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Chapter 1: Problem 23

Multiply or divide as indicated. See Examples 4 and 5 . $$ \frac{-9}{3} $$

Short Answer

Expert verified
The result of \( \frac{-9}{3} \) is \(-3\).

Step by step solution

01

Identify the operation

The given expression \( \frac{-9}{3} \) involves division. This fraction indicates that we need to divide \(-9\) by \(3\).
02

Perform the division

To divide \(-9\) by \(3\), divide the absolute values first: \(9 \div 3 = 3\). Since the original number \(-9\) is negative and \(3\) is positive, the result will be negative. Therefore, the result of \(-9 \div 3\) is \(-3\).

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Key Concepts

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

Negative Numbers
Negative numbers are a fundamental part of mathematics and appear frequently in everyday life. They are numbers less than zero and are often associated with loss, decrease, or opposite directions.
For example, if you owe someone money, you might think of that as negative dollars.
When working with negative numbers in mathematical operations like division or multiplication, it is crucial to pay attention to the signs of the numbers involved:
  • **Positive divided by positive** equals a positive result.
  • **Negative divided by positive** results in a negative outcome.
  • **Positive divided by negative** also gives a negative result.
  • **Negative divided by negative** produces a positive result.
This rule also applies to multiplication. Understanding this sign rule is important for correctly solving problems involving negative numbers.
Absolute Value
Absolute value is a concept that measures the distance of a number from zero on the number line, without considering its direction. It is denoted by two vertical bars around the number, such as \(|-9|\).
The absolute value of a number is always non-negative because it describes magnitude without regard to sign. For example:
  • The absolute value of \( -9 \) is 9, denoted as \(|-9| = 9\).
  • Similarly, the absolute value of 9 is 9, written as \(|9| = 9\).
When dividing or multiplying negative numbers, it's often helpful to calculate with absolute values first and then apply the rules of negative numbers for the sign of the result.
This approach simplifies the calculation and reduces mistakes.
Fractions
Fractions represent parts of a whole and are composed of two numbers: the numerator (top part) and the denominator (bottom part). For the fraction \(\frac{-9}{3}\),
  • The **numerator** is \(-9\), which signifies the number of parts being considered.
  • The **denominator** is \(3\), representing the total number of equal parts into which the whole is divided.
Fractions can also indicate division, where the numerator is divided by the denominator. In this case, \(-9\) divided by 3 is calculated.
When dealing with fractions, it is essential to understand their properties:
  • If both the numerator and denominator have the same sign, the fraction is positive.
  • If the signs differ, the fraction is negative.
For \(\frac{-9}{3}\), since the numerator is negative and the denominator is positive, the result is a negative fraction. Understanding these basic properties and rules helps in performing operations with fractions accurately.

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Most popular questions from this chapter

In your own words, explain why every natural number is also a rational number but not every rational number is a natural number.

Evaluate each expression when \(x=9\) and \(y=-2 .\) See Example 12 $$ \frac{5+2|y-x|}{x+6 y} $$

Simplify each expression. See Examples \(11,14,\) and \(15 .\) $$ -9+4 x+18-10 x $$

Evaluate each expression when \(x=9\) and \(y=-2 .\) See Example 12 $$ 4 x-10 y $$

Simplify each expression. See Examples I through 11 . $$ \frac{-\sqrt{16}-(6-2.4)}{-2} $$
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