/*! 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 42 Find each quotient. \(\frac{38... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 42

Find each quotient. \(\frac{38}{-19}\)

Short Answer

Expert verified
-2

Step by step solution

01

Identify the Numbers

In this step, identify the numbers involved in the division. Here, the two numbers are 38 and -19.
02

Consider the Signs

When dividing numbers with different signs, the quotient will be negative. In this case, you have positive 38 and negative -19, so the result will be negative.
03

Divide the Absolute Values

Ignore the signs for a moment and divide the absolute values of the numbers. Calculate \(\frac{38}{19}\). The result is 2.
04

Apply the Correct Sign

Since you are dividing a positive number by a negative number, the final quotient should be negative. Therefore, \(\frac{38}{-19} = -2\).

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.

Quotient
Let's start by understanding what a quotient is. A quotient is the result you get when you divide one number by another. In the exercise provided, you are asked to find the quotient of \(\frac{38}{-19}\). This simply means, you need to see how many times one number (the divisor) goes into another number (the dividend). In this case, the dividend is 38 and the divisor is -19.
The quotient can be a whole number, a fraction, or even a negative number, depending on the numbers you are dividing.
Absolute Values
Absolute value is the non-negative value of a number without considering its sign. It tells you how far a number is from zero. For instance, the absolute value of both 38 and -19 is 38 and 19, respectively.
When you need to divide numbers, considering absolute values can simplify the process. In our exercise, even though we are dealing with 38 and -19, we temporarily ignore the signs and consider only 38 and 19. This makes our division straightforward: \(\frac{38}{19} = 2\).
Only after dividing the absolute values do we reapply the sign based on the original numbers.
Sign Rules
When working with integer division, knowing the sign rules is essential. The sign of the quotient depends on the signs of the dividend and divisor.
Here are the rules to remember:
  • Positive 梅 Positive = Positive
  • Negative 梅 Negative = Positive
  • Positive 梅 Negative = Negative
  • Negative 梅 Positive = Negative

In the provided exercise, 38 is positive, and -19 is negative. According to our sign rules, a positive number divided by a negative number will result in a negative quotient. That is why \(\frac{38}{-19} = -2\).

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

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \((2 x+y)(3 a)\)

Write a numerical expression for each phrase, and simplify the expression. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

Solve each problem. Nadine enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were $$ \begin{array}{lllll} -19, & 28, & -5, & \text { and } & 13 . \end{array} $$ What was her final score for the four turns?

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 8 if its last three digits form a number divisible by \(8,\) and not otherwise. (a) Is 2,923,296 divisible by \(8 ?\) (b) Is 7,291,623 divisible by \(8 ?\)

Write a numerical expression for each phrase, and simplify the expression. \(30 \%\) of the product of -8 and 5
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

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.