Problem 83 - Elementary Algebra

Question

\(-15-(3-8)\)

Step-by-Step Solution

Answer

-10

Step 1 - Simplify Inside the Parentheses

First, simplify the expression inside the parentheses. The expression is (3 - 8). Calculate the difference: 3 - 8 = -5.

Step 2 - Substitute Back into the Expression

Now, substitute -5 back into the original expression to get: -15 - (-5).

Step 3 - Simplify the Expression

Next, simplify the expression by removing the parentheses: -15 - (-5) equates to: -15 + 5.

Step 4 - Perform the Addition

Finally, add the two numbers: -15 + 5 = -10.

Key Concepts

order of operations

When solving algebraic expressions, always follow the order of operations. This ensures you perform calculations in a structured and logical way. Remember the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

In our original exercise, \( -15-(3-8) \), the first step is to simplify the expression inside the parentheses (3 - 8). Parentheses have the highest priority. Performing the subtraction within the parentheses first simplifies the problem. Always handle operations within parentheses before moving on to the rest of the expression.
By following this order, you ensure every part of the expression is handled correctly.

simplifying expressions

Simplifying expressions can make them easier to work with and understand. In the given problem, \( -15-(3-8) \), the first step involves simplifying what’s inside the parentheses. (3 - 8) simplifies to -5.
Now, replace the original parentheses with the simplified value to form \( -15 - (-5) \). Simplifying doesn't just mean reducing numbers; it also encompasses handling parentheses, combining like terms, and following operation rules.
By breaking complex problems into simpler parts, you make them more manageable. This approach is vital for understanding and solving algebra efficiently.

negative numbers

Negative numbers can be tricky. They are numbers less than zero and are represented with a minus (-) sign. In our problem, we work with -15 and -5. When handling expressions with negative numbers, remember these key points:

• Subtracting a negative is the same as adding the positive equivalent. For example, (-15 - (-5)) becomes (-15 + 5).
• Negative plus negative results in a more negative number. For example, -3 + (-2) equals -5.
• Negative minus positive results in an even more negative number. For example, -4 - 2 equals -6.

When you see double negatives, always convert them to a positive before proceeding. This makes operations with negative numbers less confusing and ensures accuracy.

addition and subtraction

Addition and subtraction are basic yet crucial parts of algebra. Understanding how to add and subtract both positive and negative numbers is vital.
In our exercise, after simplifying, we reached \( -15 - (-5) \). Because subtracting a negative is the same as adding a positive, this simplifies further to \( -15 + 5 \).
Here’s a recap of common scenarios:

• Positive + Positive: Simply add the numbers. Example, 3 + 5 = 8.
• Negative + Negative: Add the numbers and keep the negative sign. Example, -3 + (-2) = -5.
• Positive + Negative: Subtract the smaller absolute value from the larger and keep the sign of the larger. Example, 6 + (-4) = 2.
• Negative - Negative: Convert to addition of a positive. Example, -3 - (-2) converts to -3 + 2 = -1.

Mastering these rules will help you tackle any algebraic expression with confidence.