Problem 92 - Elementary Algebra

Question

Simplify. (-16) 3

Step-by-Step Solution

Answer

-48

Step 1: Identify the Operation

The question asks us to simplify the expression (-16) 3. This expression represents multiplication between -16 and 3.

Step 2: Multiply the Numbers

Multiply the absolute values of the two numbers: \( 16 \times 3 = 48 \)

Step 3: Determine the Sign

Since one number is negative (-16) and the other number is positive (3), the product will be negative. Thus, the result will be \(-48\).

Step 4: Combine Result

Combine the results from steps 2 and 3 to arrive at the final simplified form of the expression:\((-16) \times 3 = -48\)

Key Concepts

Integer Operations

Understanding integer operations is essential for solving problems involving whole numbers. In mathematics, operations such as addition, subtraction, multiplication, and division are performed on integers.

• Integer multiplication, like the one in our exercise, involves determining the product of two or more integers.
• It is crucial to remember that integers can be either positive, negative, or zero.
• When multiplying integers, you must consider both the sign and the absolute values of the numbers involved.

In the simple multiplication of integers such as (-16) 3, you need to:

• Multiply the absolute values: Ignore the signs for a moment and focus on multiplying the numbers themselves.
• Determine the sign of the product: This depends on the signs of the integers involved.

Mastering operations with integers will improve your ability to tackle various math problems confidently.

Negative Numbers

Negative numbers are integral in the world of mathematics just as positive numbers are. They are numbers less than zero and are typically denoted by a minus sign (-).

• Understanding negative numbers is fundamental when dealing with operations, as they affect the outcome significantly.
• In multiplication, a negative number changes the sign of the product if the other factor is positive, as demonstrated in our exercise with (-16) 3.
• Multiplying a negative number by a positive one results in a negative product.
• Conversely, multiplying two negative numbers results in a positive product.

Grasping this concept helps in recognizing patterns and solving algebraic expressions effectively.

Absolute Values

Absolute values represent the magnitude of a number regardless of its sign. It can be thought of as the distance of a number from zero on the number line.

• The absolute value of a negative number is its positive counterpart, and the absolute value of a positive number remains unchanged.

For instance:

• The absolute value of -16 is 16: \(|{-16}| = 16\).
• When multiplying integers such as in our exercise, first calculate using their absolute values.
• Only after multiplying, apply the sign rule based on whether the original integers were positive or negative.

Understanding absolute values provides clarity and precision in mathematical operations involving positives and negatives.