Problem 99 - Elementary and Intermediate Algebra

Question

Simplify each expression, if possible. $$ -0.2 r-(-0.6 r) $$

Step-by-Step Solution

Answer

The expression simplifies to \(0.4r\).

Step 1: Identify the Expression

The expression to simplify is \(-0.2r - (-0.6r)\). This involves a subtraction that includes a negative term.

Step 2: Simplify the Subtraction of a Negative

Subtracting a negative is equivalent to adding a positive. Therefore, the expression \(-0.2r - (-0.6r)\) can be rewritten as \(-0.2r + 0.6r\).

Step 3: Combine Like Terms

Both terms \(-0.2r\) and \(0.6r\) are like terms because they both contain \(r\). To simplify, combine them by adding the coefficients: \(-0.2 + 0.6 = 0.4\). Thus, the simplified expression is \(0.4r\).

Key Concepts

Simplifying Expressions

Simplifying expressions is a vital skill in algebra, where the goal is to rewrite an expression in its simplest form. This process often involves several steps, including handling subtraction and addition of terms as well as working with different kinds of numbers like negatives.
Start by identifying the expression you want to simplify. In our case, we have \(-0.2r - (-0.6r)\). Next, focus on the operation involved, which is subtraction.

• In situations where subtraction is applied to a negative, remember subtracting a negative is like adding a positive.
• Therefore, \(-0.2r - (-0.6r)\) transforms to \(-0.2r + 0.6r\), making it easier to simplify.

This mental shift simplifies how you look at expressions, making the math less intimidating and much more manageable.

Combining Like Terms

The heart of simplifying algebraic expressions often lies in combining like terms. Like terms are terms that have the same variable raised to the same power. They can be combined by adding or subtracting their coefficients.
In our expression, after transformation, we have \(-0.2r + 0.6r\).

• Notice that both terms contain the variable \(r\), making them like terms.
• To simplify, combine these terms by adding the coefficients: \(-0.2\) and \(0.6\).
• Adding these gives \(0.4\), leading to the simplified expression being \(0.4r\).

Combining like terms reduces the complexity of the expression, making it tidier and less complex to handle in further mathematical operations.

Negative Numbers

Negative numbers can be tricky, but with practice, they become easier to handle. Understanding how negative numbers affect mathematical operations is crucial for simplifying expressions.

• When subtracting a negative, think of it as adding the absolute value of that number. For instance, \(-(-0.6r)\) becomes \(+0.6r\).
• Negative numbers affect the direction of counting, so flipping a negative to a positive makes it easier to simplify expressions.
• Practice makes perfect, so continue practicing with negative numbers in different contexts to gain confidence.

Embrace negative numbers as friendly integers that simply point in a different direction on the number line.