Problem 47 - Algebra 2

Question

Find the value of each expression. $$ -5(3-18) $$

Step-by-Step Solution

Answer

The expression evaluates to 75.

Step 1: Solve the Expression Inside Parentheses

First, identify and solve the mathematical operation inside the parentheses. In this expression, we need to calculate \((3 - 18)\). Subtract 18 from 3 to get \(-15\).

Step 2: Multiply the Result by -5

Now, take the result from Step 1, which is \(-15\), and multiply it by \(-5\). Calculate \(-5\times(-15)\). Since a negative multiplied by a negative gives a positive, the result is \(75\).

Key Concepts

Parentheses in Algebra

When working with algebraic expressions, parentheses play a crucial role in determining the order of operations. Parentheses are used to group parts of an expression that need to be calculated first. This is important because it influences how the entire expression is simplified or calculated.

Think of parentheses as instructing you to focus your attention there before tackling the rest of the equation. For example, in the expression \(-5(3 - 18)\), the subtraction inside the parentheses is done first. Here’s a quick breakdown:

• First, look inside the parentheses: \(3 - 18\)
• Calculate \(3 - 18\), which equals \(-15\)

Once the parentheses are resolved, you can move on to other operations like multiplication.

Negative Numbers

Negative numbers can be tricky but knowing how to handle them is vital in algebra. In our exercise, -5 is a negative number, as is the result from our parentheses, -15.

One important rule with negative numbers is that the closer a number is to zero on the negative side, the larger it is in value. That can sometimes cause confusion.

When subtracting with negatives, you essentially add the opposite. For instance:

• \((3 - 18) = -15\)
• We are subtracting 18 — essentially adding \(-18\) to 3.

Understanding this behavior can help prevent mistakes in calculations involving negative numbers.

Multiplication Rules

Understanding the rules of multiplication and their interaction with negative numbers is key in algebra.

A straightforward rule is that multiplying two negative numbers results in a positive number.

In our example of \(-5 \times -15\), we deal with two negatives:

• When you multiply \(-5\) by \(-15\), you receive a positive result, \(75\).
• Negative times negative equals positive — always remember this rule.

Additionally, multiplying a negative by a positive number results in a negative number and vice versa. Mastering these basics helps tackle more complex problems without tripping over the basic arithmetic.