Problem 22 - Elementary Algebra

Question

Find the value of each of the following expressions. $$ (4)(-18) $$

Step-by-Step Solution

Answer

Answer: -72

Step 1: Identify the numbers

In this expression, we have two numbers to multiply: 4 and -18.

Step 2: Perform multiplication

Now, we simply need to multiply these two numbers together: $$ (4) (-18) = -72 $$

Step 3: Write down the final answer

So, the value of the expression \((4)(-18)\) is equal to -72.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-) before them, such as -1, -18, or -5. They are very common in mathematics and can represent various real-world scenarios. For example, negative numbers are often used to signify debt or temperatures below zero.

When it comes to multiplication involving negative numbers, there are specific rules to remember:

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

By understanding these basic rules, you can easily perform calculations that involve negative numbers and avoid common mistakes.

Mastering Integer Operations

Integer operations encompass addition, subtraction, multiplication, and division with integers. Integers include all positive and negative whole numbers, as well as zero. Operations with integers follow specific rules, particularly when it comes to negative numbers.

With integer multiplication, the sign of the product is determined by the signs of the multiplicands:

• If both numbers are positive, the product is positive.
• If one number is positive and the other is negative, the product is negative.
• If both numbers are negative, the product is positive.

For example, in the expression \(4\) (-18), we multiply a positive integer by a negative integer, resulting in \(-72\). This follows the rule that multiplying a positive number and a negative number results in a negative product.

Simplifying Algebraic Expressions

An algebraic expression is a combination of numbers, variables (like \( x \) or \( y \)), and operations (like addition, subtraction, multiplication, and division). While the exercise we looked at does not include variables, understanding how to handle numbers, particularly negative ones, is crucial.

When simplifying expressions with multiplication, the same rules apply whether dealing with plain numbers or terms that include variables. Consider this expression: \( 3x(-2) \). By understanding integer rules, this expression simplifies to \(-6x\).

Key steps to simplify expressions include:

• Identifying and grouping like terms.
• Applying the basic arithmetic operations, respecting rules for negative numbers.
• Double-check for accuracy by reviewing the multiplication rules outlined earlier.

Breaking down an expression into smaller, manageable parts can make the simplification process straightforward and manageable.