This page includes Long Multiplication worksheets for students who have mastered the basic multiplication facts and are learning to multiply 2, 3, 4 and more digit numbers. Sometimes referred to as long multiplication or multidigit multiplication, the questions on these worksheets require students to have mastered the multiplication facts from 0 to 9.
There are a variety of strategies for completing long multiplication including the classic paper and pencil methods, lattice multiplication (which we feature on this page), mental strategies, manipulative use, technology, and various other paper and pencil algorithms. MultiDigit multiplication can be a frustrating experience for many students. Try to teach multidigit multiplication using more than one strategy.
Long Multiplication Worksheets
Long multiplication practice worksheets including a variety of number sizes and options for different number formats.
TwoDigit multiplication is a natural place to start after students have mastered their multiplication facts. The concept of multiplying twodigit numbers requires a knowledge of place and place value, especially if students are to fully understand what they are accomplishing with the various strategies they use. A question such as 24 × 5 can be thought of as (20 + 4) × 5. Mentally, this becomes much easier as students multiply 20 by 5 then 4 by 5 and add the two products. A good way to build understanding of place value is with base ten blocks. These manipulatives also translate very well into paper and pencil and mental math strategies.
An extra digit can throw off some students but add an extra challenge to others. Always ensure that students are ready for threedigit multiplication or both you and your student will be frustrated. Threedigit multiplication worksheets require a mastery of singledigit multiplication facts and a knowledge of a multidigit multiplication strategy that will enable students to both understand the question and get the correct answer. Fourdigit multiplication was invented in 350 B.C. as a way of punishing children who stole bread from the market. Just kidding! It's actually a great challenge for students who have experienced success with their multiplication facts and have a good handle on a long multiplication strategy. What do you give students who have mastered their multiplication facts and long multiplication and who love a challenge? Look no further than five to eightdigit multiplication. Enjoy!
There are no thousand separators in the numbers on the first worksheets. It makes it a little more difficult to read the numbers, but sometimes it is better not to have too many things in the way when students are learning long multiplication. The answer keys include answers with the steps shown, so students and teachers can diagnose any problems in the steps they took to answer the questions. The answers use a paper and pencil algorithm that is commonly used in the U.S. and other countries.
Commas are included as thousands separators for the numbers on the next worksheets. Commas are used in the U.S. and other Englishspeaking countries as a way of making numbers easier to read. As with the other long multiplication worksheets on this page, the answer keys include the steps.

5Digit by 1Digit Multiplication (CommaSeparated Thousands) 5Digit by 2Digit Multiplication (CommaSeparated Thousands) 5Digit by 3Digit Multiplication (CommaSeparated Thousands) 5Digit by 4Digit Multiplication (CommaSeparated Thousands) 5Digit by 5Digit Multiplication (CommaSeparated Thousands)

6Digit by 1Digit Multiplication (CommaSeparated Thousands) 6Digit by 2Digit Multiplication (CommaSeparated Thousands) 6Digit by 3Digit Multiplication (CommaSeparated Thousands) 6Digit by 4Digit Multiplication (CommaSeparated Thousands) 6Digit by 5Digit Multiplication (CommaSeparated Thousands) 6Digit by 6Digit Multiplication (CommaSeparated Thousands)

7Digit by 1Digit Multiplication (CommaSeparated Thousands) 7Digit by 2Digit Multiplication (CommaSeparated Thousands) 7Digit by 3Digit Multiplication (CommaSeparated Thousands) 7Digit by 4Digit Multiplication (CommaSeparated Thousands) 7Digit by 5Digit Multiplication (CommaSeparated Thousands) 7Digit by 6Digit Multiplication (CommaSeparated Thousands) 7Digit by 7Digit Multiplication (CommaSeparated Thousands)

8Digit by 1Digit Multiplication (CommaSeparated Thousands) 8Digit by 2Digit Multiplication (CommaSeparated Thousands) 8Digit by 3Digit Multiplication (CommaSeparated Thousands) 8Digit by 4Digit Multiplication (CommaSeparated Thousands) 8Digit by 5Digit Multiplication (CommaSeparated Thousands) 8Digit by 6Digit Multiplication (CommaSeparated Thousands) 8Digit by 7Digit Multiplication (CommaSeparated Thousands) 8Digit by 8Digit Multiplication (CommaSeparated Thousands)

2Digit by 2Digit Multiplication (Large Print) (CommaSeparated Thousands) 3Digit by 1Digit Multiplication (Large Print) (CommaSeparated Thousands) 3Digit by 2Digit Multiplication (Large Print) (CommaSeparated Thousands) 3Digit by 3Digit Multiplication (Large Print) (CommaSeparated Thousands)

4Digit by 1Digit Multiplication (Large Print) (CommaSeparated Thousands) 4Digit by 2Digit Multiplication (Large Print) (CommaSeparated Thousands) 4Digit by 3Digit Multiplication (Large Print) (CommaSeparated Thousands) 4Digit by 4Digit Multiplication (Large Print) (CommaSeparated Thousands)

5Digit by 1Digit Multiplication (Large Print) (CommaSeparated Thousands) 5Digit by 2Digit Multiplication (Large Print) (CommaSeparated Thousands) 5Digit by 3Digit Multiplication (Large Print) (CommaSeparated Thousands) 5Digit by 4Digit Multiplication (Large Print) (CommaSeparated Thousands) 5Digit by 5Digit Multiplication (Large Print) (CommaSeparated Thousands)

6Digit by 1Digit Multiplication (Large Print) (CommaSeparated Thousands) 6Digit by 2Digit Multiplication (Large Print) (CommaSeparated Thousands) 6Digit by 3Digit Multiplication (Large Print) (CommaSeparated Thousands) 6Digit by 4Digit Multiplication (Large Print) (CommaSeparated Thousands) 6Digit by 5Digit Multiplication (Large Print) (CommaSeparated Thousands) 6Digit by 6Digit Multiplication (Large Print) (CommaSeparated Thousands)
Separating thousands with spaces avoids any confusion with commas and periods. Various number formats in different countries and languages use commas and periods for both decimals and thousand separators, but a space is only ever used as a thousands separator. It is more common in some countries such as Canada and France, but it is being adopted more in other parts of the world.

5Digit by 1Digit Multiplication (SpaceSeparated Thousands) 5Digit by 2Digit Multiplication (SpaceSeparated Thousands) 5Digit by 3Digit Multiplication (SpaceSeparated Thousands) 5Digit by 4Digit Multiplication (SpaceSeparated Thousands) 5Digit by 5Digit Multiplication (SpaceSeparated Thousands)

6Digit by 1Digit Multiplication (SpaceSeparated Thousands) 6Digit by 2Digit Multiplication (SpaceSeparated Thousands) 6Digit by 3Digit Multiplication (SpaceSeparated Thousands) 6Digit by 4Digit Multiplication (SpaceSeparated Thousands) 6Digit by 5Digit Multiplication (SpaceSeparated Thousands) 6Digit by 6Digit Multiplication (SpaceSeparated Thousands)

7Digit by 1Digit Multiplication (SpaceSeparated Thousands) 7Digit by 2Digit Multiplication (SpaceSeparated Thousands) 7Digit by 3Digit Multiplication (SpaceSeparated Thousands) 7Digit by 4Digit Multiplication (SpaceSeparated Thousands) 7Digit by 5Digit Multiplication (SpaceSeparated Thousands) 7Digit by 6Digit Multiplication (SpaceSeparated Thousands) 7Digit by 7Digit Multiplication (SpaceSeparated Thousands)

8Digit by 1Digit Multiplication (SpaceSeparated Thousands) 8Digit by 2Digit Multiplication (SpaceSeparated Thousands) 8Digit by 3Digit Multiplication (SpaceSeparated Thousands) 8Digit by 4Digit Multiplication (SpaceSeparated Thousands) 8Digit by 5Digit Multiplication (SpaceSeparated Thousands) 8Digit by 6Digit Multiplication (SpaceSeparated Thousands) 8Digit by 7Digit Multiplication (SpaceSeparated Thousands) 8Digit by 8Digit Multiplication (SpaceSeparated Thousands)

2Digit by 2Digit Multiplication (Large Print) (SpaceSeparated Thousands) 3Digit by 1Digit Multiplication (Large Print) (SpaceSeparated Thousands) 3Digit by 2Digit Multiplication (Large Print) (SpaceSeparated Thousands) 3Digit by 3Digit Multiplication (Large Print) (SpaceSeparated Thousands)

4Digit by 1Digit Multiplication (Large Print) (SpaceSeparated Thousands) 4Digit by 2Digit Multiplication (Large Print) (SpaceSeparated Thousands) 4Digit by 3Digit Multiplication (Large Print) (SpaceSeparated Thousands) 4Digit by 4Digit Multiplication (Large Print) (SpaceSeparated Thousands)

5Digit by 1Digit Multiplication (Large Print) (SpaceSeparated Thousands) 5Digit by 2Digit Multiplication (Large Print) (SpaceSeparated Thousands) 5Digit by 3Digit Multiplication (Large Print) (SpaceSeparated Thousands) 5Digit by 4Digit Multiplication (Large Print) (SpaceSeparated Thousands) 5Digit by 5Digit Multiplication (Large Print) (SpaceSeparated Thousands)

6Digit by 1Digit Multiplication (Large Print) (SpaceSeparated Thousands) 6Digit by 2Digit Multiplication (Large Print) (SpaceSeparated Thousands) 6Digit by 3Digit Multiplication (Large Print) (SpaceSeparated Thousands) 6Digit by 4Digit Multiplication (Large Print) (SpaceSeparated Thousands) 6Digit by 5Digit Multiplication (Large Print) (SpaceSeparated Thousands) 6Digit by 6Digit Multiplication (Large Print) (SpaceSeparated Thousands)
In some places, periods are used as thousands separators and commas are used as decimals. This is very confusing to people who are used to U.S. formatted numbers.

5Digit by 1Digit Multiplication (PeriodSeparated Thousands) 5Digit by 2Digit Multiplication (PeriodSeparated Thousands) 5Digit by 3Digit Multiplication (PeriodSeparated Thousands) 5Digit by 4Digit Multiplication (PeriodSeparated Thousands) 5Digit by 5Digit Multiplication (PeriodSeparated Thousands)

6Digit by 1Digit Multiplication (PeriodSeparated Thousands) 6Digit by 2Digit Multiplication (PeriodSeparated Thousands) 6Digit by 3Digit Multiplication (PeriodSeparated Thousands) 6Digit by 4Digit Multiplication (PeriodSeparated Thousands) 6Digit by 5Digit Multiplication (PeriodSeparated Thousands) 6Digit by 6Digit Multiplication (PeriodSeparated Thousands)

7Digit by 1Digit Multiplication (PeriodSeparated Thousands) 7Digit by 2Digit Multiplication (PeriodSeparated Thousands) 7Digit by 3Digit Multiplication (PeriodSeparated Thousands) 7Digit by 4Digit Multiplication (PeriodSeparated Thousands) 7Digit by 5Digit Multiplication (PeriodSeparated Thousands) 7Digit by 6Digit Multiplication (PeriodSeparated Thousands) 7Digit by 7Digit Multiplication (PeriodSeparated Thousands)

8Digit by 1Digit Multiplication (PeriodSeparated Thousands) 8Digit by 2Digit Multiplication (PeriodSeparated Thousands) 8Digit by 3Digit Multiplication (PeriodSeparated Thousands) 8Digit by 4Digit Multiplication (PeriodSeparated Thousands) 8Digit by 5Digit Multiplication (PeriodSeparated Thousands) 8Digit by 6Digit Multiplication (PeriodSeparated Thousands) 8Digit by 7Digit Multiplication (PeriodSeparated Thousands) 8Digit by 8Digit Multiplication (PeriodSeparated Thousands)

2Digit by 2Digit Multiplication (Large Print) (PeriodSeparated Thousands) 3Digit by 1Digit Multiplication (Large Print) (PeriodSeparated Thousands) 3Digit by 2Digit Multiplication (Large Print) (PeriodSeparated Thousands) 3Digit by 3Digit Multiplication (Large Print) (PeriodSeparated Thousands)

4Digit by 1Digit Multiplication (Large Print) (PeriodSeparated Thousands) 4Digit by 2Digit Multiplication (Large Print) (PeriodSeparated Thousands) 4Digit by 3Digit Multiplication (Large Print) (PeriodSeparated Thousands) 4Digit by 4Digit Multiplication (Large Print) (PeriodSeparated Thousands)

5Digit by 1Digit Multiplication (Large Print) (PeriodSeparated Thousands) 5Digit by 2Digit Multiplication (Large Print) (PeriodSeparated Thousands) 5Digit by 3Digit Multiplication (Large Print) (PeriodSeparated Thousands) 5Digit by 4Digit Multiplication (Large Print) (PeriodSeparated Thousands) 5Digit by 5Digit Multiplication (Large Print) (PeriodSeparated Thousands)

6Digit by 1Digit Multiplication (Large Print) (PeriodSeparated Thousands) 6Digit by 2Digit Multiplication (Large Print) (PeriodSeparated Thousands) 6Digit by 3Digit Multiplication (Large Print) (PeriodSeparated Thousands) 6Digit by 4Digit Multiplication (Large Print) (PeriodSeparated Thousands) 6Digit by 5Digit Multiplication (Large Print) (PeriodSeparated Thousands) 6Digit by 6Digit Multiplication (Large Print) (PeriodSeparated Thousands)
Other Long Multiplication Strategies
Lattice, or sieve, multiplication is a great strategy for students to use to calculate long multiplication problems on pencil and paper. We've made the first step of preparing a lattice easy as the worksheets below have them predrawn. With a little practice, students can use graph paper or draw their own lattices freehand. The first factor is separated by place value along the top of the lattice, giving each place value its own column. The second factor is separated in the same way, but along the right side with one place value per row. The single digit column and row numbers are multiplied together and their product is written in the corresponding box, separating the tens and ones places on either side of the diagonal. Finally, the diagonal "rows" are summed and regrouped starting with the diagonal in the lower right hand corner which will only have a singldigit in it. The answer keys we've provided should give you a good idea of how to accomplish lattice multiplication like a pro. Once students have a little practice, you might find that this is their preferred method for calculating the products of large numbers. This method is highly scalable, which means it is a straightforward task to multiply a 10digit by a 10digit number, etc.

2Digit × 2Digit Lattice Multiplication 2Digit × 3Digit Lattice Multiplication 3Digit × 2Digit Lattice Multiplication 3Digit × 3Digit Lattice Multiplication 4Digit × 2Digit Lattice Multiplication 4Digit × 3Digit Lattice Multiplication 4Digit × 4Digit Lattice Multiplication 4Digit × 5Digit Lattice Multiplication 5Digit × 4Digit Lattice Multiplication 5Digit × 5Digit Lattice Multiplication
The distributive property of multiplication allows students to "split" factors into addends to make the multiplication easier. This also helps students learn to complete multiplication mentally rather than using paper and pencil methods. Often times, the numbers are split up by place value, so 123 becomes 100 + 20 + 3. If one wanted to multiply 123 by 4, you could multiply 100 by 4, 20 by 4 and 3 by 4 to get 400, 80 and 12 which sums to 492. If you multiply a multidigit number by a multidigit number, you can split both numbers into place value addends. For example, 938 × 74 = (900 + 30 + 4) × (70 + 4) = (900 × 70) + (900 × 4) + (30 × 70) + (30 × 4) + (8 × 70) + (8 × 4) = 63000 + 3600 + 2100 + 120 + 560 + 32 = 69412. All of the worksheets in this section have a model question included. Of course, it might be easier to complete questions with larger numbers using box multiplication.

2Digit × 1Digit Multiplication Using the Distributive Property ✎ 3Digit × 1Digit Multiplication Using the Distributive Property ✎ 4Digit × 1Digit Multiplication Using the Distributive Property ✎ 5Digit × 1Digit Multiplication Using the Distributive Property ✎ 2Digit × 2Digit Multiplication Using the Distributive Property ✎ 3Digit × 2Digit Multiplication Using the Distributive Property ✎
Multiplying on graph paper helps students "line up" their numbers when completing long multiplication questions. These worksheets include custom grids that have the right amount of room for one question.

2Digit × 1Digit Multiplication with Grid Support✎ 2Digit × 2Digit Multiplication with Grid Support ✎ 3Digit × 1Digit Multiplication with Grid Support ✎ 3Digit × 2Digit Multiplication with Grid Support ✎ 3Digit × 3Digit Multiplication with Grid Support ✎ 4Digit × 1Digit Multiplication with Grid Support ✎ 4Digit × 2Digit Multiplication with Grid Support ✎ 4Digit × 3Digit Multiplication with Grid Support ✎ 4Digit × 4Digit Multiplication with Grid Support ✎ 5Digit × 1Digit Multiplication with Grid Support ✎ 5Digit × 2Digit Multiplication with Grid Support ✎ 5Digit × 3Digit Multiplication with Grid Support ✎ 5Digit × 4Digit Multiplication with Grid Support ✎ 5Digit × 5Digit Multiplication with Grid Support ✎

2Digit × 1Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 2Digit × 2Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 3Digit × 1Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 3Digit × 2Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 3Digit × 3Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 4Digit × 1Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 4Digit × 2Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 4Digit × 3Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 4Digit × 4Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 5Digit × 1Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 5Digit × 2Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 5Digit × 3Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 5Digit × 4Digit Multiplication with Grid Support (No Regrouping Boxes) ✎ 5Digit × 5Digit Multiplication with Grid Support (No Regrouping Boxes) ✎
In case you or your students want to make up your own questions, these blanks should expedite the process.

2Digit × 1Digit Multiplication with Grid Support Blanks ✎ 2Digit × 2Digit Multiplication with Grid Support Blanks ✎ 3Digit × 1Digit Multiplication with Grid Support Blanks ✎ 3Digit × 2Digit Multiplication with Grid Support Blanks ✎ 3Digit × 3Digit Multiplication with Grid Support Blanks ✎ 4Digit × 1Digit Multiplication with Grid Support Blanks ✎ 4Digit × 2Digit Multiplication with Grid Support Blanks ✎ 4Digit × 3Digit Multiplication with Grid Support Blanks ✎ 4Digit × 4Digit Multiplication with Grid Support Blanks ✎ 5Digit × 1Digit Multiplication with Grid Support Blanks ✎ 5Digit × 2Digit Multiplication with Grid Support Blanks ✎ 5Digit × 3Digit Multiplication with Grid Support Blanks ✎ 5Digit × 4Digit Multiplication with Grid Support Blanks ✎ 5Digit × 5Digit Multiplication with Grid Support Blanks ✎
The halving and doubling strategy is accomplished very much in the same way as its name. Simply halve one number and double the other then multiply. In many cases, this makes the multiplication of two numbers easier to accomplish mentally. This strategy is not for every multiplication problem, but it certainly works well if certain numbers are involved. For example, doubling a 5 results in a 10 which most people would have an easier time multiplying. Of course, this would rely on the other factor being easily halved. 5 × 72, using the halving and doubling strategy (doubling the first number and halving the second in this case) results in 10 × 36 = 360. Practicing with the worksheets in this section will help students become more familiar with cases in which this strategy would be used.
Multiplying numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

Multiplying Binary Numbers (Base 2) Multiplying Ternary Numbers (Base 3) Multiplying Quaternary Numbers (Base 4) Multiplying Quinary Numbers (Base 5) Multiplying Senary Numbers (Base 6) Multiplying Octal Numbers (Base 8) Multiplying Duodecimal Numbers (Base 12) Multiplying Hexadecimal Numbers (Base 16) Multiplying Vigesimal Numbers (Base 20) Multiplying Hexatrigesimal Numbers (Base 36) Multiplying Various Numbers (Various Bases)