Enjoy any 5 free lessons!
You can pick. No account needed.
Watch VideoBecome a member to get full access to our entire library of learning videos, reading material, quiz games, simple DIY activities & more.
Become a member to get full access to our entire library of learning videos, quiz games, & more.
Plans & Pricingto watch this full video.
Access All Videos
and Lessons, No Limits.
Access All Videos
No credit card required,
takes 7 sec to signup.
No card required
Readytogo lessons
that save you time.
Readytogo lessons
If you are on a school computer or network, ask your tech person to whitelist these URLs:
*.wistia.com, fast.wistia.com, fast.wistia.net, embedwistiaa.akamaihd.net
Sometimes a simple refresh solves this issue. If you need further help, contact us.
Long Division (Standard Algorithm for Division)
 Show lesson plan & teacher guide
 Show answers to discussion questions
 Show video only
 Allow visiting of other pages
 Hide assessments
 We will learn how to divide using the standard algorithm.
 We’ll see that we can use the standard algorithm to divide 2, 3 and 4 digit numbers.
 And we'll see how this knowledge can help us do experiments, bake cookies, and pollinate trees!

Discussion Questions

Before VideoWhat is place value? How does the place value of a digit compare to the place value of the digit on its right?ANSWER

Place value is the value of a digit based on its place in a number. The place value of a digit is 10 times the place value of the digit to its right.

Thousands place.

6 × 100 + 7 × 10 + 2 × 1, or 6 one hundreds, 7 tens, and 2 ones.

When I break a number up to divide using an area model, I break it apart by place value. When I divide a number using partial quotients I try to find the largest multiple of the divisor so that there is none of the greatest place value left after I subtract.

Students may use partial quotients or an area model. Some may think of the problem as 48 ÷ 12 = 4, and then multiply by 10 to get 40.


After VideoWhat are the four repeated steps of the standard algorithm for long division?ANSWER

Divide, Multiply, Subtract, Bring down

When I divide, I can look at multiples of the divisor to help me find the dividend.

When there are no more digits to bring down and I have a remainder of 0, or when there are no more digits to bring down and the remainder is smaller than the divisor.

The standard algorithm is a very efficient way to divide.

I can start by making a list of multiples of 7. 4 is less than 7, so consider multiples of 7 close to 45. Multiply: 7 × 6 = 42. Subtract: 45 – 42 = 3. Bring down the 6 to make 36. Find multiples of 7 close to 36. Multiply: 7 × 5 = 35. Subtract: 36 – 35 = 1. Bring down the 4 to make 14. Find multiples of 7 close to 14. Multiply: 7 × 2 = 14. Subtract: 14 – 14 = 0. No numbers remain to bring down, and the remainder is 0. 4,564 ÷ 7 = 652.



Vocabulary

Area model
DEFINE
A rectangular diagram or model used for multiplication and division problems, in which the factors or the quotient and divisor define the length and width of the rectangle. Also called the box method.

Partial quotients
DEFINE
A strategy for division where we subtract multiples of the divisor from the dividend until we get to 0, or as close to 0 as possible.

Algorithm
DEFINE
A procedure in mathematics or a description of a set of steps that we can use to solve a mathematical computation.

Long division
DEFINE
A process of dividing a number that has at least three digits by one that is two digits or more, sometimes leaving a remainder.

Standard algorithm for division
DEFINE
A series of repeated steps for performing division problems. The steps in order are: divide, multiply, subtract, bring down.

Partitioning
DEFINE
Division into equal parts.

Dividend
DEFINE
In division, the amount or number to be divided.

Divisor
DEFINE
In division, a number that divides another number, either completely or with a remainder.

Area model
DEFINE

Reading Material
Download as PDF Download PDF View as Separate PageWHAT IS THE STANDARD ALGORITHM FOR LONG DIVISION?The standard algorithm for long division gives a quick and efficient process to divide any two numbers. The process is the same no matter what numbers you use.
To better understand long division…
WHAT IS THE STANDARD ALGORITHM FOR LONG DIVISION?. The standard algorithm for long division gives a quick and efficient process to divide any two numbers. The process is the same no matter what numbers you use. To better understand long division…LET’S BREAK IT DOWN!
Divide a 3Digit Number by a 1Digit Number
A batch of elephant toothpaste needs 936 milligrams of hydrogen peroxide divided equally among 4 containers. Divide 936 ÷ 4 to find how many milligrams go into each container. The standard algorithm for long division is a series of steps repeated in this order: divide, multiply, subtract, bring down. With the standard algorithm, we solve division problems one place value at a time. Start with the 9 in 938. Multiply: What multiple of 4 is closest to (but less than) 9? 4 × 2 = 8. Record a 2 in the hundreds place above the 9. Subtract: 9 8 =1. Bring down: the next digit in 938 is 3. Write it next to the 1 to make 13. Repeat all the steps. 4 × 3 = 12, which is closest to 13. Write a 3 in the tens place above the line. Subtract 13 – 12 to get 1. Bring down the last digit, 6 to make 16. Repeat the steps again. 4 × 4 = 16. Write a 4 above the ones place. 16 – 16 = 0. There are no digits left to bring down, so you are done! The number above the line is 234 and the last subtraction resulted in 0. 936 ÷ 4 = 234. Try this one yourself: What is 875 ÷ 7?
Divide a 3Digit Number by a 1Digit Number A batch of elephant toothpaste needs 936 milligrams of hydrogen peroxide divided equally among 4 containers. Divide 936 ÷ 4 to find how many milligrams go into each container. The standard algorithm for long division is a series of steps repeated in this order: divide, multiply, subtract, bring down. With the standard algorithm, we solve division problems one place value at a time. Start with the 9 in 938. Multiply: What multiple of 4 is closest to (but less than) 9? 4 × 2 = 8. Record a 2 in the hundreds place above the 9. Subtract: 9 8 =1. Bring down: the next digit in 938 is 3. Write it next to the 1 to make 13. Repeat all the steps. 4 × 3 = 12, which is closest to 13. Write a 3 in the tens place above the line. Subtract 13 – 12 to get 1. Bring down the last digit, 6 to make 16. Repeat the steps again. 4 × 4 = 16. Write a 4 above the ones place. 16 – 16 = 0. There are no digits left to bring down, so you are done! The number above the line is 234 and the last subtraction resulted in 0. 936 ÷ 4 = 234. Try this one yourself: What is 875 ÷ 7?Divide a 4Digit Number by a 1Digit Number
You want to complete a trip of 1,421 miles in 6 days. Divide 1,421 ÷ 6 to find how many miles you must drive each day. To divide using the standard algorithm, write 1,421 under the division symbol and 6 to the left. Use the steps multiply, subtract, and bring down to find the quotient. What multiple of 6 is closest to 14? 6 × 2 = 12. Write a 2 in the hundreds position. Subtract: 14 – 12 = 2. Bring down the next digit, 2, to make 22. What multiple of 6 is closest to 22? 6 × 3 = 18. Write 3 in the tens position. Subtract: 22 – 18 = 4. Bring down the next digit, 1, to make 41. What multiple of 6 is closest to 41? 6 × 6 = 36. Write 6 above the ones position. Subtract: 41 – 36 = 5. There are no more digits to bring down. 5 is less than 6 so 5 cannot be evenly divided into 6 groups. 1,421 ÷ 6 = 236 with a remainder of 5. You need to drive a little more than 236 miles each day. Try this one yourself: Divide 2,576 ÷ 8.
Divide a 4Digit Number by a 1Digit Number You want to complete a trip of 1,421 miles in 6 days. Divide 1,421 ÷ 6 to find how many miles you must drive each day. To divide using the standard algorithm, write 1,421 under the division symbol and 6 to the left. Use the steps multiply, subtract, and bring down to find the quotient. What multiple of 6 is closest to 14? 6 × 2 = 12. Write a 2 in the hundreds position. Subtract: 14 – 12 = 2. Bring down the next digit, 2, to make 22. What multiple of 6 is closest to 22? 6 × 3 = 18. Write 3 in the tens position. Subtract: 22 – 18 = 4. Bring down the next digit, 1, to make 41. What multiple of 6 is closest to 41? 6 × 6 = 36. Write 6 above the ones position. Subtract: 41 – 36 = 5. There are no more digits to bring down. 5 is less than 6 so 5 cannot be evenly divided into 6 groups. 1,421 ÷ 6 = 236 with a remainder of 5. You need to drive a little more than 236 miles each day. Try this one yourself: Divide 2,576 ÷ 8.Divide a 3Digit Number by a 2Digit number
You want to divide a batch of 384 cookies among 12 middle school teachers. Solve 384 ÷ 12 using the standard algorithm for long division. The same process works no matter how many digits are in the divisor or dividend. Start by asking what multiple of 12 is less than or equal to 38? 12 × 3 = 36, so write 3 in the tens place and subtract to find the remainder: 38 – 36 = 2. Bring down the 4 to make 24. What multiple of 12 is closest to 24? 12 × 2 = 24, so write 2 in the ones position and subtract to find the remainder 24 – 24 = 0.There are no more digits to bring down. 384 ÷ 12 = 32. You can give each teacher 32 cookies. Yum! Try this yourself: What is 224 ÷ 32?
Divide a 3Digit Number by a 2Digit number You want to divide a batch of 384 cookies among 12 middle school teachers. Solve 384 ÷ 12 using the standard algorithm for long division. The same process works no matter how many digits are in the divisor or dividend. Start by asking what multiple of 12 is less than or equal to 38? 12 × 3 = 36, so write 3 in the tens place and subtract to find the remainder: 38 – 36 = 2. Bring down the 4 to make 24. What multiple of 12 is closest to 24? 12 × 2 = 24, so write 2 in the ones position and subtract to find the remainder 24 – 24 = 0.There are no more digits to bring down. 384 ÷ 12 = 32. You can give each teacher 32 cookies. Yum! Try this yourself: What is 224 ÷ 32?Divide a Large MultiDigit Number by a MultiDigit Number
It takes 23 bees to pollinate one apple tree. If we have a total of 31,359 bees, how many apple trees can they pollinate? Solve 31,359 ÷ 23 by using the standard algorithm for long division. Consider the first two digits of 31,359. What multiple of 23 is closest to 31? 23 × 1 = 23, so write a 1 in the thousands place and subtract to find the difference: 31 – 23 = 8. Bring down the 3 to make 83. 23 × 3 = 69, so write 3 in the hundreds place and subtract to find the difference: 83 – 69 = 14. Bring down the 5 to make 145. 23×6=138, so write 6 in the tens place and subtract 145138 =7. Bring down the 9 to make 79. 23×3=69, so write 3 in the ones place and subtract 7969=10. There are no more digits to bring down and 10 cannot be divided into 23 equal groups. 31,359 ÷ 23 = 1,363 with a remainder of 10. The bees can pollinate 1,363 apple trees. Try this yourself: What is 53,922 ÷ 43?
Divide a Large MultiDigit Number by a MultiDigit Number It takes 23 bees to pollinate one apple tree. If we have a total of 31,359 bees, how many apple trees can they pollinate? Solve 31,359 ÷ 23 by using the standard algorithm for long division. Consider the first two digits of 31,359. What multiple of 23 is closest to 31? 23 × 1 = 23, so write a 1 in the thousands place and subtract to find the difference: 31 – 23 = 8. Bring down the 3 to make 83. 23 × 3 = 69, so write 3 in the hundreds place and subtract to find the difference: 83 – 69 = 14. Bring down the 5 to make 145. 23×6=138, so write 6 in the tens place and subtract 145138 =7. Bring down the 9 to make 79. 23×3=69, so write 3 in the ones place and subtract 7969=10. There are no more digits to bring down and 10 cannot be divided into 23 equal groups. 31,359 ÷ 23 = 1,363 with a remainder of 10. The bees can pollinate 1,363 apple trees. Try this yourself: What is 53,922 ÷ 43? 
Practice Word Problems

Practice Number Problems

Teacher Resources
These downloadable teacher resources can help you create a full lesson around the video. These PDFs incorporate using class discussion questions, vocabulary lists, printable math worksheets, quizzes, games, and more.
Select a Google Form
Choose a way to play this quiz game

Questions appear on the teacher's screen. Students answer on their own devices.
Start a Free Trial Today. Get a $5 Amazon Gift Card!
Teachers! Start a free trial & we'll send your gift card within 1 day. Only cards left. Try it now.
This email is associated with a Science Kit subscription. Kit subscriptions are managed on this separate page: Manage Subscription

Science & Math$_{/yr}

Science Only$_{/yr}
Use the standard algorithm to divide: 828 ÷ 9
Use the standard algorithm to divide: 744 ÷ 62
Use the standard algorithm to divide: 21,361 ÷ 41
access all lessons
• No credit card required •
"My students loved the videos. I started the video subscription in May and used them as a review before the state test, which I know contributed to 100% of my class passing the state test."
Rhonda Fox 4th Grade Teacher, Ocala, Florida• No credit card required •
"My students loved the videos. I started the video subscription in May and used them as a review before the state test, which I know contributed to 100% of my class passing the state test."
Rhonda Fox 4th Grade Teacher, Ocala, Florida• No credit card required •
Already a member? Sign In
* no credit card required *
* no credit card required *
* no credit card required *
no credit card required
Skip, I will use a 3 day free trial
Enjoy your free 30 days trial

Unlimited access to our full library
of videos & lessons for grades K5. 
You won’t be billed unless you keep your
account open past your 14day free trial. 
You can cancel anytime in 1 click on the
manage account page or by emailing us.

Unlimited access to our full library of videos & lessons for grades K5.

You won't be billed unless you keep your account open past 14 days.

You can cancel anytime in 1click on the manage account page.
Cancel anytime in 1click on the manage account page before the trial ends and you won't be charged.
Otherwise you will pay just $10 CAD/month for the service as long as your account is open.
Cancel anytime on the manage account page in 1click and you won't be charged.
Otherwise you will pay $10 CAD/month for the service as long as your account is open.
We just sent you a confirmation email. Enjoy!
DonePlease login or join.