Question

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ -3.6-(-6) $$

Short answer

The evaluation of the expression \( -3.6 - (-6) \) results in \( 2.4 \).

Step-by-step solution

Rewrite the expression

The subtraction rule states that subtraction of a number is the same as addition of its negative. So, rewrite the given expression \( -3.6-(-6) \) as \( -3.6+6 \).

Evaluate the expression

Now, simply add the two numbers in the expression \( -3.6+6 \). It results in \(2.4\).

Key concepts

Equivalent Addition Expression

Understanding the concept of an equivalent addition expression can be quite handy, especially when dealing with subtraction involving negative numbers. It's based on a fundamental principle of algebra that subtraction can be thought of as the addition of a negative number. Rather than saying you're taking something away, you're adding its opposite. To put this into practice, let’s consider a subtraction expression like \(-3.6 - (-6)\). Using the subtraction rule, we can convert this into an equivalent addition expression. This is done by recognizing that subtracting a negative number is the same as adding its positive counterpart. So, \(-3.6 - (-6)\) becomes \(-3.6 + 6\). The key takeaway is to remember that subtraction of a negative leads to addition.

When you come across subtraction in an algebraic expression, look for opportunities to convert it into equivalent addition. This simplifies your calculations and is particularly useful when the numbers are not as straightforward as in our example.

Negative Numbers

Negative numbers often trip students up, but they are just as important as their positive counterparts. A negative number represents a value that is less than zero. It’s often used to denote loss, deficit, or quantities in the opposite direction.

Understanding Negative Numbers

Negative numbers can be thought of in terms of money. If you have \(-\$5\), you owe \(5; if you gain \(-\$5\), it means you lose \)5 from what you have. When subtracting negative numbers, as seen in the expression \(-3.6 - (-6)\), we are essentially adding the positive version of the subtracted number. To grasp this better, imagine taking away a debt—you'd naturally have more money, which is why \(-3.6 - (-6)\) becomes \(-3.6 + 6\).

Tips for Working with Negative Numbers

• Always consider the sign in front of a negative number; it indicates the operation that should be performed.
• Use number lines to visualize the addition and subtraction of negative numbers.
• Remember that two negatives make a positive when considering operations.

Mastering the concept of negative numbers not only helps in algebra but also sets a strong foundation for advanced mathematics concepts.

Evaluating Expressions

Evaluating expressions is like following a recipe where each step is crucial to ensure the final dish comes out as intended. In algebra, 'evaluating' refers to the process of finding the numerical value of an expression. This process usually involves several steps that can include operations such as addition, subtraction, multiplication, division, and more:

Steps for Evaluating Expressions

To evaluate an expression like \(-3.6 + 6\), we follow a methodical approach. First, ensure that the expression is in its simplest form, which we achieved by using the subtraction rule. Next, perform the arithmetic by combining the like terms. In our case, \(-3.6 + 6 = 2.4\).

Tips for Smooth Evaluation

• Always perform operations in the correct order, observing the rules of the order of operations (PEMDAS/BODMAS).
• Combine like terms sensibly; if you make a mistake here, the final answer will be incorrect.
• Write down each step carefully. Evaluating expressions should not be done in a rush; take your time to ensure accuracy.

Evaluating expressions correctly is critical as it reflects your understanding of the algebraic concepts and the arithmetic involved, leading to the right solution.