Problem 60 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(-5(4-7)\)

Step-by-Step Solution

Answer

15

Step 1: Identify the Expression

The expression to solve is \( -5(4-7) \).

Step 2: Simplify Inside Parentheses

First, perform the operation inside the parentheses: \(4 - 7\). \(4 - 7 = -3\).

Step 3: Multiply

Now, multiply the result of the parentheses by \( -5 \): \(-5 * -3 \).

Step 4: Calculate

Finally, calculate the multiplication: \(-5 * -3 = 15 \).

Key Concepts

Understanding Parentheses

Parentheses in mathematics are used to indicate operations that should be performed first. They help in organizing expressions and ensure the correct order of operations is followed.
The general rule states that you should always start with the operations inside the parentheses before moving on to other calculations.
For example, in the problem \(-5(4-7)\), we first need to simplify the expression inside the parentheses, \(4-7\). By doing this, we can break down complex expressions into simple steps:

• Look for parentheses and solve the expression inside them first.

Following this step-by-step guarantees accurate results and avoids confusion.

How Multiplication Works

Once we've simplified the expression inside the parentheses, the next step is to handle the multiplication. In our example, the simplified expression is \(-3\). Now we move on to multiplying it with \(-5\).
Multiplication is a mathematical operation used to find the total number of objects in a given number of groups. The multiplication of two negative numbers results in a positive number, a key rule to remember.
Therefore, \(-5 \times -3 \) becomes \(-5 \times -3 = 15\).
Important points about multiplication:

• Multiplying two positive numbers or two negative numbers results in a positive product.
• Multiplying a positive number by a negative number results in a negative product.

This rule is crucial when dealing with both integers and more complex algebraic expressions.

Simplification Process

Simplification in math involves reducing an expression to its simplest form. This makes it easier to understand and solve. In our exercise \(-5(4-7)\), we simplified the expression in two main steps:

• First, we simplified the inside of the parentheses: \(4-7 = -3\).
• Second, we multiplied the simplified result by \(-5\).
• Finally, we found the result: \(-5 \times -3 = 15\).

Simplification is essential for tackling more complex equations and making calculations manageable.
Always remember to:

• Work step-by-step.
• Pay close attention to signs (plus and minus).
• Double-check your work for accuracy.

Simplifying step-by-step ensures that no errors are made and that you arrive at the correct solution.