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Chapter 1: Problem 10

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

Short Answer

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

Step by step solution

01

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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鈥檛 matter if the number is positive, negative, or even a fraction; the result will always be zero.
  • Zero property of multiplication: Any real number 脳 0 = 0
  • Commutative property: Changing the order of factors does not change the product, e.g., a 脳 b = b 脳 a.
  • Associative property: The way in which numbers are grouped does not change the product, e.g., (a 脳 b) 脳 c = a 脳 (b 脳 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.

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Most popular questions from this chapter

Simplify each series of additions and subtractions. $$-1.9-3-(-0.26)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I found the variation in U.S. temperature by subtracting the record low temperature, a negative number, from the record high temperature, a positive number.

Simplify each series of additions and subtractions. $$-6-2+3-10$$

Perform the indicated subtraction. $$1.4-(-1.4)$$

Simplify each series of additions and subtractions. $$-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$$
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