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Chapter 1: Problem 45

Multiply. $$ (-31) \cdot(-27) \cdot 0 $$

Short Answer

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Step by step solution

01

Apply the Zero Property of Multiplication

First, notice that one of the factors in the multiplication is 0. According to the Zero Property of Multiplication, any number multiplied by 0 equals 0.
02

Calculate the Product

Multiply the numbers together. Because \((-31) \cdot (-27) \cdot 0 = 0\), the result is zero. No need to perform the multiplication of the other numbers, as any number multiplied by 0 is always 0.

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Key Concepts

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

Multiplication
Multiplication is a fundamental arithmetic operation where numbers, called factors, are combined to get a product. It's essentially repeated addition. For instance, multiplying 2 by 3 means adding 2 three times (2 + 2 + 2). Multiplication is represented by the symbol \(*\) or sometimes \((\cdot)\). In the exercise, \((-31) \cdot (-27) \cdot 0\), each number is a factor. Here, you'll get a product by multiplying these three factors together.
Zero Property
The Zero Property of Multiplication states that any number multiplied by zero results in zero. This is a crucial rule in mathematics that simplifies calculations. In the exercise, \((-31) \cdot (-27) \cdot 0\), you immediately know the answer is zero without needing to multiply \(-31\) and \(-27\). Why? Because one factor is zero. The moment you multiply anything by zero, the product is always zero. This property is key to quickly solving multiplication problems involving zero.
Algebra
Algebra involves using symbols and letters to represent numbers and express mathematical relationships. In this exercise, knowing algebraic rules like the Zero Property of Multiplication can make solving problems faster. You don't need to compute unnecessary multiplications once you spot a zero. Algebra helps us understand and apply these properties systematically, making math more efficient and organized. Remembering these principles can save time and effort in solving various problems.

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Most popular questions from this chapter

A gambler loses a wager and then loses "double or nothing" (meaning the gambler owes twice as much) twice more. After the three losses, the gambler's assets are \(-\$ 20 .\) Explain how much the gambler originally bet and how the \(\$ 20\) debt occurred.

Evaluate. $$ \frac{a^{3}-4 a}{a(a-3)}, \text { for } a=-2 $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ |13.5+8(-4.7)|^{3} $$

List in order from least to greatest. $$-\frac{2}{3}, \frac{1}{2},-\frac{3}{4},-\frac{5}{6}, \frac{3}{8}, \frac{1}{6}$$

List in order from least to greatest. $$-23,4,0,-17$$
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