Problem 100 - Elementary and Intermediate Algebra

Question

Simplify each expression, if possible. $$ -1.1 m-(-2.4 m) $$

Step-by-Step Solution

Answer

The simplified expression is \(1.3m\).

Step 1: Rewrite the Expression to Remove the Parentheses

The expression is given as \(-1.1m - (-2.4m)\). According to the rules of arithmetic, subtracting a negative is the same as adding a positive. So we rewrite the expression as \(-1.1m + 2.4m\).

Step 2: Combine Like Terms

Now, we need to combine \(-1.1m\) and \(2.4m\). These are like terms because they both include the variable \(m\). To combine them, simply add the coefficients: \(-1.1 + 2.4 = 1.3\). Therefore, the expression simplifies to \(1.3m\).

Key Concepts

Combining Like Terms

In algebra, combining like terms is an essential skill. It helps simplify expressions to make them more manageable and easier to understand. Like terms are terms that have the same variable raised to the same power. This means that only the coefficients of such terms can be combined.

• For instance, in the expression \(-1.1m + 2.4m\), both terms have the variable \(m\), making them like terms.
• You can add their coefficients, which are \(-1.1\) and \(2.4\), to simplify the expression.

This strategy is particularly helpful for simplifying longer and more complex expressions by effectively reducing the number of terms to work with. It's like cleaning up a messy desk; once you've cleared away the unnecessary clutter, everything becomes a lot clearer!

Arithmetic Operations

Understanding arithmetic operations is important in simplifying algebraic expressions. The basic operations are addition, subtraction, multiplication, and division. Each has specific rules, especially when it involves variables.

• Addition and subtraction are straightforward, but remember: subtracting a negative is the same as adding a positive. This rule changes the expression from \(-1.1m - (-2.4m)\) to \(-1.1m + 2.4m\).
• Multiplication and division involve coefficients and should respect the order of operations, also known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

When applying these operations, always pay close attention to the signs and terms to avoid errors, as arithmetic is the backbone of algebraic simplification.

Negative Numbers in Algebra

Negative numbers often seem intimidating, but they are friendly once you get to know them. In algebra, handling negative numbers correctly is crucial.

• A negative sign indicates a value less than zero, and often represents subtraction or the opposite of a positive value.
• Key thing to remember is that subtracting a negative number is the same as adding its positive counterpart. For example, the negative of \( -2.4m \) becomes \( +2.4m \) when subtracted from another term.

When dealing with negative coefficients, it's important to accurately reflect their effect on the expression. Mistakes with signs can lead to errors in calculations. Practice and familiarity with these rules will help refine your algebra skills.