Problem 80 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ (9-3)-15 $$

Step-by-Step Solution

Answer

-9

Step 1: Evaluate the Expression Inside the Parentheses

First, calculate the expression inside the parentheses. Here we have \[ 9 - 3 = 6 \]

Step 2: Subtract the Result Outside the Parentheses

Next, subtract the number outside the parentheses from the result obtained in Step 1. This means we perform the operation: \[ 6 - 15 = -9 \]

Key Concepts

Subtraction Within Parentheses

In this exercise, we start with the expression \( (9 - 3) - 15 \). The first step is to handle the operation within the parentheses. Parentheses are crucial in math because they tell us which part of the expression to solve first.

In our example, it's \(9 - 3\). We subtract 3 from 9, which equals 6. Thus, the expression inside the parentheses simplifies to 6.

Evaluating Expressions

Once we've simplified the expression inside the parentheses, we can then evaluate the rest of the expression. The original expression \( (9 -3) - 15 \) now becomes \(6 - 15\).

Evaluating this new expression is straightforward because it simply involves subtracting two numbers. Start with the number 6 and subtract 15 from it. This results in -9. The final answer to our expression is -9.

Remember, always perform the simplifications step-by-step to avoid mistakes.

Order of Operations

The order of operations is a fundamental concept in math that dictates the correct sequence to evaluate a mathematical expression. We'll use the mnemonic PEMDAS to remember the right order:

• P: Parentheses first
• E: Exponents (powers and roots)
• MD: Multiplication and Division (from left to right)
• AS: Addition and Subtraction (from left to right)

In our example, (9 - 3) - 15, we first solved the expression in the parentheses: (9 - 3) to get 6. Following PEMDAS, we moved from parentheses to subtraction, evaluating the simplified expression 6 - 15 to get the final result of -9.

Always sticking to the order of operations ensures consistency and correctness in solving math problems.