Problem 51 - Algebra 1

Question

Evaluate the expression. (Review 2.1 ) $$\left|\frac{-2}{3}\right|$$

Step-by-Step Solution

Answer

The absolute value of \(-\frac{2}{3}\) is \(\frac{2}{3}\)

Step 1: Identify the expression inside the absolute value

The expression inside the absolute value is \(-\frac{2}{3}\).

Step 2: Apply the absolute value

Calculate the absolute value of \(-\frac{2}{3}\) which is \(\frac{2}{3}\). The absolute value simply removes the negative sign from the number.

Key Concepts

Math Expression Evaluation

When tackling math expressions, it's crucial to understand the role of absolute value, especially when combined with fractions and negative numbers. An absolute value tells us how far a number is from zero on a number line, regardless of its direction. To evaluate expressions that include absolute values, follow these simple steps:

• Identify the Expression: Determine the numbers or fractions involved, noting any negative signs.
• Apply the Absolute Value: Convert the identified expression to its absolute value by removing any negative signs. This step helps simplify the problem significantly.
• Final Evaluation: Perform any further calculations as necessary once the absolute value has been applied.

Math expression evaluation often requires us to break down complex expressions into their components, such as recognizing the difference between the mathematical operations of addition, subtraction, multiplication, division, and the use of absolute values. Understanding these principles can really sharpen your skills.

Fractions

Fractions represent portions of a whole and can seem tricky when they combine with other math concepts like absolute values. A fraction consists of two parts: the numerator (top part) and the denominator (bottom part). Here’s how to work with fractions in the context of absolute value:

• Identifying Negative Signs: Notice if the fraction is negative, as in the problem at hand, \(-\frac{2}{3}\).
• Apply Absolute Value: By applying absolute value, remove the negative sign, turning \(-\frac{2}{3}\) into \(\frac{2}{3}\). The size of the fraction doesn’t change, only its sign does.
• Add, Subtract, Multiply, or Divide: Once simplified to an absolute value, you can treat it like any other positive fraction in operations.

Understanding how fractions work with absolute value is essential for conquering more complex math problems, as it trains you to simplify expressions accurately.

Negative Numbers

Negative numbers can often cause confusion, but they are straightforward once you understand their relationship with absolute values. A negative number is simply any number less than zero.

• On the Number Line: Negative numbers are situated to the left of zero. They have equal distance from zero as their positive counterparts, just in the opposite direction.
• Impact of Absolute Value: The key function of absolute value in expressions is to convert any negative number into its positive equivalent, effectively measuring its distance from zero.
• Simplifying Expressions: In problems like \(-\frac{2}{3}\), applying absolute value immediately simplifies the expression to a positive form, \(\frac{2}{3}\).

Once you master the idea that absolute value makes negative numbers positive, working with them in math becomes much more intuitive.