Long Division Worksheets: 4-Digit by 1-Digit

Long division 4-digit by 1-digit is the biggest long division that grade 4 asks for, with up to four rounds of the same four steps. The four PDFs on this page have problems that divide evenly, problems with remainders and a mixed set, and every answer key shows each step. They follow standard 4.NBT.B.6 of the Common Core standards for grade 4 number and operations in base ten, and the notes below show how the digits of the answer line up and how estimating keeps the answer sensible.

About these worksheets

Four-digit dividends are the largest that grade 4 divides by a single digit (Common Core 4.NBT.B.6). The steps are the same, but there are up to four rounds of divide, multiply, subtract and bring down, so tidy columns matter.

Tips

• Estimate first: 7,251 ÷ 4 is a bit less than 8,000 ÷ 4 = 2,000.
• Keep each answer digit exactly above the last digit you brought down.
• After each subtraction, check that what is left is smaller than the divisor.

Long division 4-digit by 1-digit worksheets: what is in the set

There are 4 long division 4-digit by 1-digit worksheets on this page, and every one has an answer key except for any cut-out games. Two sets have problems that divide evenly, one has problems with remainders, and one is a mix.

Long division practice worksheets: how the sets are built

The long division practice worksheets in this pack have four sets with nine problems each. Two sets divide evenly, one set has a remainder in every problem, and one set is a mix of both. Each set has fewer problems than the sheets with smaller numbers, because a four-digit division takes much longer, and every answer key shows each round of the four steps.

Long division 4-digit by 1-digit: four worked examples

Long division 4-digit by 1-digit follows the same four steps, repeated up to four times. These tables show the steps for four problems. Wikipedia’s article on long division explains why the method works for numbers of any size. The first has a zero in the answer, because 6 does not go into 3:

5,436 ÷ 6 = 906

The second has a remainder, and the answer starts in the thousands, because 4 goes into the first digit 7:

7,251 ÷ 4 = 1,812 R3

The third and the fourth have more than one zero in the answer, which is the hardest case:

6,305 ÷ 7 = 900 R5

3,090 ÷ 5 = 618

4 digit by 1 digit division worksheets: how long is the answer?

The 4 digit by 1 digit division worksheets have answers of three or four digits. The answer has four digits only if the first digit of the dividend is at least as big as the divisor, and the rest of the dividend is not too small. This table counts the 9,000 dividends from 1,000 to 9,999 for each divisor from 2 to 9, with the share that has a zero in the answer:

With a divisor of 2 most dividends have a four-digit answer, and with a divisor of 9 only 1,000 of 9,000 do. A zero in the answer is also common, since with a divisor of 9 about 27% of the answers have a zero in them. This is the reason why every long division of this size should be checked for missing zeros.

Rounds and digits: how many steps does it take?

Every digit of the dividend takes one round of the four steps, except the first digits that the divisor cannot go into. The number of digits in the answer is the number of rounds. This table shows six problems, with the rounds and the digits in the answer:

A child can use this rule to check the layout before starting: count the digits of the dividend, and decide whether the answer will have the same number of digits or one fewer. The largest answer a child can get with a 4-digit dividend is shown in the next table:

Long division 4 digit: estimating with compatible numbers

For long division 4 digit problems, an estimate is a quick check that the answer has the right number of digits and about the right size. Round the dividend to a number that the divisor goes into easily, such as 7,200 for 7,251 when the divisor is 4. This table shows six estimates and the exact answers:

The estimate for 3,090 ÷ 5 is 3,000 ÷ 5 = 600, and the exact answer is 618, so they are close. The estimating with rounding page has the estimating skills, and the rounding worksheets page has the rounding.

Long division worksheets grade 5: why they still matter

Many long division worksheets grade 5 classes use four-digit dividends as a warm up, before they move on to two-digit divisors. A child who can do this page without mistakes is ready for the long division 2-digit divisors page. The Common Core standard 5.NBT.B.6 continues the work, as the Common Core standards for grade 5 number and operations in base ten describe, and the main change is that guessing the digit of the answer is harder.

Children who struggle with grade 5 long division often have not learned the one-digit case well enough. A good test is to ask for 9,036 ÷ 9 and 8,008 ÷ 8, both with zeros in the answer, and to see whether the child gets 1,004 and 1,001 without help.

Checking a long division answer by multiplying

The check for long division is to multiply the answer by the divisor and add the remainder. The result must be the starting number. This table checks six answers:

The check uses the 2-digit by 1-digit multiplication skills, extended to four digits in the multiplication worksheets pages. A child who can both multiply and divide with large numbers can check each operation with the other.

Common mistakes with long division 4-digit by 1-digit

With four digits there are more chances for a column to slip. This table shows five mistakes, what went wrong and the fix:

Long division 4-digit by 1-digit word problems

Story problems for four-digit division use large numbers from real life. Ask children to estimate first, divide and say what the remainder means:

Games and activities for long division 4-digit by 1-digit

Children learn long division 4-digit by 1-digit best when they play with it. These games use things that are found at home or in a classroom:

• Big number race: two players roll four dice for a number and one die for a divisor, and the first to divide correctly wins
• Zero hunt: sort problems in a set into those with a zero in the answer and those without, before solving them
• Estimate then check: estimate each answer with a compatible number, then use a calculator to check
• Long division relay: each child does one round of the four steps and passes the paper on
• Digit cards: draw four digit cards and a divisor, and divide the number they make
• Check partner: swap worksheets and check each answer by multiplying

Extra support and extra challenge with long division 4-digit by 1-digit

For children who need more support: make sure the 3-digit long division is secure first. Use grid paper, one digit to a box, and mark the place of each digit of the answer before starting. Write the multiples of the divisor next to the problem, and do one sheet at a time with the answer key beside the work.

For children who need more challenge: ask for the answer to 10,000 ÷ 8 using the zeros, for the biggest 4-digit number that divides by 6 with a remainder of 5, and for a division with two zeros in the answer. Writing a story for 6,305 ÷ 7, in which the remainder matters, is a good challenge.

How to tell that a child is ready to move on from long division 4-digit by 1-digit

1. The child lines up the digits of the answer correctly.
2. The child writes the zeros in the answer.
3. The child estimates and checks every answer.
4. The child divides 4-digit numbers with and without remainders.

When all four are true, long division 4-digit by 1-digit is secure, so move on to the long division 2-digit divisors page.

A 20-minute lesson on long division 4-digit by 1-digit

A short lesson is the best way to introduce long division 4-digit by 1-digit. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where long division 4-digit by 1-digit fits across the grades

No skill stands alone. This table shows what children learn before and after long division 4-digit by 1-digit, with the standard that goes with each step:

This page is the last of the one-digit divisor pages. The whole sequence is on the long division worksheets page.

Helping at home with long division 4-digit by 1-digit

Parents do not need to be experts to help with long division 4-digit by 1-digit. These suggestions work well, and each takes only a few minutes:

• Use real numbers, such as the miles of a trip divided by the days.
• Ask the child to estimate before dividing.
• Look for zeros in the answer when the child checks.
• Use grid paper, one digit to a box.
• Check each answer by multiplying and adding the remainder.

How to check progress in long division 4-digit by 1-digit

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for long division 4-digit by 1-digit

Most children need about a week of short sessions for long division 4-digit by 1-digit. This plan follows the order of the worksheets on this page:

When the plan for long division 4-digit by 1-digit is complete, move on to the long division 2-digit divisors page. The whole sequence is on the long division worksheets page.