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Explore The Kits Long Division (Standard Algorithm for Division)
LESSON MATERIALS
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Long Division (Standard Algorithm for Division)
What you will learn from this videoWhat you will learn
- 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!
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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.
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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
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Reading Material
Download as PDF Download PDF View as Seperate 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 3-Digit Number by a 1-Digit 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 3-Digit Number by a 1-Digit 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 4-Digit Number by a 1-Digit 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 4-Digit Number by a 1-Digit 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 3-Digit Number by a 2-Digit 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 3-Digit Number by a 2-Digit 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 r