Back To Course

High School Algebra I: Help and Review25 chapters | 292 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jennifer Beddoe*

Long division is a method by which a person can perform more complex division problems using only a pencil and paper. This lesson will define long division, show how to perform the operation, and give some examples. There will be a quiz at the end to give you some practice.

**Long division** is a mathematical operation which allows you to perform complicated division problems using pencil and paper. It breaks down the more complex problem into simpler steps. With the advances in computers and calculators, the need to know long division has faded. However, it is a good skill to have and an excellent way to exercise the brain.

A long division problem is not written as a fraction or like you might write a smaller problem. Problems that need to be worked out the long way are written out like this, with the dividend under the long division bracket, the divisor to the left of the bracket and the quotient on top of the bracket.

The terms are the same; there is still a divisor, dividend and quotient, they are just are written in such a way to make it easier to calculate. In order to work out a long division problem, you first break it down into manageable division problems.

Let's look at the problem 965 / 5.

You need to divide 5 into each of the numbers in 965.

- 5 will go in to 9 one time. 5 x 2 = 10, and that is too much, but 5 x 1 = 5, and that will work. Place a 1 above the 9 (above the line) then write a 5 under the 9. This is to show that 5 x 1 is 5.
- Subtract 5 from 9 to get 4 and then bring down the 6. 4 is the remainder from the first mini-division problem, and the 6 is the number you will use for the second mini-division problem.
- Now divide 5 into 46. 5 x 45 = 9, so 9 is the number we will write on top and then put 45 under the 46.
- 46 - 45 = 1, which makes 1 the remainder.
- Bring down the 5 to complete the final mini problem: 15 / 5 = 3
- Write a 3 above the 5, and 5 x 3 = 15.
- 15 - 15 = 0, there is no remainder and the problem is complete.

965 / 5 = 193

Let's go through some examples.

You can also work long division problems with very large numbers.

For this example, 31 will not divide into 3, so you need to include the next number, 0. Since 31 also will not divide into 30 include the next number.

305 / 31 is the first mini-division problem to work out. After that, the problem continues as usual. By the time you are done, we know that 305,753 / 31 = 9,863.

Long division problems don't always work out evenly. Sometimes, there will be a remainder.

The remainder can be written in two ways. The first is like in this example, 'R4' which tells you that there is a remainder of 4. The other way is a fraction with the remainder as the numerator and the divisor as the denominator. For this problem, that would be 4 / 7. Either way is correct.

**Long division** is a method for solving complex division problems without a calculator. All it takes is a piece of paper, a pencil, and some brain power. In order to work out a long division problem, you first break it down into manageable division problems. For problems that have a remainder, it can be written in one of two ways: 'R' plus the leftover number, or the leftover number as part of a fraction.

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
9 in chapter 5 of the course:

Back To Course

High School Algebra I: Help and Review25 chapters | 292 lessons

- What are the Different Types of Numbers? 6:56
- Graphing Rational Numbers on a Number Line 5:02
- Notation for Rational Numbers, Fractions & Decimals 6:16
- The Order of Real Numbers: Inequalities 4:36
- Finding the Absolute Value of a Real Number 3:11
- What Are Composite Numbers? - Definition & Examples 4:38
- What Are Odd & Even Numbers? - Definition & Examples 6:38
- What are Real Numbers? - Definition & Properties 4:50
- What is Long Division? - Definition & Examples 3:29
- Go to High School Algebra - Real Numbers: Help and Review

- Inclusion in Recruitment, Interviews & Hiring
- Computer Science 105: Introduction to Operating Systems
- High School 101: High School Readiness
- Communications 301: Diversity and Intercultural Communication
- Communications 106: Communication in the Digital Age
- Operating System Fundamentals
- Cultural Differences in Nonverbal Communication
- Techniques for Inclusive Hiring & Onboarding
- Intro to Inclusion in Recruitment, Interviews & Hiring
- Implementing Inclusion in Recruitment & Screening
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits
- CLEP Exam Question Formats
- CLEP Exam Costs & Registration Deadlines
- CLEP Exam List & Credits Offered

- Static vs. Non-Static Methods in Java
- South African Flag Lesson for Kids: Colors & Meaning
- Monkey Facts: Lesson for Kids
- Peter Senge: Learning Organizations & Systems Thinking
- Students with Dual-Sensory Impairment: Characteristics & Accommodations
- Pharmaceutical Compounding: Equipment & Supplies
- How Physiology of the Brain Affects Emotional Intelligence
- Risk Reporting: Communication & Techniques
- Quiz & Worksheet - The Crucible & Symbols
- Quiz & Worksheet - Various Perspectives on Organizations
- Animal Adaptations: Quiz & Worksheet for Kids
- Quiz & Worksheet - Serving Alcohol Responsibly
- Quiz & Worksheet - Email Message Anatomy
- How to Cite Sources Flashcards
- Evaluating Sources for Research Flashcards

- GACE Biology: Practice & Study Guide
- SAT Prep: Practice & Study Guide
- Common Core Math Grade 8 - Geometry: Standards
- Building a Virtual Team
- Physics 101 Syllabus Resource & Lesson Plans
- General Science: Science & Society
- General Science: The Circulatory System
- Quiz & Worksheet - History of Psychoactive Inhalants
- Quiz & Worksheet - The Sapir-Whorf Hypothesis
- Quiz & Worksheet - Characteristics of the Hebrews in History
- Quiz & Worksheet - Characteristics of a Nomadic Lifestyle
- Quiz & Worksheet - Structural & Functional Respiratory System Changes Due to Age

- Pseudoscience: Examples & Definition
- Inclusive Fitness: Definition & Theory
- Chinese New Year Activities for Kids
- Renaissance Lesson Plan
- Time Management Lesson Plan
- Response to Intervention (RTI) in Ohio
- How to Pass Common Core Assessments
- Medical Terminology Resources
- How to Find Study.com Corporate Learning Courses
- Plant Experiments for Kids
- Excelsior College BS in Business Degree Plan Using Study.com
- NGSS Life Science for Middle School

Browse by subject