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Chapter 2: Problem 7

Multiply. See Examples 1 through 4. $$ 0(-11) $$

Short Answer

Expert verified
The product is 0.

Step by step solution

01

Identify the Numbers to Multiply

We need to multiply two numbers: 0 and -11. The multiplication involves one of the numbers being zero, which is an important part of the multiplication rules.
02

Apply the Zero Property of Multiplication

The Zero Property of Multiplication states that any number multiplied by zero is zero. So, when we multiply 0 by -11, we will get 0.

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Key Concepts

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

Multiplication
Multiplication is one of the four basic arithmetic operations, just like addition, subtraction, and division. It involves combining groups of equal sizes. In simple terms, if you multiply a number by another number, you are essentially adding that number to itself repeatedly. For example:
  • 4 multiplied by 3 (\(4 \times 3\)) means adding 4 three times: 4 + 4 + 4, which equals 12.
  • In mathematical terms, it is represented by the symbols 'x' or '*', but often left implied with parentheses, like \((ab)\).
When performing multiplication, it is essential to remember properties like the commutative property, where \(a \times b = b \times a\). This means numbers can be multiplied in any order and yield the same result.
Negative Numbers
Negative numbers are numbers less than zero and are represented with a minus sign (e.g., -1, -2, -3, etc.). These numbers have specific rules when involved in arithmetic operations, especially multiplication.
  • Multiplying a positive number by a negative number results in a negative product. For instance, \(3 \times -2 = -6\).
  • Conversely, multiplying two negative numbers yields a positive product, such as \(-2 \times -3 = 6\).
  • Moreover, any negative number multiplied by zero will always produce zero, illustrating the zero property of multiplication.
Understanding how negative numbers interact in multiplication is crucial in solving more complex equations and mathematical problems.
Basic Arithmetic Concepts
The foundations of arithmetic are crucial in understanding more complex mathematical relationships. Basic arithmetic includes operations like addition, subtraction, multiplication, and division. Among these, multiplication has several fundamental properties:
  • Commutative Property: Order does not affect the outcome (\(a \times b = b \times a\)).
  • Associative Property: Grouping doesn鈥檛 change the product (\((a \times b) \times c = a \times (b \times c)\)).
  • Distributive Property: Distributing multiplication over addition (\(a \times (b + c) = (a \times b) + (a \times c)\)).
  • Zero Property: Any number multiplied by zero results in zero, which was effectively demonstrated in the original exercise, \(0 \times -11 = 0\).
These properties help simplify and solve arithmetic problems efficiently. Building a strong understanding of these concepts is vital for students, as they serve as the cornerstones for more advanced mathematical computations and problem-solving scenarios.

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Most popular questions from this chapter

Find the opposite of each integer. $$ -85 $$

Insert \(<\) or \(>\) between each pair of integers to make a true statement. $$ -12 \quad-10 $$

Simplify. $$ -|-18| $$

Insert \(<,>,\) or \(=\) between each pair of numbers to make a true statement. $$ 0 \quad-9 $$

Write the given numbers in order from least to greatest. $$ 2^{2},-|3|,-(-5),-|-8| $$
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