Problem 10 - Introductory Algebra for College Students

Question

perform the indicated multiplication. $$0(-11)$$

Step-by-Step Solution

Answer

The result of the multiplication 0(-11) is 0

Step 1: Multiplication of a number with zero

From the basic rule of multiplication, it states that any real number, when multiplied by zero, always produces the result as zero. Hence, multiplying \(0\) with \(-11\) would also provide the result as zero.

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Step 6: Conclude with the answer

The result of the multiplication 0(-11) is 0

Key Concepts

Multiplication Rules

In multiplication, several important rules help us understand how numbers interact with each other. One of the most fundamental rules is the zero property of multiplication. This rule states that any number multiplied by zero equals zero. It doesn’t matter if the number is positive, negative, or even a fraction; the result will always be zero.

• Zero property of multiplication: Any real number × 0 = 0
• Commutative property: Changing the order of factors does not change the product, e.g., a × b = b × a.
• Associative property: The way in which numbers are grouped does not change the product, e.g., (a × b) × c = a × (b × c).

These rules simplify calculations and allow us to solve complex problems more easily. They are fundamental, making the foundation of multiplication solid and consistent for real numbers.

Real Numbers

Real numbers include all the numbers that can be found on the number line. This means it includes positive numbers, negative numbers, and zero. Real numbers can be whole numbers, fractions, or decimals. Some key points about real numbers include:

• They are divided into rational numbers (such as fractions and integers) and irrational numbers (such as the square root of 2 and pi).
• In arithmetic, real numbers allow us to perform operations like addition, subtraction, multiplication, and division consistently.
• Real numbers adhere strictly to the properties of multiplication, including the zero property, making calculations with them reliable and predictable.

Understanding real numbers helps in recognizing how they interact with various arithmetic operations, including multiplication. It is crucial to grasp these concepts as they are applied in everyday mathematics.

Basic Arithmetic

Basic arithmetic forms the backbone of mathematics and consists of simple operations: addition, subtraction, multiplication, and division. Multiplication, as highlighted in the exercise about zero, is crucial because it shows how combining quantities can be simplified. In basic arithmetic:

• Addition results in the total of numbers combined.
• Subtraction represents the difference between numbers.
• Multiplication summarizes repeated addition or scaling a number by another.
• Division calculates how many times one number fits into another.

These operations are foundational for more complex mathematics and practical tasks like budgeting, cooking, and problem-solving. Mastering basic arithmetic ensures a smoother transition to advanced mathematical concepts and applications.