Problem 85 - Elementary Algebra

Question

Simplify. -42

Step-by-Step Solution

Answer

-42 is already in its simplest form.

Step 1: Identify the Expression

The given expression is -42, which is already a single term and a simplified expression.

Step 2: Understand the Concept of Simplification

Simplification usually means to reduce an expression to its simplest form. In this case, there's nothing to combine or further simplify, as the expression consists of only a negative integer.

Step 3: Present the Final Simplified Form

Since the expression is already simplified, we recognize that -42 is the simplest form possible.

Key Concepts

Negative Integers

Negative integers are numbers less than zero. They are shown with a minus sign (-) in front. For example, -1, -10, and -42 are all negative integers. These numbers are essential in math, as they help us understand the concept of direction or balance.

• Negative integers can represent debts or withdrawals in financial calculations.
• They also show temperature drops below zero in weather forecasts.
• They are used in number lines to identify points below a defined origin.

The minus sign in front of an integer is critical, as it tells us the direction on the number line. Moving left from zero gives us negative numbers. Recognizing and using these numbers correctly helps us solve more complex mathematical problems.

Expression Simplification

Expression simplification involves reducing a mathematical expression to its most basic form. It's vital in making equations easier to understand and solve. Simplification might require us to combine like terms, reduce fractions, or remove unnecessary parts. However, single terms like -42, which contain no additional operations or expressions, are already in their simplest state.
When simplifying expressions:

• Look for like terms - numbers or variables with the same parts.
• Combine constants - add or subtract numbers without variables.
• Use operations - implement steps like multiplication or division if necessary.
• Remember to simplify inside parentheses first.

Recognizing when an expression cannot be further simplified is just as important. It saves time and ensures accuracy in solving math problems.

Simplest Form

The simplest form of an expression is when it cannot be reduced or simplified any further. An expression in its simplest form is often easier to interpret and use. In the case of a single number, like our example of -42, it is already as simple as it gets.
When identifying the simplest form:

• Check that there are no like terms left to combine.
• Ensure any possible factorization is completed.
• Verify that fractions are in their simplest form.
• Look for and simplify radicals if they exist.

The simplest form is vital for clarity and efficiency in mathematics. It ensures we are working with the most condensed version of an equation or expression, making problem-solving more straightforward.