Back To Course

Division: Help & Review9 chapters | 48 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

A quotient is the answer to a division problem. This lesson will give a definition of the word and describe how to find a quotient in different ways. There will also be a quiz for you to check your understanding.

The word **quotient** is from the Latin *'quotiens*', which means 'how many times'. A quotient is the answer to a division problem. A division problem describes 'how many times' a number will go into another. The first known usage of the word in mathematics is found around 1400-1500 AD in England.

There are at least two different ways to find the quotient of two numbers. You can also find the quotient of an algebra problem.

**Fractions**

The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.

The quotient can also be the solution to a division problem involving two fractions.

Solve the above example using:

A = 2

B = 3

C = 4

D = 7

When you plug in the numbers, you get:

(2/3) / (4/7)

Since division is the opposite of multiplication, you can turn this division problem into a multiplication problem by multiplying the top fraction by the reciprocal of the bottom fraction.

(2/3) x (7/4) = 14/12

This fraction can be reduced to 1 1/6

Therefore, 1 1/6 is the quotient of the division problem (2/3) / (4/7).

**Division**

You can also find the quotient of an arithmetic division problem.

24 divided by 4 is 6. This means that 24 can be divided into 6 equal groups, each containing 4 items.

The answer to a larger division problem is also the quotient. For the above problem, the quotient is 18.

If the division problem does not work out evenly, there will be a remainder. The quotient is still the whole number, but the amount 'left over' is the remainder.

**Algebra**

Not all quotients have to be numbers. You can also find the quotient to an algebraic problem involving **variables**.

You can divide one **monomial** by another.

24*ab* / 8*a*

First, divide the numbers:

24 / 8 = 3

Then, simplify the variables. The *a* in both the numerator and the denominator will cancel each other out and you are left with the *b*

So, the answer is 3*b*.

Or you can divide a **polynomial** by a monomial.

In this example, the polynomial 15*x*^2 + 10*x* is being divided by 5*x*.

The first step is to split out each term of the **numerator** and divide them each by the **denominator**. This makes the problem easier to solve and will save on confusion in the long run.

After dividing each term, the solution to the division problem, or quotient is:

3*x* + 2

You can also divide one polynomial by another polynomial.

**The Quotient Rule**

The **Quotient Rule** is used in calculus as a method for finding the derivative of a special type of function.

Let's review. The word **quotient** is from Latin *'quotiens*' meaning 'how many times.' As a mathematical term, quotient refers to the answer to a division problem. It can also refer to an arithmetic problem, a problem using fractions, or an algebraic problem involving variables. You can find the quotient by working out the division problem.

1. Quotient, from the Latin 'quotiens' meaning 'how many times,' is the answer to a division problem.

2. There are two ways to find the quotient of a problem: making a fraction and performing division in arithmetic or algebraic problems.

3. The Quotient Rule is used in calculus to find the derivative of a special function.

After watching this lesson, you should be able to:

- Explain what a quotient is
- Determine the quotient of a problem using fractions or division in algebra and arithmetic problems
- Understand how the Quotient Rule is used

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
6 in chapter 1 of the course:

Back To Course

Division: Help & Review9 chapters | 48 lessons

- What are the Different Types of Numbers? 6:56
- How to Perform Division: Steps & Examples 3:56
- Performing Long Division with Large Numbers: Steps and Examples 9:12
- Dividing By Zero: Definition & Concept
- Quotient Rule: Formula & Examples 4:38
- Quotient: Definition & Meaning 3:23
- Go to Introduction to Division: Help & Review

- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- U.S. Politics & Civics Lesson Plans
- US History - Civil War: Lesson Plans & Resources
- HESI Admission Assessment Exam: Factors & Multiples
- HESI Admission Assessment Exam: Probability, Ratios & Proportions
- HESI Admission Assessment Exam: 3D Shapes
- HESI Admission Assessment Exam: Punctuation
- HESI Admission Assessment Exam: Linear Equations, Inequalities & Functions
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison
- TACHS Prep Product Comparison
- Top 50 Blended Learning High Schools
- EPPP Prep Product Comparison

- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Logical Thinking & Reasoning Questions: Lesson for Kids
- Symmetry Project Ideas
- The Cask of Amontillado Discussion Questions
- Op Art Lesson Plan for Elementary School
- Quiz & Worksheet - Dolphin Mating & Reproduction
- Octopus Diet: Quiz & Worksheet for Kids
- Quiz & Worksheet - Frontalis Muscle
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Common Core Math Worksheets & Printables
- Life Skills Resources for Teachers

- NYSTCE Biology (006): Practice and Study Guide
- Antigone Study Guide
- American Literature for Teachers: Professional Development
- Organizational Behavior Textbook
- STAAR Reading - Grade 8: Test Prep & Practice
- Campbell Biology Chapter 7: Membrane Structure and Function
- 8th Grade Math: Percents
- Quiz & Worksheet - Animal Bite & Poison First Aid
- Quiz & Worksheet - The Distribution of Flora & Fauna in Europe
- Quiz & Worksheet - Geography's Impact on East Asian Migration Patterns
- Quiz & Worksheet - Practice with Mass & Volume
- Quiz & Worksheet - How Creativity Changes with Age

- Puns in Julius Caesar
- Newt Facts: Lesson for Kids
- What is the PE CSET Like?
- ACT Workkeys Scores
- 504 Plans in California
- ACT Workkeys Scores
- Benefits of Study.com vs. Traditional College
- NATA Certification Requirements
- Resources for Speech Education
- 6th Grade Summer Reading List
- When Do You Apply for Community College?
- How to Ace Your Job Interview

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject