Problem 18 - Prealgebra

Question

Find each of the following products. (Multiply.) $$-4(5)(-6)$$

Step-by-Step Solution

Answer

The product is 120.

Step 1: Understand the Expression

We need to find the product of the numbers \(-4\), \(5\), and \(-6\). This means we will multiply them together. Identify the expression and look for basic multiplication of three numbers together.

Step 2: Multiply the First Two Numbers

First, multiply the two numbers at the beginning of the expression: \(-4 imes 5\). Calculate \(-4 imes 5 = -20\).

Step 3: Multiply the Result with Third Number

Next, take the result of \(-20\) and multiply it by the third number, which is \(-6\). So, calculate \(-20 imes -6\).

Step 4: Determine the Result of Multiplying Negative Numbers

When multiplying negative numbers, the product of two negative numbers is positive. Calculate \(-20 imes -6 = 120\).

Step 5: Final Result

The final result of multiplying all three numbers \(-4 imes 5 imes -6\) is \(120\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are essential in representing values below zero, like temperatures, debts, or elevations below sea level. The key characteristic of negative numbers is the negative sign (-) that appears in front of them. This sign indicates the number is below zero. Understanding negative numbers is crucial for many areas of mathematics, including algebra and calculus.

Here are some important properties of negative numbers:

• They are less than zero.
• They have a negative sign "-" placed in front of them.
• When added to a positive number, they can decrease the positive number's magnitude.
• Two negative numbers multiplied together result in a positive number.
• Multiplying a negative number by a positive number results in a negative number.

Negative numbers are used in real-life scenarios such as indicating loss or decrease. For example, if you withdraw money from your account, the balance might go negative, indicating a negative number.

Multiplying Negative and Positive Numbers

When you multiply negative and positive numbers, there are specific rules that you need to remember. These rules help determine the sign of the final product.

The rules for multiplying negative and positive numbers are:

• A positive number multiplied by a positive number results in a positive product.
• A negative number multiplied by a positive number results in a negative product.
• A negative number multiplied by another negative number results in a positive product.

For instance, consider this multiplication: - If we have \(-4 \times 5\), this pair has a negative and a positive number, so the product is negative, \(-20\).- Then, \(-20 \times -6\) involves multiplying two negative numbers, resulting in a positive \(120\).Remembering these rules will make solving multiplication problems involving negative numbers easier. Always check the number of negative signs to determine if the final product will be positive or negative.

Prealgebra Concepts

Prealgebra lays the groundwork for more advanced levels of mathematics such as algebra, geometry, and beyond. It's like the first step in a staircase, setting a stable base for future learning.

The primary focus of prealgebra is:

• Understanding and using numbers, including fractions, decimals, and negative numbers.
• Developing skills in basic operations, such as addition, subtraction, multiplication, and division.
• Learning to solve simple equations and expressions.
• Grasping the relations between numbers, such as factors, multiples, and prime numbers.
• Basic understanding of ratios, proportions, and percentages.

These concepts help students build confidence in math and prepare them for more complex topics in algebra. By mastering these foundational skills, students gain the ability to tackle challenges they might face in higher mathematics. Prealgebra is essential, even in solving exercises like multiplying \(-4 \times 5 \times -6\), where understanding how negative and positive numbers interact is crucial.