Problem 91 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 6-(-8)-11 $$

Step-by-Step Solution

Answer

The evaluated expression is 3.

Step 1: Handle the Negative Sign

Starting from the left, we first handle the subtraction with a negative number, which is equivalent to addition. So, we rewrite the expression as \(6 + 8 - 11\).

Step 2: Apply the Order of Operations

Now, we can apply the order of operations, which means that we should perform the addition before the subtraction. This gives us \(14 - 11\).

Step 3: Complete the Calculation

Finally, we perform the remaining subtraction operation, which gives us the final answer: \(14 - 11 = 3\).

Key Concepts

Understanding Negative Numbers

Negative numbers might seem a bit tricky, but think of them as the opposite of positive numbers. Imagine a number line: positive numbers are to the right of zero, while negative numbers are to the left. Negative numbers are useful for representing losses, depths, or even temperatures below freezing.

When handling negative numbers in arithmetic operations, it can be helpful to remember:

• Subtracting a negative number is the same as adding its positive counterpart. In math terms: if you have \(a - (-b)\), it transforms to \(a + b\).
• Adding two negative numbers together results in a more negative number. Example: \((-3) + (-5) = -8\).

Negative numbers follow the same arithmetic rules as positive numbers, so once you get the hang of them, they become much easier to work with!

Introduction to Arithmetic Expressions

Arithmetic expressions are mathematical phrases that include numbers, operators (such as plus and minus signs), and sometimes variables. They can range from simple, like \(3 + 2\), to complex algebraic expressions.

When working with arithmetic expressions, especially those that involve various operations, it's essential to understand the order of operations, often remembered by the acronym PEMDAS:

• Parentheses: Always solve the expressions inside parentheses first.
• Exponents: Next, resolve any exponents or powers.
• Multiplication and Division: Move from left to right, handling these equally.
• Addition and Subtraction: Finally, solve these from left to right.

Understanding and correctly applying these rules ensures that arithmetic expressions are solved accurately, regardless of their complexity.

The Process of Subtraction

Subtraction involves taking away a number from another, and in simple terms, it answers the question of "how much more?" or "what's left?". When you're familiar with positive numbers, subtraction is straightforward, but negative numbers add a twist.

Here's a quick guide to handling subtraction:

• To subtract two positive numbers, set the smaller number apart from the larger number, such as \(7 - 5 = 2\).
• When subtracting a negative number, convert the operation into addition. For example, \(9 - (-4)\) becomes \(9 + 4\).

The principle "subtracting a negative means adding" is crucial in simplifying expressions. By learning and applying this fundamental rule, subtraction, whether in simple problems or more intricate expressions, becomes less daunting.