2-Digit Multiplication

2-digit multiplication or double-digit multiplication is done by arranging the numbers in a way such that the given numbers are placed one below the other. A 2-digit number can be multiplied with a single digit, with another 2-digit number, a 3-digit number, and so on. Let us learn more about 2-digit multiplication, the steps for multiplication, and solve a few examples to understand the concept better.

What is 2-Digit Multiplication?

2-digit multiplication is the method of multiplying 2-digit numbers arranged in two place values, i.e., ones and tens. The method of multiplying numbers is the same as multiplying single digits. However, in double digits, we multiply each digit one by one by the multiplier. This means the multiplier is first multiplied with the ones digit of the multiplicand and then it is multiplied with the tens digit of the multiplicand. Let us learn about 2-digit by 1-digit multiplication and 2-digit by 2-digit multiplication in the following sections.

2-Digit by 1-Digit Multiplication

Multiplying 2-digit numbers with 1-digit numbers is quite simple. Let us understand this using the following steps and example.

Example: Multiply 23 × 2

  • Step 1: Place the one-digit number below the 2-digit number. This makes the one-digit number the multiplier. Multiply the one-digit number (the multiplier) with the ones digit of the multiplicand. Here, 2 is the multiplier and the ones digit of the multiplicand is 3. So, 2 × 3 = 6. This partial product (6) will be placed under the ones column.
  • Step 2: Now, multiply the multiplier with the tens digit of the multiplicand. Here, 2 is the multiplier and the tens digit of the multiplicand is 2. This means 2 × 2 = 4. This partial product (4) will be placed in the tens column. Therefore, 23 × 2 = 46

2 Digit Multiplication

Now, let us learn how to multiply 2-digit numbers with 2-digit numbers.

2-Digit by 2-Digit Multiplication

2-digit by 2-digit multiplication means when both the numbers that are to be multiplied are of two digits. The multiplication starts with the ones place first and then moves on to the tens place. The numbers are placed one below the other. Although any of the two numbers can be placed on top or below, it is preferable to place the smaller number below because that makes multiplication easier. Let us understand this multiplication with the help of the following example. Let us multiply 34 × 12. In this case let us consider 34 to be the multiplicand and 12 as the multiplier.

2 Digit by 2 Digit Multiplication

  • Step 1: Place the multiplicand (34) on top and the multiplier (12) below it as shown in the figure given above. Multiply the ones digit of the multiplier with the multiplicand. Here, 34 is the multiplicand and the ones digit of 12 is 2. This will give 34 × 2 = 68. This is the first partial product that will be placed in one line.
  • Step 2: Multiply the multiplicand with the tens digit of the multiplier. Here, 34 is the multiplicand and the tens digit of the multiplier is 1. This will be 34 × 1 = 34. It should be noted that we need to place a zero below the ones digit of the partial product and then write the second partial product. (This 0 is placed here because we are actually multiplying 34 by 10 in this step). So we get 340 here.
  • Step 3: Add both the partial products to get the final product. This will be 68 + 340 = 408.

Now, let us learn about 2-digit multiplication in which we have carry-overs.

2-Digit Multiplication With Regrouping

2-digit multiplication with regrouping or carrying over happens when a number is carried forward. Let us understand this with the following example and steps. Let us multiply 45 × 6.

2 Digit Multiplication With Regrouping

  • Step 1: Multiply the multiplier with the ones digit of the multiplicand. Here, the multiplicand is 45 and the ones digit in 45 is 5, and the multiplier is 6. So, this will be 6 × 5 = 30.
  • Step 2: Since the product obtained in step 1 is 30, we will carry over 3 to the preceding tens column and write 0 below the ones column as the partial product.
  • Step 3: Now, we will multiply the multiplier with the tens digit of the multiplicand. Here, the tens digit of the multiplicand is 4 and the multiplier is 6. So, this will be 6 × 4 = 24. At this point, we need to add the number that was carried over in the previous step. This means 24 + 3 = 27. Therefore, the final product is 270.

2-digit multiplication with decimals is quite similar to the regular multiplication using a few rules of decimal numbers. Let us learn more about it in the following section.

2-Digit Multiplication With Decimals

2-digit multiplication with decimals is done in the same manner as the usual multiplication of double-digits keeping in mind the rules of decimal numbers. While multiplying such numbers we can ignore the decimal point until we have obtained the final result. Once the final result is obtained, we count the number of decimal places in both the numbers, add them and place the decimal point according to that. Let us understand this with an example and multiply 2.5 × 1.1

2 Digit Multiplication With Decimals

  • Step 1: Arrange the numbers vertically according to the place value. Do not align the numbers based on the decimal point.
  • Step 2: Multiply the ones digit of the multiplier with the multiplicand. Here, it is 25 × 1 = 25.
  • Step 3: Place a zero below the ones digit of the partial product.
  • Step 4: Multiply the tens digit of the multiplier with the multiplicand. This will be 25. Place this next to the 0 below the partial product.
  • Step 5: Add the two products to get the final product. Here, 25 + 250 = 275.
  • Step 6: Place the decimal point after 2 places from the right in the final product. Since the multiplicand and the multiplier have 1 decimal place each, this makes it 1 + 1 = 2 decimal places. Therefore, we place the decimal point after 2 places from the right and we get 2.5 × 1.1 = 2.75

☛ Related Topics

  • 2-Digit Subtraction
  • 2-Digit Addition
  • 3-Digit Addition
  • 3-Digit Subtraction
  • 3-Digit Multiplication
  • 4-Digit Addition
  • 4-Digit Subtraction
  • Multiplication and Division of Integers

Examples on 2-Digit Multiplication

Example 1: Find the product of 67 × 20.

Solution: Let us understand this 2-digit multiplication using the following steps.

  • Multiply 0 with both 7 and 6.
  • Place a zero below the ones digit of the partial product.
  • Multiply 2 with both 7 and 6.
  • Add the products to obtain the final answer.

Example of 2 Digit Multiplication

Therefore, 67 × 20 = 1340.

Example 2: Multiply 31 × 7

Solution: Let us do this 2-digit multiplication using the following steps.

  • Multiply 7 with 1, that is, 7 × 1 = 7
  • Now multiply 7 with 3, that is, 7 × 3 = 21
  • Write them together as 217
  • Therefore, 31 × 7 = 217

Example 3: State true or false with respect to 2-digit multiplication.

a.) 10 × 11 = 110

b.) 20 × 20 = 40

a.) True, 10 × 11 = 110

b.) False, 20 × 20 = 400

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Practice Questions on 2-Digit Multiplication

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FAQs on 2-Digit Multiplication

2-digit multiplication is a method of multiplying a 2-digit number with another number. The numbers are placed one below the other to perform multiplication. The number written on top is known as the multiplicand and the number written below is the multiplier. 2-digit numbers can be multiplied with 1-digit numbers, 2-digit numbers , and so on.

How to do 2-Digit Multiplication?

The following steps explain the process of 2-digit multiplication. For example, let us multiply 42 × 3

  • Arrange the numbers one below the other such that the bigger number (42) is on top and the smaller one (3) is below it. So, 3 becomes the multiplier while 42 becomes the multiplicand.
  • Start multiplying the multiplier with the ones digit of the multiplicand. Here, 3 will be multiplied with 2 which will give 3 × 2 = 6. This 6 will be written as the partial product.
  • Then, multiply 3 with the tens digit of the multiplicand, that is 4, which will be 3 × 4 = 12. Now, writing both the products together, the final product will be 42 × 3 = 126

How to do Two-Digit Multiplication with Carrying?

Two-digit multiplication with carrying is done when the product of one column is more than 9. The extra digit is carried over to the next column and added to that particular product. For example, let us multiply 45 × 7.

  • Place 45 on top and 7 below it so that 45 becomes the multiplicand and 5 becomes the multiplier.
  • Multiply 7 with 5 and it will give 7 × 5 = 35. Since the product is a two-digit number 35, we will carry over 3 to the tens column and write 5 below the ones column as the partial product.
  • Now, multiply the multiplier with the tens digit of the multiplicand. Here, the tens digit of the multiplicand is 4 and the multiplier is 7. So, this will be 7 × 4 = 28. At this point, we need to add the number that was carried over in the previous step. This means 28 + 3 = 31. Therefore, the final product is 315.

How to do 2-Digit by 1-Digit Multiplication?

2-digit by 1-digit multiplication is done in the same way as single-digit multiplication. For example, let us multiply 13 × 2.

  • The double-digit (13) is written on top and the single digit (2) is written below, so 13 becomes the multiplicand and 2 becomes the multiplier.
  • We start multiplying the bottom digit (multiplier) with the ones digit of the multiplicand. Here, we will multiply 2 with 3 which will be 2 × 3 = 6. We will note down this 6.
  • Then we move on and multiply the bottom digit (multiplier) with the tens digit of the multiplicand. Here, 2 × 1 = 2. This will also be written along with with the product obtained in the previous step. So, this will give the product as, 13 × 2 = 26.

How to do 2-Digit by 2-Digit Multiplication?

2-digit by 2-digit multiplication is the process of multiplication where a 2-digit number is multiplied with another 2-digit number. For example, let us multiply 23 × 14.

  • Place 23 on top and 14 below it so that 23 becomes the multiplicand and 14 becomes the multiplier.
  • Multiply the ones digit of the multiplier with the multiplicand. Here, 23 is the multiplicand and the ones digit of 14 is 4. After multiplying 23 with 4 we get 23 × 4 = 92. This is the first partial product that will be placed in one line.
  • Multiply the multiplicand with the tens digit of the multiplier. This means we will multiply 23 with 1 and it will be 23 × 1 = 23. It should be noted that we need to place a zero below the ones digit of the partial product and then write the second partial product next to it. (This 0 is placed here because we are actually multiplying 23 by 10 in this step.) So we get 230 here.
  • Now we will add both the partial products to get the final product. This will be 92 + 230 = 322.
  • Therefore, the final product is 23 × 14 = 322.

How to do 3-Digit by 2-Digit Multiplication?

3-digit by 2-digit multiplication means we multiply a 3-digit number with a 2-digit number. The rules that are followed for the multiplication of a 2-digit number with the other digit numbers apply to this multiplication as well. For example, let us multiply 243 × 45.

  • We place the 3-digit number (243) on top and the 2-digit number (45) below it, so 243 becomes the multiplicand and 45 becomes the multiplier.
  • Multiply the ones digit of the multiplier with the multiplicand. Here, 243 is the multiplicand and the ones digit of 45 is 5. After multiplying 243 with 5 we get 243 × 5 = 1215. This is the first partial product that will be placed in one line.
  • Now, multiply the multiplicand with the tens digit of the multiplier. This means we will multiply 243 with 4 and it will be 243 × 4 = 972. We need to place a zero below the ones digit of the partial product and then write the second partial product next to it. So we get 9720 here.
  • Now we will add both the partial products to get the final product. This will be 1215 + 9720 = 10935
  • Therefore, the final product is 243 × 45 = 10935.
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How to Do Double Digit Multiplication

Last Updated: November 3, 2023 Fact Checked

This article was reviewed by Grace Imson, MA and by wikiHow staff writer, Jessica Gibson . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 779,450 times.

Double digit multiplication is simply single-digit multiplication done twice. It starts off just the same with multiplying the numbers in the ones place, and then you add a second round of multiplication using the numbers from the tens place. After getting the basic formula down, there are also a few tricks you can master in order to get this process going as quickly as possible.

Calculating Double Digits by Double Digits

Step 1 Write the double-digit numbers on top of each other.

  • For example, if you're multiplying 22 by 43, you can put either number on the top or bottom.

Step 2 Multiply the bottom one's number by the top one's number.

  • So for 22 x 43, you'll multiply 3 by 2 to get 6.

Step 3 Multiply the bottom one's number by the number of the top ten.

  • For example, with 22 x 43, you'll now need to multiply 3 by the other 2 to get 6. The number under your line should be 66.

Step 4 Place a zero under your result.

  • So if you've got 66 as your first result, put a 0 right under the 6 in the ones place.

Step 5 Multiply the bottom tens number by the top one's number.

  • For example, 4 x 2 = 8, so write an 8 next to the 0.

Step 6 Multiply the bottom tens number by the number of the top ten.

  • For 4 x 2, write another 8 next to the 80 you already have written down.

Step 7 Add both of your results to get a final answer.

  • For example, you'll need to add 66 + 880 to get 946.

Carrying Results

Step 1 Multiply and carry results that are larger than 9.

  • For example, if you're multiplying 96 by 8, when you multiply the 6 by 8, you'll get 48. Instead of writing 48 below your line, write an 8 and carry the 4.

Step 2 Multiply the tens place and add the carried value.

  • For example, for 96 x 8, multiply 8 and 9 to get 72. Then add the 4 that you carried to get 76. This will give you a final answer of 768.

Step 3 Continue multiplying and carrying if necessary.

Practice Problems and Answers

how to solve two digit multiplication problem

Community Q&A

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Divide by a Two‐Digit Number

  • ↑ http://www.ducksters.com/kidsmath/long_multiplication.php
  • ↑ https://www.ducksters.com/kidsmath/long_multiplication.php
  • ↑ http://www.numbernut.com/arithmetic/multiply-2digit.html
  • ↑ http://www.numbernut.com/arithmetic/multiply-carry.html

About This Article

Grace Imson, MA

To do double digit multiplication, start by putting one number on top of the other number and draw a line under them. Then, multiply the bottom ones number by the top ones number and write the answer under the line. Next, multiply the bottom ones number by the top tens number and write that answer next to the first answer. Once you've done that, place a 0 under your result. Multiply the bottom tens number by the top tens number, then add both results together to get your final answer! To learn how to carry results that are greater than 9, scroll down! Did this summary help you? Yes No

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2 Digit Multiplication Worksheets

2 Digit Multiplication Worksheet picture

Welcome to our 2 Digit Multiplication Worksheets page. We have plenty of worksheets on this page to help you practice the skills of multiplying 2-digit numbers by 2 digits.

There are also step-by-step instructions and some worked examples to help you master this skill.

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  • How to Multiply two 2-Digit Numbers

2 Digit Multiplication Worked Examples

2 digit multiplication video, 2-digit multiplication worksheets.

  • 2-Digit by 2-Digit Multiplication Challenges
  • Easier/Harder Worksheets
  • More Recommended Math Resources

We have a range of resources on this page to help you learn to multiply 2-digit by 2-digit numbers.

There are pratice worksheets, worked examples and a video to help you learn this skill.

As well as standard multiplication worksheets, we have a range of extra challenges for students who are already confident with 2-digit multiplication.

These sheets are aimed at 4th grade (or similar level) students.

Before you learn to multiply two 2-digit numbers, you should be confident multiplying a 2-digit number by a single digit .

How to Multiply two 2-digit numbers

How to multiply a 2-digit number by a 2-digit number.

In this example, we are working out 39 x 25.

Step 1) Multiply the ones digit of the first 2-digit number (at the top) and the ones digit of the second 2-digit number together.

  • Write the number of ones below the line in the ones place.
  • Carry over any tens and write them above the first 2-digit number in the tens place.

5 x 9 = 45. Write the 5 below the line in the ones place. Carry over 4 tens.

Step 2) Multiply the tens digit of the first 2-digit number and the ones digit of the second 2-digit number together, adding on any tens that you carried over.

  • Write the number below the line in the tens place (or in the hundreds and tens place if the answer has 2 digits).

5 x 3 = 15. 15 + 4 = 19. Write the 1 in the hundreds place and 9 in the tens place below the line.

We have now worked out: 39 x 5 = 195.

Step 3) We now have to work out 39 x 20. Put a 0 in the ones place underneath the 5. This is a placeholder because we are multiplying by tens. Cross out any numbers which were carried over so that we do not confuse them with the next steps.

Step 4) Multiply the ones digit of the first number and the tens digit of the second number together.

  • Write the number below the line in the tens place carrying over any tens above the tens digit of the first number.

2 x 9 = 18. Write the 8 in the tens place to the left of the 0 we wrote in Step 3) and carry over 1 above the tens digit of the first number.

Step 5) Multiply the tens digit of the first number and the tens digit of the second number together, adding on any numbers that we carried over.

2 x 3 = 6. 6 + 1 = 7. Write the 7 in the hundreds place to the left of the 8 we wrote in Step 3).

We have now worked out: 39 x 20 = 780.

Step 6) Finally we have to add up the answers from the two multiplications we have just worked out.

We need to add up 195 and 780 (the answers from 39 x 5 and 39 x 20) to find 39 x 25.

Adding the two numbers using the standard method gives us:

Our final answer is 39 x 25 = 975.

Example 1) Work out 37 x 13.

3 x 7 = 21. Write the 1 in the ones column underneath the line. Carry the 2 tens into the tens column above the number 3.

Write the answer below the tens digit.

3 x 3 = 9. 9 + 2 = 11. Write the 1 in the hundreds place and 1 in the tens place below the line.

This tells us that 37 x 3 = 111.

Step 3) We now have to work out 37 x 10. Put a 0 in the ones place underneath the 1. Cross out the '2' which we carried over so that we do not confuse it in the next steps.

1 x 7 = 7. Write the 7 in the tens place to the left of the '0' we have just written.

1 x 3 = 3. Write the 3 in the hundreds place to the left of the '7' we have just written.

This tells us that 37 x 10 = 370.

Step 6) We now have to add up the two answers from the two multiplications we have just worked out.

We need to add up 111 and 370.

Adding the two numbers using the standard algorithm gives us:

This gives us a final answer of: 37 x 13 = 481

Example 2) Work out 46 x 35.

5 x 6 = 30. Write the 0 in the ones column underneath the line. Carry the 3 tens into the tens column above the number 4.

5 x 4 = 20. 20 + 3 = 23. Write the 2 in the hundreds place and 3 in the tens place below the line.

This tells us that 46 x 5 = 230.

Step 3) We now have to work out 46 x 30. Put a 0 in the ones place underneath the 1 to use as a placeholder. Cross out the '3' which we carried over so that we do not confuse it in the next steps.

3 x 6 = 18. Write the 8 in the tens place to the left of the '0' we have just written. Carry the 1 over and write it above the 3 we crossed out.

3 x 4 = 12. 12 + 1 = 13. Write the 1 in the thousands place and 3 in the hundreds place to the left of the '8' we have just written.

This tells us that 46 x 30 = 1380.

We need to add up 230 and 1380.

This gives us a final answer of: 46 x 35 = 1610

Example 3) Work out 79 x 28.

8 x 9 = 72. Write the 2 in the ones column underneath the line. Carry the 7 tens into the tens column above the number 7.

8 x 7 = 56. 56 + 7 = 63. Write the 6 in the hundreds place and 3 in the tens place below the line.

This tells us that 79 x 8 = 632.

Step 3) We now have to work out 79 x 20. Put a 0 in the ones place underneath the 2 to use as a placeholder. Cross out the '7' which we carried over so that we do not confuse it in the next steps.

2 x 9 = 18. Write the 8 in the tens place to the left of the '0' we have just written. Carry the 1 over and write it above the 7 we crossed out.

2 x 7 = 14. 14 + 1 = 15. Write the 1 in the thousands place and 5 in the hundreds place to the left of the '8' we have just written.

This tells us that 79 x 20 = 1580.

We need to add up 632 and 1580.

This gives us a final answer of: 79 x 28 = 2212

We have created a short video to show you how to multiply two 2-digit numbers.

In the video, you will see:

  • four different examples of 2 digit multiplication
  • step-by-step instructions

These sheets are aimed at 4th graders.

Sheet 1 involves 2-digit by 2-digit multiplication with smaller numbers and answers up to 1000.

Sheets 2 to 4 have harder 2-digit numbers to multiply and answers that are generally larger than 1000.

  • Multiplication 2 Digits by 2 Digits Sheet 1
  • Sheet 1 Answers
  • PDF version
  • Multiplication 2 Digits by 2 Digits Sheet 2
  • Sheet 2 Answers
  • Multiplication 2 Digits by 2 Digits Sheet 3
  • Sheet 3 Answers
  • Multiplication 2 Digits by 2 Digits Sheet 4
  • Sheet 4 Answers

2 Digit Multiplication Challenges

These 2-digit multiplication worksheets have been designed for more able students who need that extra challenge!

  • 2 Digit by 2 Digit Multiplication Challenge 1
  • 2 Digit by 2 Digit Multiplication Challenge 2
  • 2 Digit by 2 Digit Multiplication Challenge 3

Looking for some easier Multiplication Worksheets?

These sheets are aimed at 3rd graders.

We have a range of 2-digit by 1-digit multiplication worksheets and challenges available on our 3rd grade multiplication page.

There are also some worked examples and support to help you master this skill.

2 Digit by 1 Digit Multiplication

  • Multiplication Worksheets for 3rd Grade 2-digits by 1-digit

Looking for some harder Multiplication Worksheets?

We have more 2-digit multiplication worksheets, including 2-digit x 3-digit multiplication problems on this page.

  • More Double digit Multiplication Worksheets (harder)

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

  • Multi-Digit Multiplication Worksheet Generator

Need to create your own long or short multiplication worksheets quickly and easily?

Our Multiplication worksheet generator will allow you to create your own custom worksheets to print out, complete with answers.

  • Single Digit Multiplication Worksheets Generator

Multiplication Table Worksheets

Here you will find a range of Multiplication Worksheets to help you become more fluent and accurate with your tables.

Using these sheets will help your child to:

  • learn their multiplication tables up to 10 x 10;
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All the free 3rd Grade Math Worksheets in this section are informed by the Elementary Math Benchmarks for 3rd Grade.

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Using these games will help your child to learn their multiplication facts to 5x5 or 10x10, and also to develop their memory and strategic thinking skills.

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Multiply 2-digit numbers by 2-digit numbers

Related Pages Divide 2-digit numbers by 1-digit numbers More Lessons for Grade 4 Math Math Worksheets

These lessons help Grade 4 students learn how to multiply 2-digit numbers by 2-digit numbers. They include examples, solutions, videos, stories, and songs to help with multiplication skills.

The following diagram shows how to multiply a 2-digit number by a 2-digit number. Scroll down the page for more examples and solutions on multiplying 2-digit numbers.

2 Digit Multiplication

2-digit × 2-digit Multiplication Worksheets (printable & online)

Multiplying 2 digit number by another 2 digit number with regrouping

  • Multiply by the one’s place.
  • Put a zero to hold the ones’ place.
  • Multiply by the number in the ten’s place.
  • Add the numbers together.

Multiplication of two-digit numbers

Multiply 2 digits by 2 digits

Multiplying a 2-digit number by a 2-digit number

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Multiplication (2-Digits Times 2-Digits)

The worksheets below require students to multiply 2-digit numbers by 2-digit numbers. Includes vertical and horizontal problems, as well as math riddles, task cards, a picture puzzle, a Scoot game, and word problems.

Multiplication 2-Digits Times 2-Digits Worksheets

2-Digit Times 2-Digit Worksheets

Common Core

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Multi-Digit Multiplication Worksheet Generator

Here's a tool that you can use to make your own customized PDF math worksheets. You can select the number of digits in both factors. You can also toggle between horizontal and vertical problems.

Games and Task Cards

Lattice multiplication.

English and Spanish Versions Available

This index page can direct you to any type of multi-digit multiplication worksheets on our website. Includes multiplying by 1, 2, and 3-digit numbers. Also have money, decimal, and fraction multiplication.

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Multiplication Games (Printable)

PDF with answer key:

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Lesson Plan for Introduction to Two-Digit Multiplication

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  • Ph.D., Education, University of Illinois at Urbana-Champaign
  • M.A., Curriculum and Instruction, University of Illinois at Urbana-Champaign

This lesson gives students an introduction to two-digit multiplication. Students will use their understanding of place value and single digit multiplication to begin multiplying two-digit numbers.

Class: 4th grade

Duration: 45 minutes

  • coloring pencils or crayons
  • straight edge

Key Vocabulary: two-digit numbers, tens, ones, multiply

Students will multiply two two-digit numbers correctly. Students will use multiple strategies for multiplying two-digit numbers.

Standards Met

4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Two-Digit Multiplication Lesson Introduction

Write 45 x 32 on the board or overhead. Ask students how they would begin to solve it. Several students may know the algorithm for two-digit multiplication. Complete the problem as students indicate. Ask if there are any volunteers who can explain why this algorithm works. Many students who have memorized this algorithm don't understand the underlying place value concepts.

Step-by-Step Procedure

  • Tell students that the learning target for this lesson is to be able to multiply two-digit numbers together.
  • As you model this problem for them, ask them to draw and write what you present. This can serve as a reference for them when completing problems later.
  • Begin this process by asking students what the digits in our introductory problem represent. For example, "5" represents 5 ones. "2" represents 2 ones. "4" is 4 tens, and "3" is 3 tens. You can begin this problem by covering the numeral 3. If students believe that they are multiplying 45 x 2, it seems easier.
  • Begin with the ones: 4 5 x 3 2 = 10  (5 x 2 = 10)
  • Then move on to the tens digit on the top number and the ones on the bottom number: 4 5 x 3 2 10 (5 x 2 = 10) = 80 (40 x 2 = 80. This is a step where students naturally want to put down “8” as their answer if they aren’t considering the correct place value. Remind them that “4” is representing 40, not 4 ones.)
  • Now we need to uncover the numeral 3 and remind students that there is a 30 there to consider: 4 5 x 3 2 10 80 = 150 (5 x 30 = 150)
  • And the last step: 4 5 x 3 2 10 80 150 = 1200 (40 x 30 = 1200)
  • The important part of this lesson is to constantly guide students to remember what each digit represents. The most commonly made mistakes here are place value mistakes.
  • Add the four parts of the problem to find the final answer. Ask students to check this answer using a calculator.
  • Do one additional example using 27 x 18 together. During this problem, ask for volunteers to answer and record the four different parts of the problem: 27 x 18 = 56 (7 x 8 = 56) =160 (20 x 8 = 160) = 70 (7 x 10 = 70) =200 (20 x 10 = 200)

Homework and Assessment

For homework, ask students to solve three additional problems . Give partial credit for the correct steps if students get the final answer wrong.

At the end of the mini-lesson, give students three examples to try on their own. Let them know that they can do these in any order; if they want to try the harder one (with larger numbers) first, they are welcome to do so. As students work on these examples, walk around the classroom to evaluate their skill level. You will probably find that several students have grasped the concept of multi-digit multiplication fairly quickly, and are proceeding to work on the problems without too much trouble. Other students are finding it easy to represent the problem, but make minor errors when adding to find the final answer. Other students are going to find this process difficult from beginning to end. Their place value and multiplication knowledge are not quite up to this task. Depending on the number of students who are struggling with this, plan to reteach this lesson to a small group or the larger class very soon.

  • Practice Multiplication Skills With Times Tables Worksheets
  • A Lesson Plan to Teach Rounding by 10s
  • Two-Digit Multiplication Worksheets to Practice With
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  • Understanding the Factorial (!) in Mathematics and Statistics
  • 4th Grade Math Lesson on Factor Trees
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  • How to Solve 2 Digit Multiplication Problems

ffImage

Understanding Double Digit Multiplication with Solved Examples

Multiplication is one of the easiest mathematical operations and it is all about combining numbers or other quantities under specific rules to obtain their product. It's a process of repeated addition of a number with respect to the other number. For example, 6X5 means we add 6, 5 times; 6+6+6+6+6=30. This addition process is very complicated and therefore these multiplication methods come in handy.

Before we start, we should at least know the basics of multiplication which are

Multiplicand (the first number) X Multiplier (the second number) = Product

Any number multiplied by 0 makes the product equal to 0. e.g.- 5x0=0

Any number multiplied by 1 equals the same number. e.g.- 5x1=5

Three Simple Methods of Double Digit Multiplication

There are 3 main methods of 2-digit by 2-digit multiplication , which are discussed below.

The traditional method

Box/window method

Lattice method

1. Using the Traditional Method

Step 1: Set the problem up. So, we will have to align them according to their place value .

Step 2: Multiplying the number in the one's place and tens place of the multiplier with the entire multiplicand separately.

Note: We need to put 0 before we do the second digit of the multiplier.

Step 3: Add both the values which we got from multiplying separately.

carried = 5

Step 1 of Multiplication

Step 1 of Multiplication

5X2 = 10, 1 will be carried forward to the tens place

Step 2 of Multiplication

Step 2 of Multiplication

2X2 = 4 and +1 that we

4X5 = 20, 2 carried forward

4X2 = 8 and +2 (carry)= 10. We drop down the 1 as well because there is no further number available to carry.

Step 3 of Multiplication

Step 3 of Multiplication

Step 4 of Multiplication

Step 4 of Multiplication

50+1000 we get 1050 which is our final product.

2. Box/Window Method

Step 1: Make a box table or a grid of 2X2 as we are doing a 2-digit multiplication equation.

Step 2: Breaking these factors up into their expanded forms. So, 32 becomes 30 and 2; 34 becomes 30 and 4.

Note: Label the expanded form of the multiplicand on the top and the expanded form of the multiplier on the left-hand side of the grid.

Step 3: We multiply the numbers that meet in each space on the box. Follow the image above.

Step 4: Add all those small products that we got in order to obtain the final product.

Expanded forms of Factors

Expanded forms of Factors

Step 2 of the box Method

Step 2 of the box Method

900+60+120+8=1088 -> Final Product

3. Lattice Method

Step 1: Make a grid that matches according to the number of digits required. In this case, we require a 2X2 grid as we are doing 2 digits multiplication.

Note: There is no need to expand the factors so we directly label the multiplicand on top of the grid and the multiplier on the right-hand side of the grid.

Step 2: Multiply the numbers that meet in each space and write the tens place value of the product on the top of the box and the ones place value of the same on the bottom of the box.

Step 3: Adding the numbers which are in the same lane.

Step 1 of the Lattice Method

Step 1 of the Lattice Method

2X4=08 (we put 0 in the tens place)

Steps of Lattice Method

Steps of Lattice Method

We put 0 as it is because there is no other number to add it with.

0+8+2=10 (1 has been directly put into the thousands place)

So, our final product is 1050.

Solved Examples

Below are some of the 2-digit by 2-digit multiplication problems:

Q1. 98X66=?

Solution of Q 1

Solution of Q 1

Q2. 75X39=?

Solution of Q 2

Solution of Q 2

Practice on Your Own

In this article, we were able to understand 3 main methods which can be used to multiply numbers which are of 2 digits. If we see, the traditional method is handier and is very easy to multiply numbers that are more than 2 digits as well. We also understood the steps involved in all the 3 methods with the help of images that had the procedures illustrated. You can visit our website to download and practise some multiplication two-digit numbers worksheets for better understanding.

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FAQs on How to Solve 2 Digit Multiplication Problems

1. What is a multiplication wheel?

Multiplication wheel is the easiest way to learn times tables for beginners who are very new to multiplication. It is a method where the number (multiplicand) written at the centre of the wheel is multiplied by the numbers which are surrounding it (multiplier) and the product is written in the blanks.  This method speeds up the ability to memorise single-digit multiplication. Teachers often make it interesting by using artistic and crafty methods to explain the multiplication wheel for better understanding and learning. 

2. What is the commutative law of multiplication?

According to the commutative law of multiplication and addition, the product of two integers will not change regardless of their positionings. The product of two numbers will stay the same even if their positions are interchanged. For example, 6X5=5X6=>30 (in the case of multiplication) and 6+5=5+6=>11 (in the case of addition).  It is called commutative because the numbers can travel back and forth or be swapped and still will have the same answer. 

3. What is the formula for multiplying a decimal by a whole number?

Performing regular multiplication without considering the decimal point at the beginning is similar to multiplying a decimal by a whole number. After analysing the numbers, the decimal point is placed according to their decimal places. Therefore, all multiplicands and multipliers in the product must be placed in a way that makes the decimal point equal to the sum of the decimal places in the product. 

how to solve two digit multiplication problem

Strategies for Teaching Multi-Digit Multiplication

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Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

Common Core requires that we teach students strategies before we introduce them to the traditional algorithms. When it comes to teaching multi-digit multiplication, it’s common for teachers to focus solely on the partial products method and forget about the rest. Instead, I like to scaffold my students’ learning first so that they are ready for both partial products and the traditional algorithm with more concrete methods.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

It’s important that we are teaching students in the way that they learn best. One method of scaffolding is to start all concepts in a concrete manner and then work toward a more abstract manner. I talk about this in my post, Teaching Math so Students Get It . In this case of teaching my students how to multiply multi-digit numbers, I first start with the area model, then work up to the box model, introduce the distributive property, and then move into the partial products method. Depending on your grade level and standards, then you may teach the traditional algorithm after. This allows for scaffolding, instead of rescuing students later on.

The Area Model as a Multi-Digit Multiplication Strategy

When I introduce my students to the area model, I first remind them of what this model looks like with basic multiplication numbers, such as 7 x 8. I provide students with base-ten blocks and have them create an array. Then I ask them to “just try” creating one with a larger number such as 27 x 4. Then, depending on how that goes, we will create the model. I will either model it or guide them. I remind students of place value and together we first create the sides of our array. For instance, in the problem 27 x 4, we create the two tens and the seven ones using our base ten blocks on one side and create the four ones on the other.

Next, we have to fill in the space to create an array. I express that we could do this with actual one base ten blocks, but it would take us a long time. Instead, it would be best to use the larger ones that would fit. This is an important step because later they will need this when they get to double digits and with understanding division. Once everything is filled in, we now count our total blocks for that section and add them up to get our final answer. You can see this in the anchor charts below, found in my fourth grade multi-digit multiplication math workshop unit (or found on TpT here ).

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

Using the area model with 2-digit numbers by 2-digit numbers is essentially the same, except the area model is just a bit larger. (I don’t recommend moving into the 2-digit by 2-digit model until after you have had plenty of practice with all of the multi-digit numbers by 1 digit. This post is to assist all multi-digit multiplication needs.) This area model typically involves more tens and hundreds.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

The Box Model as a Multi-Digit Multiplication Strategy

The box model follows the area model perfectly!

As seen in the image below, I typically create an area model first and then draw boxes around it to show my students the relationship between the two. Instead of actually usually manipulatives (concrete), we are now moving into drawing our models. In fact, in my math workshop and in my class, I often have my students draw symbols of the base-ten blocks after they have created the area model, so the transition is even nicer.

Now students are in the semi-concrete or representational stage. They are drawing the boxes and placing the numbers outside the box so that they can determine the answers for each box through multiplication.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

The box model is really no different except that now they are not physically manipulating any base-ten blocks. This is a great time to mention decomposing, because that will be something you’ll be mentioning a lot during both the distributive property and later in other concepts, such as area.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

When I talk about decomposing, I like to remind my students that this is really no different than what they did when they broke numbers up into the expanded form.

how to solve two digit multiplication problem

When students work on the 2-digit numbers by 2-digit numbers, they are now working with a 4-square box. Just as before, they are only multiplying the boxes in a grid-like way and then adding them up. See the charts below for a more detailed explanation.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

The Distributive Model as a Multi-Digit Multiplication Strategy

For some reason, teachers don’t like to tackle the distributive property and/or the students fear it. But, if you have worked your way up using the previous methods, this strategy isn’t as scary as it appears.

Since we just talked about decomposing numbers in the last strategy, students should now know they can take the larger number and break it up into smaller numbers. I give them the freedom to choose how they break it up. Then I provide them with boxes to break it up and multiply away!

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

Down at the bottom of this distributive property chart (above), you can see that I have turned the box sideways and have used colored pens. I did this intentionally before I moved into partial products. I wanted to make sure students are seeing what each box is made up of. For instance, the first box (in red) is 100 x 6, the second box (in yellow-orange) is 20 x 6, and the third box is 3 x 6. Then I showed them how it’s written out and added up. I did this for two reasons. First, because they will see this again when we get to partial products (next), and second because they will see it when they learn to use the distributive property in algebra (FOIL) later.

Partial Products as a Multi-Digit Multiplication Strategy

Most teachers are likely aware of the Partial Products method. In case you are not, it’s really just taking the larger number and breaking it out into expanded form and then having the other factor multiply each of the expanded form factors. Then they are added up to get the final product. (See chart below.)

You’ll notice that my colors are back. Whenever possible, I use colors to help differentiate each step. I remind students that we are using the distributive property (which is not scary now!) and decompose our larger number into the expanded form. Then we multiply each new factor one at a time. I always write each new product with the multiplication problem next to it so students can see where I got it from. Then, after we have found all the products to each of those, we add them up to find our final product. This strategy also helps later when introducing the “placeholder” in the traditional algorithm.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

When we get to double digits, it is the same thing, but I like to introduce a method called the “bow tie method.” Just as before, students would decompose both factors into an expanded form. Then they multiply in a bow tie method. If you look at the illustration below, you can see this method through the use of the colors. I actually have my students draw it on their papers to help them so they don’t miss a factor as they are multiplying. As they work through the bow tie method, they record the products for each one. Once finished, they add the products together to get the final product.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

Understandably, if you prefer to have your students begin preparing for the traditional algorithm, you could have them do the “bow tie” method in the traditional algorithm motions, like in the chart below. Overall, the point of the “bow tie” method is to make sure no factors are missed or hit twice.

Do your students struggle with multiplying large numbers? Help them learn multi-digit multiplication with strategies such as the area model, the box method, the partial products method, and the distributive property today! Click here to find out more.

For students to truly be ready for multi-digit multiplication with the traditional algorithm, they must first go through the strategies that Common Core requires. This requires us to also teach in the way that students learn best. If you want your students to do well with multi-digit multiplication, you will need to scaffold the concepts by first starting with the concrete method of using an area model, working to a semi-concrete, representational model of the box method, and then into both the distributive property and the partial products method.

Using just one method will not cut it. Students need this gradual release with multi-digit multiplication before they’ll be ready or they just won’t fully understand the concept and be successful.

Grab the FREEBIE!

To help your students practice these strategies, I have a freebie to get you started! Click here to download the freebie!

Then check out my multi-digit multiplication lesson plans, games, and activities that go along with these anchor charts so that you can save time lesson planning today. Purchase the 4th grade Large Numbers Multiplication Math Workshop Unit here on my website or found on TpT by clicking here .

how to solve two digit multiplication problem

Check out these related 4th Grade Math Workshop Units!

Multiplication & Division Basics Guided Math Workshop Grade 4

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Multiplication Tricks

Multiplication tricks are required to calculate long and difficult multiplication problems. For single digit, 2-digit and even for 3-digit numbers, it is easy to do the multiplication. But for larger numbers which have more digits such as 4, 5, 6, 7,etc., it takes a long time to solve it. Therefore, we will learn here some magic maths tricks for fast calculation. These tricks can also be used to prepare for competitive exams.

In Maths, there is a number of arithmetic calculations or operations which includes multiplication and division, addition, subtraction, differentiation, integration, etc. Each calculation has its own method to calculate the relation between the numbers based upon the operation performed on them. Along with the methods, it is always useful to learn some multiplication tricks to save time.

What are Multiplicand and Multiplier?

It is necessary to know, what are the numbers called when we apply multiplication operation in them.

  • The multiplicand is the number which is being multiplied
  • The multiplier is the number which is multiplying the first number.

For example : In this operation, 45 × 20, 45 is the multiplicand and 20 is the multiplier.

How to Multiply Fast?

Here are some tips and tricks with the help of which, you can easily solve multiplication problems. These tricks you can use in competitive exams as well. Students can by-heart multiplication tables to calculate fats. Let check the multiplication tricks for different numbers.

Multiplication by 2: It denotes to double a number.

For example; 5 × 2, here we have to double the number 5, so we can use addition method here, i.e.

Multiplication by 3:  It denotes triple times of a number.

Example: 5 × 3 = 5 + 5 + 5 = 15

Multiplication by 4: It denotes double of a double number.

Example: 5 × 4: double of 5 is 10. Thus double of 10 is 20(10+10)

Multiplication by 5: If a number is multiplied by 5, then divide the number by 2 and multiply by 10.

Example: 8 × 5: 8 divide by 2 = 4, multiply 4 by 10, 4 × 10 = 40.

Multiplication by 8: Double → Again Double → Again Double

Example: 5 × 8: 5 + 5 = 10; 10 + 10 = 20; 20 + 20 = 40

Multiplication by 9: Add +1 to 9 and minus the number with itself, which is to be multiplied.

Example: 5 × 9: 9+1 × 5-5 = 10 × 5 – 5 = 50 -5 = 45

Multiplication Table

Multiplication method is basically designed to form tables of different numbers. It is always suggested for students to learn by heart the tables from 2 to 20 at least, which will help to solve multiplication problems very easily.

Let us create a table for multiplication of 2 to 10 numbers, which will help you to memorize the table.

With this table, you can see each number is appearing twice. There is a duplicate for each number inside the table. For example, 3 × 6 = 18 but also 6 × 3 = 18.

Learning from the table is the general trick of multiplication. Now let us learn about multiplying tricks of 4 digit numbers along with the general method and rounding up method.

Also, learn:

General Method for Multiplication

In this method, we apply the simple procedure of multiplication.

For example 6780

————–

So you can see there are only one digit multiplier and 4 digit multiplicand. Easily with the help of a table, you can solve such problems.

List of Important Multiplication Tricks

Case 1: Multiplication of the given number by 5 n . (5, 25, 125, …)

Step 1: Add as many zeroes at the end of the given number, as there is a power of 5

Step 2: Divide the resultant number by 2 (Po wer o f 5 ) , to get the result.

Multiply 94 by 125

Given: 94 × 125

Here 125 = 5 3 . The power of 5 is 3.

Step 1: Now, add 3 zeros at the end of 94, and hence it becomes 94000

Step: Now, divide 94000 by 2 3 . Hence, it becomes 

Therefore, 94 × 125 is 11750

Case 2: In the multiplication of two numbers, if the sum of whose unit digit is 10, and the remaining digits are the same in both the numbers.

Step 1: Multiply the unit digits of the numbers

Step 2: Now multiply the digit (which are same) with its consecutive number

Step 3: Finally, append the result obtained in step 1 to the right of the result obtained in step 2.

Multiply 22 by 28

Given: 22 × 28

Here, the sum of the unit digit is 10 (2+8 = 10)

Step 1: Multiply unit digits: 2 × 8 = 16

Step 2: Multiply the digit 2 with its consecutive number 2 × (2+1) = 2 x 3 = 6

Step 3: Append 16 to the right side of 6. Hence, it becomes 616.

Therefore,  22 × 28 is 616.

Case 3: Multiplication of the given number by 9 n . (9, 81, 729)

Step 1: Identify the power of 9, such that step 2 has to be performed based on the power of 9.

Step 2: Multiply the given number by 10, and then subtract the given number from the result obtained.

Multiply 232 by 81.

Here the power of 9 is 2. (9 2  = 81)

Hence, step 2 has to be performed twice.

  • (232 × 10) – 232 = 2088
  • (2088 × 10) – 2088 = 18792

Therefore, the product of 232 and 81 is 18792.

Case 4: Multiplication of a number by a given number whose unit digit is 9

Step 1: Split the second number, such that it should be equal to the given number

Step 2: Now, apply distributive property of multiplication over addition or subtraction, as per the problem requirement

Step 3: Simplify the arithmetic operation

Example: Multiply 142 by 49

Step 1: Split the second number, and hence it becomes 142 × (50-1)

Step 2: Now, apply the distributive property of multiplication over subtraction.

= (142×50)-(142×1)

= 7100 -142

Therefore, 142 × 49 =  6958

Case 5: Multiplication of a number by a given number which contains all the digits a 9

Step 1: Split the given number (multiplier) in the form of (10 n  – 1)

Step 2: Now, apply the distributive property of multiplication over subtraction

Step 3: Simplify the arithmetic operations

Multiply 436 by 999

Step 1: 999 can be written as (1000-1). Hence, the given problem is written as 436×(1000-1)

436×(1000-1) = (436×1000) – (436×1)

436×(1000-1) = 436000 – 436

436×(1000-1) = 435564

Therefore, the product of 436 and 999 is 435564.

Case 6: Multiplication of the given numbers which are close to the powers of 10. (10 1 , 10 2 , 10 3 , …)

Step 1: Write down the two numbers with the difference from the base number

Step 2: Now take the sum of two numbers, which are obtained in step 1 (Considering the sign also) along with either of the two diagonals. This should be the first part of the answer)

Step 3: Now, take the product of two numbers (numbers obtained from step 1), with the consideration of the symbols. This should be the second part of the answer.

Step 4: Combine the first part (result from step 2) and the second part (result from step 3) of the solution together to get the final solution.

Multiply 93 by 94

93 = (93 – 100) = -7

94 = (94 -100) =  -6 

Take the sum of two numbers along either of two diagonals (Consider the sign also)

Diagonal sum ⇒ 93 + (-6) = 94 +(-7) = 87

Therefore, the first part of the solution is 87

Step 3: Take the product of two numbers: -7 ×-6 = 42

Therefore, the second part of the solution is 42

Step 4: Combine the first and second part of the solution together, and hence it becomes 8742

Therefore, 93 × 94 = 8742.

Rounding Up Method for Multiplication

In this method, we round up the complex numbers in the simple form to make the multiplication easier. Let us explain to you with example problems.

Multiplication Tricks for a 2-digit number

Rounding the number 58 to 60,

Multiplying the rounded amount to itself;

Subtracting 120-4=116

So, 116 is the final answer.

If we right, 22 as 20+2 and then multiplying them separately,

26 × 20 and 26 × 2 and adding them.

—— ——

520  +   52     = 572

So the answer for 26 × 22 is 572.

In the same way, you can practice more of multiplication problems by using these simple multiplication tricks.

Frequently Asked Questions on Multiplication Tricks

Mention the multiplication tricks for 4.

While multiplying 4 with any number, use the double-up tricks twice. For example, 3 ×4 is the same 3+3 = 6, then 6+6 = 12. Hence the answer should be 12.

Mention the multiplication tricks for 5?

We know that 5 can be written as 10/2. If any number is multiplied by 5, first multiply the given number by 10, and then divide the resultant number by 2. For example, 12 × 5. To simplify this, multiply 12 by 10, hence the result becomes 120. Now, divide 120 by 2, we get 60. Therefore, 12 × 5 = 60.

Mention the multiplication tricks for 8?

The multiplication trick for 8 is double, double and double again. For example, 4×8. Now, double the number 4 = 4+4 = 8 Now, double the number 8 = 8+8 = 16 Now, double the number 16 = 16+16 = 32

Write down the multiplication tricks for 10

Add the zero at the end of the given number. For example, 5 × 10. Now add zero at the end of the number 5, hence, the answer becomes 5.

Mention the multiplication tricks for 12

Assume, we need to multiply 6 by 12 Step 1: Multiply the given number by 10. (6×10 = 60) Step 2: Multiply the given number by 2. (6 × 2 = 12) Step 3: Add the result obtained from step 1 and step 2 (60+12 = 72) Hence, 6 ×12 = 72

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Long Multiplication Calculator

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Calculator Use

Multiplication of positive or negative whole numbers or decimal numbers as the multiplicand and multiplier to calculate the product using long multiplication. The solution shows the work for the Standard Algorithm.

How To Do Long Multiplication

Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand:

  • Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
  • Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number
  • Write the answer below the equals line
  • If that answer is greater than nine, write the ones place as the answer and carry the tens digit
  • Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
  • When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
  • Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
  • When you finish multiplying, draw another answer line below your last row of answer numbers.
  • Use long addition to add your number columns from right to left, carrying as you normally do for long addition.

Long Multiplication with Decimals

Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow.

  • Count the total number of decimal places contained in both the multiplicand and the multiplier.
  • Ignore the decimals and right align the numbers one on top of the other as if they were integers
  • Multiply the numbers using long multiplication.
  • Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1.

Example Long Multiplication with Decimals

Multiply 45.2 by 0.21

There's 3 total decimal places in both numbers.

Ignore the decimal places and complete the multiplication as if operating on two integers.

Rewrite the product with 3 total decimal places.

Answer = 9.492

Therefore: 45.2 × 0.21 = 9.492

Long Multiplication with Negative Numbers

When performing long multiplication you can ignore the signs until you have completed the standard algorithm for multiplication. Once you complete the multiplication follow these two rules:

  • If one number is positive and one number is negative make the product negative.
  • If both numbers are negative or both numbers are positive make the product positive.

Long Multiplication Example: Multiply 234 by 56

Long Multiplication Steps: Stack the numbers with the larger number on top. Align the numbers by place value columns.

Multiply the ones digit in the bottom number by each digit in the top number 6 × 4 = 24 Put the 4 in Ones place Carry the 2 to Tens place

6 × 3 = 18 Add the 2 that you carried = 20 Put the 0 in the Tens place Carry the 2 to the Hundreds place

6 × 2 = 12 Add the 2 that you carried = 14 This is the last number to multiply so write the whole number answer. No need to carry the 1.

Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number. 5 × 4 = 20 Add a row to your multiplication answer When you write your answer, shift one column to the left Put the 0 in Ones place Carry the 2 to Tens place

5 × 3 = 15 Add the 2 that you carried = 17 Put the 7 in the Tens place Carry the 1 to the Hundreds place

5 × 2 = 10 Add the 1 that you carried = 11 This is the last number to multiply so write the whole number answer. No need to carry the 1.

Add the numbers in the columns using long addition 4 + 0 = 4 0 + 0 = 0 4 + 7 = 11 write the 1 and carry 1 1 + 1 + 1 = 3

Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.

Related Calculators

If you need help with long addition see our Long Addition Calculator to add numbers by long addition and see the work.

For long division see the Long Division Calculator to divide numbers by using long division with remainders. This calculator also shows the work.

If you need to multiply fractions visit our Fractions Calculator . You can do fraction multiplication, addition, subtraction and division here.

Math is Fun shows examples of Long Multiplication in an animated video.

Long multiplication is an algorithm and you can find examples of multiplication algorithms at Wikipedia.

Goodman, Len . "Long Multiplication." From MathWorld --A Wolfram Web Resource, created by Eric W. Weisstein . Long Multiplication

Cite this content, page or calculator as:

Furey, Edward " Long Multiplication Calculator " at https://www.calculatorsoup.com/calculators/math/longmultiplication.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 19, 2023

IMAGES

  1. 2 Digit Multiplication Worksheets

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  2. Multiplication Anchor Chart (plus free task cards!)

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  5. How to solve 2-digit by 2-digit multiplication~Revised

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  6. How to Solve 2-digit by 2-digit Multiplication Problems

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VIDEO

  1. The Magical 4-Digit Multiplication Trick

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  4. 3 Digit by 2 Digit Multiplication Review

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  6. Multiplication Review: 3 Digit by 2 Digit

COMMENTS

  1. 2 Digit Multiplication

    Step 1: Place the one-digit number below the 2-digit number. This makes the one-digit number the multiplier. Multiply the one-digit number (the multiplier) with the ones digit of the multiplicand. Here, 2 is the multiplier and the ones digit of the multiplicand is 3. So, 2 × 3 = 6. This partial product (6) will be placed under the ones column.

  2. 3 Ways to Do Double Digit Multiplication

    1 Write the double-digit numbers on top of each other. Place 1 of the double-digit numbers on top and the other double-digit number directly below it. While there's no right or wrong way to place the numbers, if you have a double-digit that ends with a zero such as 40, place it on the bottom, and put any number with more (nonzero) digits on top.

  3. Multiplying 2-digit by 2-digit: 36x23 (video)

    Multiplying 2-digit by 2-digit: 36x23 Google Classroom About Transcript Learn to multiply two-digit numbers. In this video, we will multiply 36 times 23. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted jude khattar 10 years ago what if you multiply negative numbers what will happen? • 6 comments

  4. Multiplying 2-digit numbers (video)

    Multiplying 2-digit numbers Google Classroom About Transcript Learn to multiply two-digit numbers. In this video, we will multiply 36 times 27. Created by Sal Khan. Questions Tips & Thanks Want to join the conversation? Sort by: Top Voted ⓜⓐⓣⓗⓛⓔⓣⓔ 5 years ago Isn't multiplication repeated addition? I don't understand it that well • 12 comments

  5. Multiplying 2-digit by 2-digit: 23x44 (video)

    Multiplying 2-digit numbers Multiplying 2-digit by 2-digit: 36x23 Multiplying 2-digit by 2-digit: 23x44 Multiply 2-digit numbers Multiplying multi-digit numbers Multi-digit multiplication Math > Arithmetic (all content) > Multiplication and division > Multi-digit multiplication © 2024 Khan Academy Terms of use Privacy Policy Cookie Notice

  6. Double Digit Multiplication

    There are 3 ways to multiply double digits by double digits: the traditional method, which involves long multiplication the box method, which uses a 2x2 digit product system the partial-product...

  7. 2 Digit Multiplication Worksheet

    In this example, we are working out 39 x 25. Step 1) Multiply the ones digit of the first 2-digit number (at the top) and the ones digit of the second 2-digit number together. Write the number of ones below the line in the ones place. Carry over any tens and write them above the first 2-digit number in the tens place.

  8. Multiplication of Two Digit Numbers

    1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Schedule a free class Table of Contents Multiplication of Two-digit Numbers Multiplication of Two-Digit Numbers What is Multiplication using a Partial Product? Steps to Multiply Two-Digit Numbers Solved Examples Frequently Asked Questions Multiplication of Two Digit Numbers

  9. Multi-step Multiplication of Two-digit Numbers

    Frequently Asked Questions What are Multi-step Problems? Some math problems can be solved in a single step and these problems are usually direct and easy. There are also certain math problems that can only be solved in multiple steps. We need to apply a different strategy while dealing with such problems.

  10. Multiply 2-digit numbers by 2-digit numbers

    Multiplying a 2-digit number by a 2-digit number Show Video Lesson Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page.

  11. Multiplication (2-Digits Times 2-Digits)

    Game: Multiplication Scoot(2-Dig by 2-Dig) In this classroom game, students solve a series of math problems on task cards. The cards have 2-digit by two-digit multiplication problems on them. 4th through 6th Grades. View PDF.

  12. 2-Digit by 2-Digit Multiplication

    Need help with how to multiply 2-digit numbers by 2-digit numbers? You're in the right place!Whether...

  13. Two-Digit Multiplication Lesson Plans

    Two-Digit Multiplication Lesson Introduction. Write 45 x 32 on the board or overhead. Ask students how they would begin to solve it. Several students may know the algorithm for two-digit multiplication. Complete the problem as students indicate. Ask if there are any volunteers who can explain why this algorithm works.

  14. How to solve 2-digit by 2-digit multiplication~Revised

    12K 2.1M views 13 years ago This video goes over the process of solving 2-digit by 2-digit multiplication problems. This video is intended for students (I have 5th grade on the...

  15. 2 Digit Multiplication: Learn Definition, Facts & Examples

    Step 1: Make a box table or a grid of 2X2 as we are doing a 2-digit multiplication equation. Step 2: Breaking these factors up into their expanded forms. So, 32 becomes 30 and 2; 34 becomes 30 and 4. Note: Label the expanded form of the multiplicand on the top and the expanded form of the multiplier on the left-hand side of the grid.

  16. Multiplying two 2-digit numbers using partial products

    a year ago. we figured out a way to multiply a two-digit number times one-digit number. What we did is we broke up the two-digit numbers in terms of its place value, so the three here in the tenths place that's three tens, this is seven ones. So we view 37 sixes as the same thing as 30 sixes, three tens times six plus seven sixes, seven times six.

  17. How to Solve 2-Digit Multiplication Made Easy Multiplying ...

    How to Solve 2-Digit Multiplication Made Easy 😀Multiplying 2 Digit Numbers by Math Ninja Lampofilm 51.2K subscribers Subscribe Subscribed 3.7K 260K views 2 years ago Learning Fun...

  18. How to Solve a Multiplication Problem

    For each potion she used 5 + 5 + 5 pounds. Or, expressed in a different way: 3 x 5 = 15 pounds. Now we know that she used 15 pounds of magic herbs for each potion and we know that she made 10 bottles of potion, so: In total, to make all of the potions, she used 15 x 10 = 150 pounds of magic herbs. 4) This last step is very important.

  19. Strategies for Teaching Multi-Digit Multiplication

    Using the area model with 2-digit numbers by 2-digit numbers is essentially the same, except the area model is just a bit larger. (I don't recommend moving into the 2-digit by 2-digit model until after you have had plenty of practice with all of the multi-digit numbers by 1 digit. This post is to assist all multi-digit multiplication needs.)

  20. List of Important Multiplication Tricks and Tips

    5 + 5 = 10 Multiplication by 3: It denotes triple times of a number. Example: 5 × 3 = 5 + 5 + 5 = 15 Multiplication by 4: It denotes double of a double number. Example: 5 × 4: double of 5 is 10. Thus double of 10 is 20 (10+10) Multiplication by 5: If a number is multiplied by 5, then divide the number by 2 and multiply by 10.

  21. How to Solve 2-digit by 2-digit Multiplication Problems

    Steps to solving 2-digit by 2-digit multiplication problems

  22. Long Multiplication Calculator

    Long Multiplication Example: Multiply 234 by 56. Long Multiplication Steps: Stack the numbers with the larger number on top. Align the numbers by place value columns. Multiply the ones digit in the bottom number by each digit in the top number. 6 × 4 = 24. Put the 4 in Ones place. Carry the 2 to Tens place.

  23. Multiplication: Standard Algorithm 3 x 2 digits Tutorial Video

    This video takes students step-by-step through a 3 x 2 digit multiplication problem using the standard algorithm. The examples included in the videos are fr...