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Chapter 1: Problem 19

Multiply or divide as indicated. See Examples 4 and 5 . $$ -17 \cdot 0 $$

Short Answer

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Step by step solution

01

Understanding the Problem

The problem asks us to multiply -17 by 0. We are simply required to perform a multiplication operation between the two given numbers.
02

Applying the Multiplication Rule

Recall that any number multiplied by 0 results in 0. Here, since we are multiplying -17 by 0, the rule still holds true regardless of the sign of the number being multiplied.
03

Perform the Multiplication

By applying the multiplication rule, calculate \( -17 \cdot 0 \). Using the rule explained, this results in \( 0 \).

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Key Concepts

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

Zero Property of Multiplication
When learning basic math concepts, the zero property of multiplication is a fundamental rule to understand. This rule states that any number, regardless of its sign or value, multiplied by zero will always result in zero.

This is because zero signifies nothingness or the absence of quantity, so multiplying something by nothing naturally results in nothing. For example, no matter if you multiply positive numbers like 50 or negative numbers like -200 by zero, the answer will always be zero.

Just remember:
  • Zero multiplied by any number equals zero: \[\ a \times 0 = 0 \quad \text{or} \quad 0 \times a = 0\ \]
  • The result is always zero, without exceptions.
Integer Multiplication
Understanding integer multiplication lays the groundwork for mastering arithmetic. Integers include all positive and negative whole numbers, as well as zero. Multiplication of integers follows specific rules and is an extension of repeated addition.

For instance:
  • If you multiply two positive integers, like 4 and 3, (\(4 \times 3\)), you add 4 three times or 3 four times, resulting in 12.
  • When you multiply a negative integer by a positive integer, like (-4) by 3, it means subtracting 4 three times, resulting in -12 (\(-4 \times 3 = -12\)).
  • If two negative integers multiply, such as (-2) and (-3), the negatives cancel out, and the result is a positive integer: (\(-2 \times -3 = 6\)).

These principles are vital for efficient problem-solving in mathematics. Whenever multiplying integers:
  • Remember, the product of a negative and a positive number is negative.
  • The product of two negative numbers is positive.
Multiplication of Negative Numbers
The multiplication of negative numbers introduces some important principles that might seem tricky at first. But once grasped, they become straightforward.

It's essential to understand that when you multiply two negative numbers, the result is always a positive number. This might sound counterintuitive, but it helps to think of it in terms of reversing a direction twice, which sets you back on the original path.

For example, -5 times -4 results in 20:
  • Imagine reversing the direction (negative) and then reversing again (negative) which places you back in the original direction (positive).

In short, whenever you are multiplying negative numbers:
  • The product of two negative numbers is positive.
  • The product of a negative number and a positive number is negative.
  • Understanding this concept helps in solving more complex mathematical problems with ease.

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Most popular questions from this chapter

Employees at Walmart constantly reorganize and reshelve merchandise. In doing so, they calculate floor space needed for displays The algebraic expression \(l \cdot w\) gives the floor space needed in square units for a display that measures length \(l\) units and width \(w\) units. Calculate the floor space needed for a display whose length is 5.1 feet and whose width is 4 feet.

The highest point on land on Earth is the top of Mt. Everest in the Himalayas, at an elevation of \(29,028\) feet above sea level. The lowest point on land is the Dead Sea, between Israel and Jordan, at 1319 feet below sea level. Find the difference in elevations.

Graph each set on a number line. $$ \left\\{-\frac{1}{3},-1 \frac{1}{3}\right\\} $$

The following graph is called a broken-line graph,or simply a line graph. This particular graph shows the past, present, and future predicted U.S. population over 65. Just as with a bar graph, to find the population over 65 for a particular year, read the height of the corresponding point. To read the height, follow the point horizontally to the left until you reach the vertical axis. (GRAPH CANNOT COPY) The percent of Americans over 65 in 1950 was \(8.1 \%\). The percent of Americans over 65 in 2050 is expected to be 2.5 times the percent over 65 in \(1950 .\) Estimate the percent of Americans expected to be over age 65 in 2050 .

Write each of the following as an algebraic expression. See Examples 12 and 13. If the measure of an angle is \(5 x\) degrees, represent the measure of its complement as an expression in \(x\).
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