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Chapter 1: Problem 91

Multiply. $$ (-17.45) \cdot 0 $$

Short Answer

Expert verified
The result is zero.

Step by step solution

01

Identify the Multiplication Rule

Any number multiplied by zero is equal to zero. This is a fundamental property of multiplication.
02

Apply the Rule

Since \((-17.45) \cdot 0\) involves multiplying a number by zero, we can apply the rule identified in Step 1.
03

Calculate the Result

Multiplying \(-17.45\) by zero yields \((-17.45) \cdot 0 = 0\). This is because anything times zero is zero.

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Key Concepts

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

Multiplication Rules
Multiplication is one of the basic operations in arithmetic and understanding its rules is fundamental. There are several key rules to remember:
  • The product of two positive numbers is positive.
  • The product of two negative numbers is positive.
  • The product of a positive number and a negative number is negative.
  • Any number multiplied by one remains the same.
  • And importantly for our exercise, any number multiplied by zero is zero.
These rules help us predict the outcome of multiplication, even without doing the calculation.
Knowing these rules makes solving multiplication problems quicker and easier.
Property of Zero
The property of zero states that any number multiplied by zero is zero. This is also known as the 'zero property of multiplication.' It's a fundamental rule in algebra and arithmetic.
Here's why this property is useful:
  • It simplifies calculations drastically. For instance, in our exercise, \(-17.45 \times 0\) immediately equals zero without needing extra steps.
  • It holds universally, meaning it applies not only to real numbers but also to variables and algebraic expressions.
Remembering this property can save you time and help you avoid mistakes in your calculations.
Basic Arithmetic
Basic arithmetic is the foundation of all math. It includes addition, subtraction, multiplication, and division.
Here are some key points about basic arithmetic:
  • Addition is combining numbers to get a sum.
  • Subtraction is taking one number away from another.
  • Multiplication is adding a number to itself a certain number of times.
  • Division is splitting a number into equal parts.
For our exercise, we focus on multiplication. Understanding that multiplication is repetitive addition shows why the property of zero works. Anything multiplied zero times (added zero times) is nothing, or zero.
These operations are building blocks for more complex math topics. Mastering them is crucial for progressing in your math journey.

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Most popular questions from this chapter

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \left|2^{2}-7\right|^{3}+4 $$

Find an equivalent expression by factoring. $$ a b+b $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 196 \in \mathbb{N} $$

Write an equivalent expression using the distributive law. $$ 5 x(y-z+w) $$

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{W} \subseteq Z $$
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