Long Division With 2-Digit Divisors Worksheets

Long division 2-digit divisors is the step in grade 5 where the four steps stay the same but guessing each digit of the answer becomes harder. The five PDFs on this page divide 3-digit and 4-digit numbers by 2-digit divisors, with and without remainders, and every answer key shows each step. They follow standard 5.NBT.B.6 of the Common Core standards for grade 5 number and operations in base ten, and the notes below show how to estimate, how to correct a guess and how to check.

Dividing by a 2-digit number

With a 2-digit divisor, the hardest step is guessing how many times it goes in. Round the divisor to the nearest ten to estimate. For 845 ÷ 23, think 84 ÷ 20, about 4. Try 4: 4 × 23 = 92, too big, so use 3. 3 × 23 = 69, and 84 − 69 = 15.

If a guess is too big, the product will be larger than the number you are dividing. If it is too small, the difference after subtracting will be as big as the divisor or bigger. Either way, change the guess by one and try again.

What is on this page

• 3-digit numbers divided by divisors from 11 to 25, dividing evenly.
• 3-digit numbers with remainders.
• 4-digit numbers divided by 2-digit divisors.

Long division 2-digit divisors worksheets: what is in the set

There are 5 long division 2-digit divisors worksheets on this page, and every one has an answer key except for any cut-out games. Three sets divide 3-digit numbers and two sets divide 4-digit numbers, with divisors from 11 to 40.

Long division 2 digit divisor worksheets: how the sets are built

The long division 2 digit divisor worksheets in this pack use divisors from 11 to 40. Three sets divide 3-digit numbers, with and without remainders, and two sets divide 4-digit numbers. The problems with divisors from 11 to 25 come first, because their multiples are the easiest to write down. Every answer key shows each round of the four steps.

Long division 2-digit divisors: the multiples list

With long division 2-digit divisors, the best help is to write the multiples of the divisor at the side of the page before starting. Then each round is a matter of finding the biggest multiple that is not bigger than the number we divide. Wikipedia’s article on long division describes the same idea as a table of multiples. This table shows the multiples of six divisors:

The list is easy to make: double the divisor to get 2 ×, double again to get 4 ×, and add to get the rest. For 23, the multiples are 23, 46, 69, 92, 115, 138, 161, 184 and 207. The times tables worksheets page has the one-digit multiples that this work depends on.

Dividing by 2 digit numbers: four worked examples

When dividing by 2 digit numbers, the four steps are the same as for one-digit divisors. These tables show the steps for four problems. The first has a first digit that needs two digits of the dividend:

672 ÷ 16 = 42

The second has a remainder:

845 ÷ 23 = 36 R17

The third has a four-digit dividend:

4,368 ÷ 12 = 364

The fourth has a zero in the answer, because 25 does not go into 15 after the 5 is brought down:

3,750 ÷ 25 = 150

2 digit divisor division: guessing the digit and correcting it

In 2 digit divisor division, the hardest step is to guess how many times the divisor goes in. A wrong guess is not a mistake, but a step in the method. If the product is bigger than the number, the guess is too big. If the difference after subtracting is as big as the divisor, the guess is too small. This table shows the trial steps for 845 ÷ 23:

The rule is to change the guess by one and try again. A child who understands this rule can always find the right digit in at most two or three tries. The multiples list at the side of the page makes each try a matter of reading, not calculating.

Long division grade 5: estimating by rounding the divisor

For long division grade 5, children are taught to round the divisor to the nearest ten and to use the first digits of the dividend to estimate. For 845 ÷ 23, round 23 to 20, and 84 ÷ 20 is about 4. This table shows six problems, the estimate for the first digit and the real digit:

The estimate is often one more than the real digit, because rounding the divisor down makes the estimate too big. That is why 4 × 23 = 92 is too big, and the digit is 3. When the divisor is rounded up, the estimate can be too small. Both cases are normal. The estimating with rounding and rounding worksheets pages have practice with rounding.

Double digit division worksheets: how long is the answer?

The double digit division worksheets in this pack use three-digit dividends first, and the answer has one or two digits. This table counts the three-digit dividends from 100 to 999 for six divisors, with the share that divide evenly:

For a divisor of 11, only the 10 dividends from 100 to 109 have a one-digit answer, and with a divisor of 20 the numbers from 100 to 199 do. About one dividend in 11 divides evenly by 11, and one in 20 by 20. The worksheets with remainders are therefore far more common than those with no remainders.

Checking long division with 2-digit divisors

The check is the same as for one-digit divisors: multiply the answer by the divisor and add the remainder. This table checks six answers:

The multiplication in the check uses the 2-digit by 2-digit multiplication skills, since the answer and the divisor can both have two digits. A child who checks each answer finds most mistakes without help.

Common mistakes with long division 2-digit divisors

Most mistakes are about the guess. This table shows five mistakes, what went wrong and the fix:

Long division 2-digit divisors word problems

Story problems use packing and sharing with bigger numbers. Ask children to estimate by rounding the divisor and then to divide:

Games and activities for long division 2-digit divisors

Children learn long division 2-digit divisors best when they play with it. These games use things that are found at home or in a classroom:

• Multiples list race: write the first nine multiples of a divisor as fast as you can, and check them with a partner
• Guess and check: guess the digit, multiply and compare, and count how many tries it takes
• Estimate first: estimate each problem by rounding the divisor, and then use the real steps
• Digit cards: draw three digit cards and a divisor card between 11 and 25, and divide
• Check partner: swap worksheets and check each answer by multiplying
• Remainder story: make up a story for a problem with a remainder, and say what the remainder means

Extra support and extra challenge with long division 2-digit divisors

For children who need more support: make sure the long division with one-digit divisors is secure. Write the multiples of the divisor at the side of the page, and use them for every round. Use grid paper to keep the digits in the right columns, and start with divisors of 11, 12 and 15, which are easier to multiply.

For children who need more challenge: ask for the answer to 10,000 ÷ 25 using doubling, for a division where the guess has to be corrected twice, and for the biggest 3-digit number that leaves a remainder of 22 when divided by 23. The 4-digit by 2-digit worksheets with no remainders are a good challenge.

How to tell that a child is ready to move on from long division 2-digit divisors

1. The child lists the multiples of the divisor.
2. The child estimates the first digit by rounding the divisor.
3. The child corrects a guess that is too big or too small.
4. The child checks the answer by multiplying and adding the remainder.

When all four are true, long division 2-digit divisors is secure, so move on to the next topic of grade 5, or review the pages on long division 3-digit by 1-digit and long division 4-digit by 1-digit.

A 20-minute lesson on long division 2-digit divisors

A short lesson is the best way to introduce long division 2-digit divisors. 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 2-digit divisors fits across the grades

No skill stands alone. This table shows what children learn before and after long division 2-digit divisors, with the standard that goes with each step:

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

Helping at home with long division 2-digit divisors

Parents do not need to be experts to help with long division 2-digit divisors. These suggestions work well, and each takes only a few minutes:

• Make the multiples list together before the homework starts.
• Ask the child to guess the first digit, and to say why it is too big or too small.
• Use a calculator only to check the answer, not to find it.
• Look for the divisors that appear in daily life, such as 12 eggs, 24 hours and 52 weeks.
• Praise a corrected guess, since it shows understanding.

How to check progress in long division 2-digit divisors

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 2-digit divisors

Most children need about a week of short sessions for long division 2-digit divisors. This plan follows the order of the worksheets on this page:

When the plan for long division 2-digit divisors is complete, the child is ready to divide any multi-digit number. The whole sequence is on the long division worksheets page.