Problem 103 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ -3(-5)(6) $$

Step-by-Step Solution

Answer

90

Step 1: Multiply the first two numbers

Start by multiplying the first two numbers: \(-3\) and \(-5\). When multiplying two negative numbers, the result is positive. So, \(-3 \times -5 = 15\).

Step 2: Multiply the result by the third number

Take the result from Step 1, which is \(15\), and multiply it by the third number: \(6\). So, \(15 \times 6 = 90\).

Step 3: Write the final simplified expression

The result from Step 2 gives the simplified expression. Thus, \(-3(-5)(6) = 90\).

Key Concepts

multiplying negative numbers

When multiplying negative numbers, it's essential to remember a few basic rules.
Negative times negative equals positive.
Negative times positive equals negative.
For example, in the problem \(-3(-5)(6)\), the first step is to multiply \(-3\) by \(-5\). Since both numbers are negative, their product is positive. So, \-3 \times -5 = 15\. This result might seem counterintuitive at first, but think of it as reversing a reversal.
Negative numbers act like a reversal on the number line. Reversing twice (negative times negative) brings us back to the positive side.
This is crucial for simplifying expressions correctly. If in doubt, always go back to these rules!

step-by-step problem solving

Breaking down problems into smaller steps makes them much easier to solve. Let's take a closer look at the step-by-step method used to solve \(-3(-5)(6)\).
Step 1: Multiply the first two numbers \(-3\) and \(-5\) to get a positive result, which is \15\.
Step 2: Take the result from Step 1 and multiply it by the next number. So, \15 \times 6 = 90\.
Step 3: Write the final simplified expression. The answer is \90\.
This approach ensures that we tackle one operation at a time, reducing the possibility of mistakes. Always check each step before moving to the next, and practice makes perfect. Try breaking down similar problems using this method to enhance your skills.

basic multiplication

Understanding basic multiplication is the key to solving more complex expressions like \(-3(-5)(6)\).
Multiplication is essentially repeated addition. When you multiply \3 \times 5\, you are adding \3\ five times: \3 + 3 + 3 + 3 + 3 = 15\. When incorporating negative numbers, remember that:

• Negative times negative equals positive
• Negative times positive equals negative
• Positive times positive equals positive

The expression \(-3(-5)(6)\) follows these rules. Start by multiplying the negatives to get a positive, then continue with straightforward multiplication.
Practice and familiarity with these rules will make even the trickiest problems easier to manage.