/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 44 Perform the operations. See Exam... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 44

Perform the operations. See Examples 4 and 5 . $$ \frac{-13.5}{-1.5} $$

Short Answer

Expert verified
The result of \(\frac{-13.5}{-1.5}\) is 9.

Step by step solution

01

Identify the Operation

The problem involves dividing two numbers, specifically dividing \(-13.5\) by \(-1.5\). This is a division operation.
02

Understand the Division Rule for Signs

When dividing two negative numbers, the quotient is positive. So, \(\frac{-a}{-b} = \frac{a}{b}\). Therefore, this operation simplifies to \(\frac{13.5}{1.5}\).
03

Perform the Division

Now, divide 13.5 by 1.5. To simplify, notice that 1.5 fits into 13.5 exactly 9 times. Thus, \(\frac{13.5}{1.5} = 9\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers that are less than zero. They are represented with a minus sign (-) in front of them. Negative numbers have unique properties that distinguish them from positive numbers. For example, when you multiply or divide two negative numbers, the result is a positive number.
Negative numbers are often used to represent values that are below a set reference point, like sea level or temperatures below zero. In mathematics, using negative numbers allows us to broaden our ability to calculate and understand different types of problems.
The Meaning of Quotient
In division, the quotient is the result you get when you divide one number by another. It's the answer to a division problem. For instance, if you divide 10 by 2, the quotient is 5. In our exercise, \(\frac{-13.5}{-1.5}\), the quotient is calculated by performing the division operation on the numerical values.
  • The divisor is the number you divide by. In \(\frac{-13.5}{-1.5}\), \-1.5\ is the divisor.
  • The dividend is the number divided, which in our example is \(-13.5\).
  • The quotient is the answer that you find on performing the division, which turns out to be 9.
Understanding what the quotient represents is vital. It provides a snapshot of how many times the divisor fits into the dividend.
Division Rule for Signs
The division rule for signs is an important principle in mathematics, especially when dealing with negative numbers. The rule dictates the sign of the quotient based on the signs of the numbers being divided:
  • When you divide two positive numbers, the quotient is positive.
  • When you divide two negative numbers, the quotient is also positive. This aligns with our exercise result where \(\frac{-13.5}{-1.5}\) turns into \(\frac{13.5}{1.5} = 9\).
  • If one number is positive and the other is negative, the quotient will be negative.
Memorizing this rule helps in quickly determining the sign of the answer without needing to rely only on computational steps.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Complete each property of addition. Then give its name. a. \(a+(-a)=\square\) b. \(a+0=\square\) c. \(a+b=b+\square\) d. \((a+b)+c=a+\square\)

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -6.07 \quad-\frac{17}{6} $$

Solve each equation. $$ \frac{2}{3}(3 m-2)=\frac{3}{4} m+\frac{11}{12} $$

Perform the operations. See Example 3 . $$ -9(-1)(-3) $$

Solve for the specified variable. $$ I_{Q}=\frac{100 M}{C} \text { for } C $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.