Problem 15 - Prealgebra

Question

Find each of the following products. (Multiply.) $$3.3(-2)(4)$$

Step-by-Step Solution

Answer

The product is -26.4.

Step 1: Multiply the first two numbers

Let's start by multiplying the first two numbers: 3.3 and -2. Remember, when multiplying a positive number by a negative number, the product is negative. So, we calculate: \[3.3 \times (-2) = -6.6\]

Step 2: Multiply the result by the third number

Now, take the result from Step 1, which is -6.6, and multiply it by the third number, 4. Again, remember that multiplying a negative number by a positive number gives a negative result: \[-6.6 \times 4 = -26.4\]

Key Concepts

Understanding Negative Numbers

Negative numbers might seem a bit intimidating at first, but they're just like any other numbers with one simple twist—they're on a different side of zero. You can picture them on a number line where zero is in the middle, positive numbers go to the right, and negative numbers venture to the left.

• Negative numbers are less than zero. On a number line, they're found to the left of zero.
• When dealing with real-world scenarios, think of negative numbers as something owing or below zero, like depths below sea level or temperatures below freezing.
• Multiplying a negative by a positive results in a negative because you're essentially flipping the direction on the number line.
• Multiplying two negatives results in a positive because the two flips cancel each other out.

Having a clear picture of what negative numbers represent and how they interact with other numbers makes them much less daunting.

The Basics of Multiplication

Multiplication is one of the foundational operations in math. Think of it as a shortcut for addition. Instead of adding the same number over and over, multiplication lets you do it in one step.

• Multiplication involves two numbers called factors that come together to form a product.
• For example, in the expression \(3.3 \times (-2)\), the numbers 3.3 and -2 are factors, and -6.6 is the product.
• Multiplication is commutative, which means the order of the numbers doesn't matter, so \(a \times b = b \times a\).
• When multiplying decimals and negatives, remember to account for the sign and place value. You can temporarily ignore the negative sign, just multiply the absolute values and then re-apply the negative sign at the end where necessary.

Understanding these fundamentals makes more complex multiplication, such as involving decimals and negative numbers, easier.

Step by Step Multiplication

Sometimes math problems can seem overwhelming, especially when they involve negative numbers or decimals. Breaking them down into smaller, more manageable steps helps clarify the process.

Let's take the example: \(3.3(-2)(4)\). Here's how you can break it down:

1. **First Step – Multiply the First Two Numbers**: Start with the first two numbers. Here, you multiply 3.3 and -2. When multiplying a positive by a negative, the result is negative, so 3.3 \times (-2) equals -6.6.

2. **Second Step – Combine with the Third Number**: Now take -6.6 and multiply it by 4. Once again, you are multiplying a negative by a positive, which yields another negative result.

• The outcome of -6.6 \times 4 is -26.4.

Following these steps lets you solve complex products systematically by focusing on one multiplication at a time. Doing this ensures accuracy and helps you understand how each part contributes to the final answer.