced math topics and problem-solving skills.

• Foundation of mathematics
• Basic arithmetic operations
• Introduction to absolute values

Number Line

A number line is a visual representation of numbers in a straight line where each point on the line corresponds to a number. It is fundamental in understanding the order and spacing of numbers.

Every number to the right is larger than the numbers to its left. Negative numbers are to the left of zero, and positive numbers are to the right. Absolute values relate to how far a number is from zero on this line. When we look at absolute values, we're essentially considering how many steps a number is from zero without regard for direction.

• Straight line representation of numbers
• Helps visualize the position of numbers
• Understanding absolute value on the number line

Simplification

Simplification in mathematics involves reducing an expression to its simplest form, making it easier to understand or solve. When we simplify \(|-200|\), we're using the idea of absolute value to determine the simplest, most direct form of the number.

Absolute value simplification tells us that negative signs don't affect the distance a number is from zero. So, simplifying \(|-200|\) means you convert it to 200, as that's its positive equivalent. Simplification helps in solving equations efficiently, making complexities more manageable.

• Reducing expressions to simplest form
• Important for solving equations
• Absolute value plays a role in simplification

Distance to Zero

The concept of distance to zero is all about determining how far a number is from zero on a number line, ignoring which direction along the line the number could be. This concept plays into understanding absolute values.

For example, \(-200\) is 200 away from zero. Whether a number is negative or positive doesn't matter when calculating its distance to zero; we only care about the magnitude. This distance is called the absolute value of a number, and concepts like symmetry help visualize why the distance remains the same if you flip to the opposite side of zero.

• Focuses on magnitude, not direction
• Relates to absolute value
• Key in comparing numbers on a number line