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Multiplication Worksheets

Multiplication worksheets for grades 2 to 6.

Our multiplication worksheets start with the basic multiplication facts and progress to multiplying large numbers in columns.  We emphasize "mental multiplication" exercises to improve numeracy skills. 

Choose your grade / topic:

Grade 2 multiplication worksheets, grade 3 multiplication worksheets, grade 4 mental multiplication worksheets.

Grade 4 multiply in columns worksheets

Grade 5 multiplication worksheets

Grade 6 multiplication worksheets.

Multiplication facts: drills and practice

Multi-digit multiplication: drills and practice

Multiplication flashcards

Topics include:

• Meaning of multiplication
• Multiplication Facts 2 & 3, 5, 10, 2-5
• Multiplication Tables of 2, 5 & 10
• Multiplication tables - missing factors
• Two times small numbers
• Two times multiples of 5
• Two times whole tens
• Two times whole tens (missing factors)
• Multiplication word problems (within 25)
• Multiplication sentences
• Multiply with arrays
• Multiply using a number line
• Multiplication facts (various practice up to 2-12)
• Multiplication tables
• Multiplication facts (missing factors)
• Multiplying 1-digit numbers by whole tens
• Multiplying 1-digit numbers by whole hundreds
• Multiply whole tens by whole tens
• Multiply whole tens (missing factors)
• Multiply in columns (1-digit by 2-4 digits)
• Multiplication word problems
• Multiplication tables 2-10, 2-12, random facts
• Multiplication tables 2-10, 2-12, missing factors
• Commutative property
• Distributive property
• Multiply 1-dit numbers by whole tens or hundreds
• Multiplying whole tens by whole tens (including missing factors)
• Multiply whole tens, whole hundreds and whole thousands
• Multiply 1-digit numbers by a number close to 100
• Multiply in parts (1-digit by 2 or 3 digits)
• Mixed multiplication and division word problems
• Mixed 4 operations word problems

Grade 4 multiplication in columns worksheets

• Multiply in columns 1-digit by 2, 3 or 4 digits
• Multiply in columns 2-digits by 2, 3 or 4 digits
• Multiply in columns 3 digit by 3 digit
• Multiply by 10, 100 or 1,000 with missing factors
• Multiplying in parts (distributive property)
• Multiply 1 digit by 3 digit numbers mentally
• Multiply in columns up to 2x4 digits and 3x3 digits
• Multiplying in columns up to 5 digit numbers

Related topics

Division worksheets

Fractions worksheets

Sample Multiplication Worksheet

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Common Core - State Standards Initiative

Multiplication is an essential math skill with an abundance of uses in everyday life. Using Math Games, children can make sure they get the hang of this skill and actually enjoy reviewing it. Our free games, PDF worksheets, apps, and digital textbook help make that possible!

Using our suite of instructional tools, kids can practice:

• Multiplication with numbers and pictures
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Teachers and parents can feel confident that students are learning the relevant material for their grade. They can also track pupils’ progress using reports sent to them by Math Games. Practicing math has never been so easy or fun, and it can happen at home or at school! Choose a skill above to begin playing.

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Multiplication Tables Online practice

On this page, you can practice any combination of the multiplication tables — very helpful for students in elementary and middle school. You can practice any single times table (such as multiplication by 9), or several tables (such as tables of 2 and 5), or all of them.

You can choose timed or untimed practice, the number of practice problems, and which exact times tables you'd like to work on.

• Multiplication Matching Game
• Math Mammoth Multiplication 1 — a self-teaching worktext helping you learn all the multiplication tables
• Learn and Master the Times Tables! — an interactive course at TinyTap, based on my book Multiplication 1 .
• Mathy's Berry Picking Game
• Structured drill videos for the multiplication tables

Math Mammoth Multiplication 1

A self-teaching worktext that covers the concept of multiplication from various angles, word problems, a guide for structural drilling, and a complete study of all 12 multiplication tables.

Available both as a download and as a printed copy .

PDF download USD $5.60

→ Learn more and see the free samples!

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Beastly lesson.

If you have a minute, check out this short & lighthearted video about our PETS. (It's kind of silly, yet has an important message for all of us kids and parents.)

Sincerely, Maria

P.S. It does briefly mention God in one spot.

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How to Multiply

Last Updated: March 29, 2024 Fact Checked

This article was reviewed by Grace Imson, MA and by wikiHow staff writer, Christopher M. Osborne, PhD . 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. There are 9 references cited in this article, which can be found at the bottom of the page. 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 816,331 times.

Multiplication is one of the four basic operations in arithmetic, along with addition, subtraction, and division. Multiplication can actually be considered repeated addition , and you can solve simple multiplication problems by adding repeatedly. For larger numbers, you'll want to do long multiplication, which breaks the process down into repeated simple multiplication and addition problems. You can also try a shortcut version of long multiplication by splitting the smaller number in the problem into tens and ones, but this works best when the smaller number is between 10 and 19.

Multiplying by Repeated Addition

• For an even quicker method for multiplying smaller numbers, practice your multiplication tables (or times tables ).

Joseph Meyer

Multiplication enables you to "add" numbers in a faster way. Consider buying 7 boxes, each containing 51 crayons. Instead of adding 51 seven times, multiplication (7 x 51) allows you to determine the total number of crayons quickly. Use it to solve problems efficiently rather than just memorizing facts.

Using Long Multiplication

• Place the 4 from the number 34 below the line under the 8, next to the number 8 that you wrote down in the previous step.
• Carry the 3 from the number 34 over the 1 in the number 187.

• Note that if the top number had 4 or more digits, you would just repeat the process until you multiplied the number in the ones place of the bottom number with all of the digits in the top number, continuing to move from right to left.

• Write down the 5 from 35 to the left of the zero (on the second row below the drawn line), and carry the 3 from the 35 above the 8 in the top number (187).

• Write down the 3 from 43 to the left of the 5 (giving you 350 on the bottom row), and carry the 4 from the 43 above the 1 in the top number.

Splitting 2-Digit Numbers into Tens and Ones

• This shortcut method works best when the smaller number is between 10 and 19. If the smaller number is between 20 and 99, you'll have to do some extra work to figure out the tens component. As a result, you'll probably find it easier to just do traditional long multiplication.
• You can also use this method with a 3-digit smaller number as well—in that case, you'll need to break it up into hundreds, tens, and ones. For example, 162 would become 100, 60, and 2. Once again, though, doing standard long multiplication will likely be easier.

Multiplication Worksheet and Problems

Community Q&A

• Remember anything multiplied by zero is zero! [17] X Research source Thanks Helpful 0 Not Helpful 0
• To multiply by 10, add a zero to the end. Thanks Helpful 11 Not Helpful 0

You Might Also Like

• ↑ http://www.aaamath.com/pro39_x2.htm
• ↑ https://www.mathsisfun.com/numbers/multiplication-long.html
• ↑ https://www.calculatorsoup.com/calculators/math/longmultiplication.php
• ↑ http://mathworld.wolfram.com/LongMultiplication.html
• ↑ https://www.ducksters.com/kidsmath/long_multiplication.php
• ↑ https://www.khanacademy.org/math/arithmetic/arith-review-multiply-divide/arith-review-multi-digit-mult/v/multiplication-6-multiple-digit-numbers
• ↑ https://www.cut-the-knot.org/Curriculum/Arithmetic/LongMultiplication.shtml
• ↑ https://www.cuemath.com/numbers/long-multiplication/
• ↑ https://www.mathsisfun.com/numbers/multiply-by-zero.html

About This Article

If you want to learn to multiply, first keep in mind that multiplication is an advanced form of addition. For example, for 5 × 3, add 5 three times: 5 + 5 + 5 =15. To multiply bigger numbers, place the larger number on top of the smaller number. Then, multiply the last digit in the bottom number by each individual digit in the top number. If your answer is a two digit number, use the digit in the one's place as your answer, and carry the digit in the 10's place to the next digit in the top number. Write each answer below the line under the problem, and if you carried a number over, add it to the corresponding answer. Then, if there's another digit in the bottom number, add a zero under your answer from the first digit and repeat the process with the next digit over. With each new digit in the bottom number, add an extra zero under the answer. Keep doing this until you've multiplied all of the bottom digits by all of the top digits. Then, add all of your answers below the line together to find your final answer. If you want to learn how to do simple multiplication equations with addition, keep reading the article! Did this summary help you? Yes No

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Multiplication

In these lessons, we will look at some examples of the multiplication of whole numbers.

Related Pages Multiplication Using Fact Families Multiplication Word Problems More Lessons for Arithmetic Math Worksheets

For more practice in multiplication, you could go to our Interactive Math Zone where you can learn the multiplication tables and generate multiplication worksheets according to your needs and get them marked online.

The first number in the multiplication is called the multiplicand, the second number is called the multiplier and the answer is called the product.

The following diagram shows the parts of a multiplication: multiplicand, multiplier and product. Scroll down the page for more examples and solutions on multiplication.

Remember : Any number multiplied by 0 becomes 0.

Example: 1,343,244,654 × 0 = 0.

Multiplication of 2 numbers a and b , written as a × b , is actually a repeated addition of the number a over b times.

Example: 6 × 4 = 6 times of 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24

To multiply numbers with more than one digit correctly, all digits must be placed in the correct position starting from the right.

If the multiplier has 2 or more digits then it is necessary to calculate the partial products first and then add them to get the final product.

Avoid the following common mistakes in multiplication .

Examples A and B have numbers in the wrong positions – wrong place values.

Example C – it is confusing to multiply more than 2 numbers at one time. Multiply the first 2 numbers and then use the result to multiply with the third number to get the final answer.

Multi-Digit Multiplication Single digit multiplier

2-digit Multiplier

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Multiplication

In math, multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life. Multiplication is used when we need to combine groups of equal sizes. Let us learn more about multiplication in this page.

What is Multiplication?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number .

Example: If there are 6 boxes of cupcakes and each box has 9 cupcakes, find the total number of cupcakes.

Solution: We can solve this question by addition but it would take longer to add these to get the answer. That is, 9 + 9 + 9 + 9 + 9 + 9 = 54 cupcakes. In other words, when we have larger numbers to work upon, then multiplication is useful.

Now, let us use multiplication to solve this problem. We will multiply the number of boxes with the number of cupcakes in each box. If we multiply 6 × 9, we will get the total number of cupcakes, which is 6 × 9 = 54 cupcakes. Thus, we can see that we get the same result in a shorter period of time. This is the reason why multiplication is also termed as repeated addition.

Multiplication Symbol (×)

In mathematics, we have different symbols. The multiplication symbol is one of the commonly used math symbols . In the example given above, we learnt about the multiplication of two numbers 6 and 9. If we observe the expression of multiplication (6 × 9 = 54), we can see that the symbol (× ) connects the two numbers and completes the given expression. Apart from the cross symbol (×), multiplication is also denoted by the mid-line dot operator (⋅) , and by the asterisk sign ( *).

Multiplication Formula

The multiplication formula is expressed as, Multiplicand × Multiplier = Product ; where:

• Multiplicand: The first number (factor).
• Multiplier: The second number (factor).
• Product: The final result after multiplying the multiplicand and multiplier.
• Multiplication symbol: '×' (which connects the entire expression)

Let us understand the multiplication formula with the help of the following expression.

7(multiplicand) × 5 (multiplier) = 35 (product)

Using this basic concept of multiplication let us learn how to solve multiplication problems.

How to Solve Multiplication Problems?

While solving multiplication problems, one-digit numbers can be multiplied in a simple way by using the multiplication tables , but for larger numbers, we split the numbers into columns using their respective place values , like ones, tens, hundreds, thousands, and so on. There are two types of multiplication problems:

• Multiplication without regrouping
• Multiplication with regrouping

Let us understand the two cases with the help of examples.

Multiplication Without Regrouping

Multiplication of two numbers without regrouping involves smaller numbers where there is no need to take a carry-over to the next higher place value. It is the basic level that could help a learner understand the basics of multiplication before moving on to the higher level of problems including regrouping. Let us understand this with the help of the example given below.

Example: Multiply 3014 by 2.

• Step 1: Start with the digit in ones place. (2 × 4 = 8)
• Step 2: Multiply 2 with the digit in tens place. (2 × 1 = 2)
• Step 3: Now, multiply 2 with the digit in hundreds place. (2 × 0 = 0)
• Step 4: Now multiply 2 with the digit in thousands place. (2 × 3 = 6)
• Step 5: 3014 × 2 = 6028.

Th H T O 3 0 1 4 × 2 6 0 2 8

Multiplication With Regrouping

Multiplication of more than two numbers with regrouping involves numbers with a 2-digit product. In this type of multiplication, we need to take a carry-over to the next higher place value. Let us understand this with the help of the example given below.

Example: Multiply 2468 with 8

Solution: Let us multiply 2468 × 8 using the steps given below and try to relate them with the figure given after the steps.

• Step 1: Start with the digit in ones place, that is, 8 × 8 = 64 ones which means 6 tens 4 ones. Now, carry 6 tens to the tens column.
• Step 2: Multiply 8 with the digit in the tens place, that is, 8 × 6 = 48 tens. Now, we will add this to the carry-over. This means, 48 + 6 (carry-over from step 1) = 54. Carry 5 to the hundreds column.
• Step 3: Multiply 8 with the digit in the hundreds place, that is, 8 × 4 = 32 hundreds. Now, let us add this to the carry-over from the previous step. This means, 32 + 5 (carry-over from step 2) = 37. We will again carry 3 to thousands column.
• Step 4: Multiply 8 with the digit in the thousands place, that is, 8 × 2 = 16 thousands. So, let us again add this to the carry-over, that is, 16 + 3 (carry-over from step 3) = 19
• Step 5: Therefore, the product of 2468 × 8 = 19744.

Multiplication Using Number Line

Multiplication on a number line means to apply the multiplication operation on a given set of numbers through a number line. A number line is a visual representation of numbers on a straight line. We know that multiplication is also known as repeated addition. So, to perform multiplication on a number line , we start from zero and move towards the right side of the number line for the given number of times.

Example: Multiply 3 × 5 using a number line.

Solution: Observe the following number line to see the working of 3 × 5 = 15. We will start from 0 and move towards the right of the number line We will form 3 groups of 5 equal intervals. This will take us to 15.

The above number line shows 3 times 5 is 15. The representation can also be written as 5 + 5 + 5 = 15. The multiplication statement is expressed as, 3 × 5 = 15.

Multiplication Word Problems

Multiplication word problems can be easily solved by carefully observing the situation and identifying the solution. Let us understand the theory behind the real-life multiplication word problems with the help of an interesting example.

Example: A box contains 245 fruits. Find the number of fruits in 4 such boxes using the multiplication formula.

Solution: To solve such multiplication word problems the easiest way is to note down the given parameters and then solve. Given: The total number of fruits in one box = 245 The number of boxes = 4 Total number of fruits in 4 such boxes = 245 × 4.

Step 1: Start with the digit in ones place. Multiply 4 × 5 = 20. Now carry 2 to the tens column. Step 2: Multiply 4 with the digit in tens place, that is, 4 × 4 = 16. Now, add this to the carry-over from the previous step. 16 + 2 (carry-over from step 1) = 18. From this, carry 1 to the hundreds column. Step 3: Multiply 4 with the digit in hundreds place, 4 × 2 = 8 hundreds. 8 + 1 (carry-over from step 2) = 9. Step 4: Therefore, the product of 245 × 4 = 980.

H T O 1 2 2 4 5 × 4 9 8 0

Therefore, the total number of fruits in 4 such boxes = 245 × 4 = 980.

Tips and Tricks on Multiplication:

Here is a list of a few tips and tricks that can be used while performing multiplication.

• In multiplication, the order of numbers does not matter. So choose the order that you are more comfortable with. When using the multiplication tables, compared to 9 × 4, students may remember 4 × 9 more easily.
• When multiplying three numbers, choose the two numbers that can be multiplied easily. For example, multiplying 5 × 17 × 2 will be difficult if we try to multiply 5 × 17 first. Instead of this, multiplying 5 and 2 gives 10 which can be easily multiplied by 17 to get 170.
• When multiplying a 2-digit number with a one-digit number, it sometimes helps to break the two-digit number as per the place values. Then multiply each part and add. For example, 37 × 4 can be solved mentally by breaking 37 as 30 + 7. Then 30 × 4 = 120 and 7 × 4 = 28. So, the final answer is 120 + 28 = 148. While this may seem more tedious when written down, it is much easier to solve mentally.
• Even if you do not remember the multiplication fact, it can be easily mentally figured out. For example, 17 × 9 is difficult to remember. But this can be restructured mentally as 17 × (10 - 1). So, the answer will be 170 - 17 = 153.

☛ Related Articles

• Long Multiplication
• Multiplication Calculator
• Multiplication Tables
• Multiplication Word Problems Worksheets
• Long Multiplication Worksheets
• Multiplication Worksheets

Multiplication Examples

Example 1: Use multiplication tricks to solve the following multiplication word problem. The price of a book is $48. Find the price of 500 such books.

Solution: Price of one book = $48 Price of 500 books = 500 × 48

H T O 5 0 0 × 4 8 4 0 0 0 +2 0 0 0 x 2 4 0 0 0 _

The price of such 500 books is $24000.

The other way to solve this question is to simply multiply 48 by 5 and attach two zeros with the final answer. So, by multiplying 48 × 5, we get 240. But the given value is 500, so our final product will be $24000.

Example 2: Solve the following multiplication word problem. What is 784 times 44?

Using the multiplication formula, 784 times 44 = 784 × 44

Therefore, 784 times 44 is 34496.

Example 3: State true or false for the following statements using the multiplication facts.

a.) Multiplication represents the basic idea of repeated subtraction.

b.) The multiplication formula is expressed as: Multiplicand × Multiplier = Product

a.) False, multiplication represents the basic idea of repeated addition of the same number.

b.) True, the multiplication formula is expressed as: Multiplicand × Multiplier = Product

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Practice Questions on Multiplication

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FAQs on Multiplication

What does multiplication mean.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number . It is used when we need to combine groups of equal sizes. For example, if 5 baskets contain 4 apples each, then to find the total number of apples we can use multiplication and solve it as 5 × 4 = 20 apples.

Which Formula is Used to Perform Multiplication?

The formula that we use to perform multiplication is 'Multiplicand × Multiplier = Product'. For example, 9 (multiplicand) × 5 (multiplier) = 45 (product)

What are the Properties of Multiplication?

The different properties of multiplication are given below.

• Commutative property of multiplication : The product of two numbers does not change if we change the order of the numbers. This property of multiplication is known as the commutative property of multiplication which is represented as A × B = B × A. For example, 12 × 13 = 13 × 12 = 156.
• Associative property of multiplication : The product of three or more numbers does not change when we change the grouping of the numbers. This property of multiplication is known as the associative property of multiplication which is represented as A × (B × C) = (A × B) × C = B × (A × C). For example, 12 × (13 × 5) = (12 × 13) × 5 = 13 × (12 × 5) = 780.
• Identity property of multiplication : If any number is multiplied by 1, the product is the number itself. For example, 12 × 1 = 12. Here, 1 is the identity element of multiplication.
• Zero property of multiplication : If any number is multiplied by 0, the product is always zero. This is the zero property of multiplication . For example, 12 × 0 = 0.
• Distributive property of multiplication : As per the distributive property of multiplication , when we multiply a number with the sum of two or more addends, we get a result that is equal to the result that is obtained when we multiply each addend separately by the number. This property is also applicable to subtraction and is represented as A × (B + C) = AB + AC, or A × (B - C) = AB - AC. For example, 12 × (13 + 5) = (12 × 13) + (12 × 5) = 216.

What is the Multiplication Symbol?

While performing multiplication, we use a cross (×) symbol which connects the entire expression, this (×) symbol is known as the multiplication symbol. For example, 7 times 4 is 28 can be represented as 7 × 4 = 28.

What are the Parts of Multiplication?

The different parts of multiplication are expressed as follows. Let us understand this with an example: 6 × 4 = 24.

• Multiplicand (Factor): Multiplicand is the first number. In this case, 6 is the multiplicand.
• Multiplier (Factor): Multiplier is the second number. In this case, 4 is the multiplier.
• Product: The final result after multiplying the multiplicand and multiplier. In this example, 24 is the product.

Give an Example of a Multiplication Sentence.

In order to solve a multiplication problem, we need to write it in the form of a multiplication sentence. For example, what is 36 times 9? We know that 36 times 9 is written in the form of a multiplication sentence as 36 × 9 = 324. Here, 36 and 9 are the factors and 324 is the product. So, 36 times 9 is 324.

How is Multiplication Related to Addition?

Multiplication represents the basic idea of repeated addition of the same number. It simplifies the task of repeated addition. For example, if there are 3 packs of pencils and each pack has 6 pencils, let us find the total number of pencils. We can solve this question by addition, that is, 6 + 6 + 6 = 18 pencils. However, when we have larger numbers to deal with, then multiplication is useful. Now, if we use multiplication to solve this problem, we need to multiply the number of packs with the number of pencils in each pack. This means, 3 × 6 = 18 pencils. Thus, we get the same result easily. Hence, multiplication is also termed as repeated addition.

What is the Difference Between Multiplication and Division?

In multiplication, we combine groups of equal sizes, while in division, we split or separate the given number into equal groups. Multiplication is the product of two or more numbers where the numbers that are multiplied are the factors and the result is termed as the product. In division , the number that is divided is called the dividend, the number which divides the dividend is called the divisor and the result is the quotient.

How is Multiplication Used in Everyday Life?

Multiplication is commonly used in our everyday lives. For example, we can calculate the price of the items according to the rate per quantity, we can find the correct quantity of the ingredient to be used in cooking, we can calculate the value of multiple items when the value of 1 item is known, and so on.

What are the Multiplication Strategies?

Multiplication strategies are different ways in which multiplication can be learned. For example, multiplication using a number line, multiplication with the help of a place value chart, separating the Tens and Ones and then multiplying them separately, and so on. These strategies help learners to understand the multiplication concept with a broader perspective.

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Multiplication Word Problem Worksheets

This page hosts a vast collection of multiplication word problems for 3rd grade, 4th grade, and 5th grade kids, based on real-life scenarios, practical applications, interesting facts, and vibrant themes. Featured here are various word problems ranging from basic single-digit multiplication to two-digit and three-digit multiplication. Another set of printable worksheets hone children's multiplication skill by multiplying large numbers. Free worksheets are included.

Single-digit Multiplication Word Problems

The printable PDF worksheets presented here involve single-digit multiplication word problems. Each worksheet carries five word problems based on day-to-day scenarios.

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Multiplication Word Problems: Two-digit times Single-digit

The word problems featured here require a grade 3 learner to find the product by multiplying a two-digit number by a single-digit multiplier.

Multiplication Word Problems: Two-digit times Two-digit

The worksheets presented here involve multiplication of two-digit numbers. Read the word problems and find the product. Apply long multiplication (also known as column multiplication) method for easy calculation.

Theme Based Word Problems

Our engaging theme-based pdf worksheets help young minds understand the fundamentals of multiplication. Answer the word problems based on three fascinating themes - Winter Season, Ice rink and Library.

Multiplication Word Problems: Three-digit times Two-digit

Read the word problems featured in these printable worksheets for grade 4 and find the product of three-digit and two-digit numbers. Write down your answers and use the answer key below to check if they are right.

Three-digit Multiplication Word Problems

Solve these well-researched word problems that involve three-digit multiplication. Perform multiplication operation and carry over numbers carefully to find the product.

Multiplication: Three or Four-digit times Single-digit

The word problems featured here are based on practical applications and fact-based situations. Multiply a three or four-digit number by a single-digit multiplier to find the correct product.

Multi-digit Word Problems: Multiplying Large Numbers

Sharpen your skills by solving these engaging multi-digit word problems for grade 5. Apply long multiplication method to solve the problems. Use the answer key to check your answers.

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How to do long multiplication

Multiplying large numbers is easy when breaking down the problem into parts!

Author Amber Watkins

Published November 14, 2023

Published Nov 14, 2023

• Key takeaways
• Long multiplication makes multiplying large numbers easy by breaking them down into parts
• Mastering long multiplication takes practice, but it’s a very important skill that will help with maths more widely 

Table of contents

What is long multiplication?

• Practice questions

Are you encountering large numbers in maths? They can seem a bit scary at first! But luckily, there’s a silly saying that can help: ‘How to eat an elephant? One bite at a time!’. It teaches us that if you have a large task, the best way to do it is in parts.

The same can be true with multiplication. When we are given large numbers to multiply, instead of trying to do the problem all at once in our heads, we can multiply those numbers in parts. 

When we multiply large numbers in parts, then add those parts together, it’s called long multiplication.

Long multiplication is the steps you follow to multiply larger numbers in an easy way. Long multiplication allows you to find partial answers and add them together to find the final product. 

For example, instead of multiplying the numbers 64 x 32 as they are, you can break up the number 32 into two parts: 30 and 2, then multiply those parts by 64. It would look like this: 

(64 x 2) +  (64 x 30) 128   +  1,920 You would get a total of 2,048. Multiplying in parts, and then adding the products together, makes multiplying large numbers easy!

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How to set up a long multiplication problem

When doing long multiplication problems in a column method, you first line up the numbers you’re multiplying in columns.

For example, would we set up the problem 64 x 32 using the column method? 

• The number 62 would be written above the number 32. The equal sign will be represented with a line underneath
• You will also have two or more rows beneath. This is where you write the partial products. The first partial product is written in the first row, the second partial product is written in the second row, and so on. 

Let’s keep this in mind when reviewing the steps for how to do long multiplication .

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Long multiplication methods: column method

Let’s learn the use what’s known as the column method to solve the following problem:

What is 33 x 21?

1. Line up the numbers in a column format.

2. Multiply each top digit by the last digit in the bottom number. Place each answer in the first row from right to left. You should have the number 33 in the first product row.

3. Once each of the top digits is multiplied by that number, cross it off. 4. Next add a zero as a place value holder in the second row to represent already multiplying by the digit in that place value.

5. Multiply each top digit by the first digit in the bottom number. You will have the number 660 in the second partial product row.

6. Finally add the two products 31 and 660 to get the final answer of 693.

Carry-over rule while doing long multiplication

If you multiply two digits and the answer is in the double digits, the carry-over rule says you must write the second digit in the partial product line, and the first digit above the next number you will need to multiply. That way it carries over. 

Let’s see how these long multiplication steps and the carry-over rule work

Long multiplication method: horizontal method

There’s also another way to do long multiplication – the horizontal method. The horizontal method allows us to break up the second number in parts and multiply those parts by the first number. Let’s learn how to do long multiplication with the horizontal method. Let’s look at this example.

Multiply 43 x 65 using the horizontal method 1. Write the second number 65 in Expanded form. Those two numbers will be the parts we multiply the first number 43 by. 65 in Expanded form is 60 + 5.                     2. Begin by multiplying 43 by the first part, 60. This can be done by multiplying 43 x 6, then adding a zero to the answer.

43 x 6 is 258.

Then add a zero, so it would be 258 0 . 3. Next we will multiply 43 by the second part 5. 

43 x 5 is 215. 4. Finally, we add the two partial products together to get the final answer.

2580 + 215 is 2,795. 

Long multiplication practice questions

Click on the boxes below to see the answers!

• Write 72 and 24 in columns. 
• Multiply  2 x 4  and 7  x 4 and write the answers in the first row. 
• Cross off the 4 and add a zero placeholder in the second row. 
• Multiply 2 x 2 and 7 x 2 and write the answers in the second row. 
• Add both columns together to get 1,728 .
• Write 48 and 62 in columns. 
• Multiply 8 x 2 and 4 x 2 and write the answers in the first row. 
• Cross off the 2 and add a zero placeholder in the second row. 
• Multiply 8 x 6 and 4 x 6 and write the answers in the second row. 
• Add both columns together to get 2,976
• Write the second number 54  in expanded form: 50 + 4. 
• Multiply 98 times the first part 50. Multiply 98 x 5 and add a zero to the answer: 4,900.
• Next multiply 98 times the second part 4: 392. 
• Finally, add those two partial products together: 4,900 + 392 = 5,292

FAQs about long multiplication

You do long multiplication by multiplying numbers in parts. You multiply each digit in the top number, by each digit in the bottom number. Finally, you add the partial products to get the final answer. 

Long multiplication helps make multiplication with large numbers easy. The more you practice long multiplication, the easier these problems will be.

The long multiplication method is often called the column method. This is because the numbers you multiply are written above and below one another in columns.

You begin learning long multiplication in Year 5 and learn to multiply even larger numbers in Year 6. 

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Lesson credits

Amber Watkins

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring. "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

Amber is an education specialist with a degree in Early Childhood Education. She has over 12 years of experience teaching and tutoring . "Knowing that my work in math education makes such an impact leaves me with an indescribable feeling of pride and joy!"

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30 Best Multiplication Tricks to Solve Complex Math Problems

Cool Multiplication Tricks for Single-digit Numbers

Multiplication on your fingertips here are some unique tricks, multiply any two-digit number with these math tricks, the best three-digit multiplication tricks for kids, simplify multiplication with larger numbers with these tricks, help your kids master the multiplication tables using these strategies, frequently asked questions (faqs).

You can bring back the joy in learning mathematics with the right multiplication tricks. They are handy math calculation strategies that kids can remember and quickly solve some of the more challenging problems for their grade level.

The right set of multiplication tactics can also help develop confidence in the subject. Kids that can’t intuitively grasp math concepts can use multiplication games to ensure that they’re aligned with the class momentum.

Let’s review some of the best math tricks that you can teach kids and get them thinking about the subject from different lenses.

1. Multiply by 10, then remove that number once for 9

When multiplying by 9, you need to multiply by 10 and then remove that number once. It’s one of the easier multiplication tricks for 9 and can be done quite quickly.

E.g., 9 X 67 is 670 – 67, which is 603

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2. The double-double multiply by 4 trick

When multiplying by 4, you can simply double the number and then double it again.

E.g., 4 X 8 can be computed as 8 times two times two or 8 X 2 X 2, which is 16 X 2 = 32

4 X 50 is 200, because 50 times two is 100, and 100 times two is 200.

3. Add a 0, divide by 2 multiply by 5 trick

One of the easy multiplication tips for a number, is that of 5. Simply add a 0 to the end of the number, and then divide the whole thing by 2.

E.g., 5 X 37 is 370 divided by 2, which is 185.

5 X 88 is 880 divided by 2, which is 440.

4. Double-double, and then double for 8

When multiplying by 8, think of it as 2 repeated thrice. Then you double-double, and then double. It’s one of the best multiplication tricks for 8.

E.g., 8 X 20 is double-double of 20, which is 80, and then double it again, which is 160.

5. Multiply by 5, and then add another for multiplying by 6

If your students are adept at multiplying by 5, then can also master multiplication by 6. This is one of the simplest multiplication tricks for 6.

E.g., 6 X 40 is (5 X 40) + 40, which is 240.

This is a helpful trick if your students are also quick in addition.

6. Here’s another cool trick for multiplying by 6

When multiplying 6 with an even number, the last digit will always be the last digit of the number. You can then find the number in the tens place by dividing it by 2.

E.g., 6 X 8 will be 4 (half of 8) and 8 giving you 48.

7. The table of 9 is on your fingertips

You can have each finger be a digit in ascending order from 1 to 10. If you want to find 9 X 5, then put down the finger numbered 5. The number of fingers before it is the first digit (4), and the fingers after it have the second digit (5). The answer is 45.  Even online math games can help kids to get kids interested in math .

8. Multiplying with numbers from 6 through 10

You can assign fingers on each hand to go from 6 to 10 in this trick. You can add stickers when starting off using finger multiplication tricks for kids. When calculating 7 x 9, you can join the fingers labeled 7 and 9, and count the number of fingers at the bottom. 6 fingers should be occupying the tens place. Next, you can multiply the fingers on the top, which is 1 and 3, giving you 3. The final answer is 63. 

9. You have the table of 7 on your fingers too!

You can visualize your fingers to have imaginary numbers. You can have your thumb be the number 6, the index finger 7, and so on. You can do this on both hands. Now, you need to rotate both hands to face each other and have two fingers touch each other. 

E.g., Let’s make both index fingers touch tips, giving us the answer to 7 X 7. We need to add up the number of fingers from the point of touching at the bottom, which is two index fingers and two thumbs. This gives us 4 . Now we need to multiply the number of fingers above the point of touching on the left hand with the right hand. This gives us 3 X 3 = 9 . Therefore the answer to 7 X 7 is 49. 

10. Round up or down to 0, add the rest

One of the best and easy multiplication tricks for large numbers is to find the tens of one of the numbers, and multiply with that quickly. Adding the remaining leftovers will be easier to calculate fully.

E.g., 22 X 83 can be rewritten as (20 X 83) + (2 X 83) which gives us 1660 + 166 = 1826.

You can also round up and subtract, when for example, you have 29 X 80, which is (30 X 80) – (1 X 80)

11. Using factors to multiply numbers

If you know quick math tricks, such as multiplication tricks for 7 or rounding up or down, then this will be easy to pull off. You can find the factors of a double-digit number to simplify your calculation.

E.g., 12 x 60 can be written as 4 x 60 and 3 x 60, which can be quickly added up to give us 720.

12. Separate and multiply to simplify with this trick

For some double-digit numbers, you can separate one of the numbers into two digits and multiply them uniquely.

E.g., 24 x 13 can be written as 24 x 10 and 24 x 3, which is 240 + 72, giving us 312

13. Multiplying a number by 11, use this cool trick

When you’re multiplying a number by 11, then you can separate that number and add their sum in the middle.

E.g., 33 X 11 is 3 (3+3) 3, which is 363.

14. The importance of the distributive property over multiplication and subtraction

If you are multiplying two-digit numbers with the unit digit 9, then you can quickly round off the number and subtract it from itself.

E.g., 49 X 64 can be written as 50 X 64 – (64) = 3200 – 64, which is 3136

15. The cross-multiplication system for 3 digits

Using the cross-multiplication system, you can calculate the multiplication of any three-digit numbers quickly. Let’s start with an alphabetical representation of the calculation. It’s one of the best ways to explain 3-digit-by-3-digit multiplication tricks. 

E.g., what is ABC X DEF?

This will be CXF, BXF + CXE, and AXF + CXD +BXE at the last three digits through the cross multiplication.

For the first two digits, we have AXD, and AXE + BXD

16. Rounding off to 1000 and adjusting from there

You can round off three-digit numbers that are near 1000, and then remove the additional distance traveled to round off.

E.g., 998 X 992 is 1000 (-2) and 1000 (-8), giving us 990016 through (1000000 – 9984) by rounding off and removing the excess distance.

17. Separating the multiplication by numbers

A great way to multiply three-digit numbers that are near 100 is to separate out the excess and multiply them separately.

E.g., 802 x 102 can be written as 802 X 100 + 802 X 2 which gives us 81804. This can help us quickly calculate three-digit numbers that are within a specific range.

18. Multiplying by 101? Just double the number

This is a handy trick that is perfect for multiplying by 101. It can help you quickly get to the answer, especially if you are rounding up or down to get an additional solution.

E.g., 28 X 101 = 2828, 47 X 101 = 4747

19. Multiply identical three-digit numbers with this trick

You can round up or down a three-digit square or a three-digit number multiplied by itself, using this trick. You can round up the first number and round down the second number and then add the distance multiplied.

E.g., 197 X 197 can become 200 X 194, giving us 38,800. The shifting of 3 on either side, has to be incorporated as a multiple which is 3 x 3 = 9, and added to the final number. The result was 38,809.

20. Measure the distance from the base

For multiplying larger numbers, you can do so by checking how close you are to a 10, 100, 1000, and so on. You can then add the distances and multiply them for ease of calculation.

E.g., 92 X 89 can be 100 (-8) and 100 (-11). Adding the distances gives us (-19). Next, 100 – 19 is 81. Multiplying that by 100 is 8100. Then you multiply -8 and -11 giving you +88. Adding them up gives you 8188.

21. How to multiply any number by 25

Simply add two zeros and divide it by 4. This is because 25 can be rewritten as 100/4, which is adding two zeros and then dividing by 4 at the end.

E.g., 1235 X 25 will be 123500 divided by 4, which is 30,875.

22. Multiplying a large number by 9? Here’s how

Add a 0 to the end of the number, and then subtract that number from itself.

E.g., 7250 X 9 will be 72500 – 7250, giving us 65,250

23. Multiplication tricks when one number is larger and the other smaller

One of the best ways to get calculating is to simply add the smaller number to each of the digits of the larger numbers through multiplication. Then adding them all up should give you the right answer.

E.g., 11,341 x 12 can be ironed out as 12 x 1 + 12 x 40 + 12 x 300, and so on. You can add all the sums up to get a quicker route to reaching the final number.  

24. Repeating digits for 12

For the table of 12, the tens place is 1, 2, 3, 4, 6, 7, 8, 9, 10, 12. The unit’s place digit is 2, 4, 6, 8, 0 repeating. You can ask your kids to forget about 5 and 11, when using these tricks to memorizing multiplication facts for 12.

E.g., 12, 24, 36, 48, (nothing with 5, skip to 6), 60, 72, etc.

25. For the table of 11, repeat the numbers until 9

It’s one of the best tricks for learning multiplication tables, and it involves a highly used table of 11. All you need to remember is that the digit will repeat itself in a series.

E.g., 11 x 3 is 33, 11 x 7 is 77, until you reach 9.

26. The table of 14 can be learnt quickly through 4

If your kid knows the table of 4, then they can focus on the multiples of 4 as 4, 8, 12, 16, etc. They can then add natural numbers from 1 onwards to get the table of 14. i.e., 1 & 4, 2 & 8, 3 & 12 which is (3 + 1) & 2.

27. A great visual trick for the table of 8

For the table of 8, you can list out the row from 8 x 1 till 8 x 5, and then have the second row be 8 x 6 until 8 x 10 and so on. The tens place will be whole numbers in ascending order, and the units place will be descending even numbers from 8 to 0.

E.g., 8 x 1 = 08

You can see that the tens place is going 0, 1, 2, and the units place digit is going 8, 6, 4, etc.

28. Let’s make that table of 13 much easier

Kids love fast multiplication tricks, especially if they need the right tactics to complete double digit multiplication tables. For 13, you can teach them to remember the multiples of 3, i.e., 3, 6, 9, 12, etc. and remember to count from 1 onwards in the tens place.

E.g., 1 & 3, 2 & 6, 3 & 9, (4 + 1) & 2. We did 4 + 1 because at 12, we carried the 1 forward.

29. The table of 15 is a breeze with this trick

For 15, the unit number will oscillate between 5 and 0 only. The tens digit will have two consecutive odd numbers, and two even.

E.g., 1 & 5, 3 & 0, 4 & 5, 6 & 0. We have 1 and 3 being odd numbers, and 4 & 6 being even.

30. Get the table of 17 using the table of 16

Kids can quickly get the table of 17 if they are aware of the table of 16, which can be calculated using the repeating last digits of 6, 2, 8, 4, 0 giving you 16, 32, 48, 64, etc. For the table of 17, you simply need to add a natural number to the table of 16 corresponding to the position in the table.

E.g., 16 x 3 = 48. You can add 3 to it to get 51, which is basically 17 x 3.

Conclusion: Strengthen Your Kids’ Multiplication Capabilities with the Right Tricks!

You can expand on these multiplication strategies with the right exercises and activities. You can opt for worksheets that help them gain confidence in their abilities, and use videos, books, toys, and other props to make it interesting. By starting young, you can help your kids establish a unique relationship with mathematics and multiplication. They can also build upon these elementary multiplication tips and create their own mechanisms to calculate intuitively.

Can kids improve in math using multiplication tips and tricks?

Kids can gain a sense of confidence, agility, and accuracy when using math tricks. This can positively impact their performance at school.

How do I start implementing multiplication strategies?

You can use charts, stickers, toys, and props, to make elementary mental math lessons more engaging.

How do I improve my child’s math scores using calculation tricks?

Repetition is key to improving your child’s math abilities. You should also explain the logic behind these tricks to get them thinking further.

Can you memorize tables without calculating the numbers?

It is easier to have a sense of mental multiplication going when working on multiplication tables. Memorizing may become more challenging for higher numbered tables, such as beyond 30.

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Word Problems and Multiplication

In our Word Problems and Multiplication lesson plan, students learn strategies for solving word problems that contain multiplication. They will practice writing word problems that require multiplication and will solve problems using multiplication.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have students solve problems as a class using each of the strategies

Description

Additional information, what our word problems and multiplication lesson plan includes.

Lesson Objectives and Overview: Word Problems and Multiplication lesson plan lists several strategies for solving word problems using multiplication. Some of the strategies include making a diagram, eliminating possibilities, and looking for patterns. Several clue words are listed to help students know when multiplication is necessary to solve a word problem. At the end of the lesson, students will be able to solve word problems using multiplication. This lesson is for students in 3rd grade and 4th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. If you’d like to add to the activity worksheet, you can have students draw cards with pictures on them to determine what their multiplication problems should be about. For an additional activity, you can have students solve problems as a class using each of the strategies. Finally, you can also have students work together to create a poster that shows their strategy for solving a word problem.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.

WORD PROBLEMS AND MULTIPLICATION LESSON PLAN CONTENT PAGES

The Word Problems and Multiplication lesson plan includes two content pages. The lesson begins by reminding students that they complete math problems every day without thinking about it. There are many real-world situations that require you to use different math operations, like multiplication. You can use different strategies to solve multiplication word problems.

The first thing you should do when solving a multiplication word problem is to explore! You should figure out what you already know, what information the problem gave to you, what you need to find out, and what question is being asked.

The second step is to plan. You need to decide what strategy you’re going to use to solve the problem. The lesson lists some problem solving strategies that you can think about using, including guess and check, look for a pattern, make an organized list, and draw a diagram.

The third step is to solve by using your chosen problem solving strategy. During this step, you’ll do all of the actual math. It’s important to have already identifies the key words in the word problem, because these will tell you which operation you will need to use (this lesson only uses multiplication, but other word problems will require the use of addition, subtraction, and division). Some words and phrases that indicate that you need to use multiplication are times, rate, each , and product of . The lesson also lists a few more.

The fourth step is to examine. You should re-read the question to make sure your answer makes sense, and check your work. If your answer doesn’t make sense for the problem, try solving using a different strategy.

The lesson then delves into two different example problems and shows how to solve them step-by-step using the four steps described above.

WORD PROBLEMS AND MULTIPLICATION LESSON PLAN WORKSHEETS

The Word Problems and Multiplication lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

CREATE YOUR OWN ACTIVITY WORKSHEET

For the activity worksheet, students will write their own multiplication problems using the pictures shown on the worksheet and numbers 100 or less.

SOLVING WORD PROBLEMS PRACTICE WORKSHEET

The practice worksheet asks students to solve four word problems.

WORD PROBLEMS AND MULTIPLICATION HOMEWORK ASSIGNMENT

For the homework assignment, students will write their own multiplication word problems (like the activity worksheet). They should be creative, use numbers 100 or less, and attach a picture if they want.

This lesson includes a quiz to test students’ understanding of the lesson material. For the quix, students will solve a multiplication word problem.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Multiplicative comparison

Here you will learn about what multiplicative comparisons are and how to use them to solve word problems.

Students will first learn about multiplicative comparisons in 4th grade and expand that knowledge through 5th grade when working with comparison statements and in 6th grade when learning about ratios.

What is multiplicative comparison?

A multiplicative comparison is a way of comparing two quantities by asking how many times larger or smaller one quantity is than the other quantity. Multiplicative comparisons involve the operations of multiplication and division to solve problems.

A model can help solve multiplicative comparison problems because it helps you to visualize the amounts that need to be compared and to find the unknown quantity.

Let’s look at a few examples.

Lucas and Ryan are working on a construction project for school. Lucas’s wood board is 5 times the length of Ryan’s board. If Ryan’s wooden board is 3 feet, how long is Lucas’s wooden board?

Draw a bar model to help visualize the situation.

Ryan has a 3 foot board.

From the model, you can see that Lucas’s board is 5 times the length of Ryan’s board. There are 5 groups of 3 feet.

So the equation is 5 \times 3=\text{ length of Lucas's board}

5 \times 3=15

Lucas’s board is 15 feet.

Mike has 3 lollipops. Michelle has 4 times as many lollipops as Mike. How many lollipops does Michelle have?

Draw a picture to model this situation.

Michelle has four times as many lollipops as Mike. So she has 4 groups of 3 lollipops.

The equation is 4 \times 3=\text { amount of lollipops}

4 \times 3=12

Michelle has 12 lollipops.

Jillian has 12 inches of hair ribbon. Suzanne has half that length. How long is Suzanne’s hair ribbon?

Draw a bar model.

The equation is, \cfrac{1}{2} \, \times 12=\text { length of Suzanne's ribbon}

12 \div 2 = \text { length of Suzanne's ribbon}

12 \div 2=6

Suzanne’s ribbon is 6 inches long.

Common Core State Standards

How does this apply to 4th grade math and 5th grade math?

• Grade 4 – Operations and Algebraic Thinking (4.OA.A.1) Interpret a multiplication equation as a comparison, for example, interpret 35 = 5 \times 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
• Grade 4 – Operations and Algebraic Thinking (4.OA.A.2) Multiply or divide to solve word problems involving multiplicative comparison, for example, by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
• Grade 5 – Number and Operations Base Ten – (5.NBT.B.7) Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

[FREE] Multiplication and Division Check for Understanding (Grade 4, 5 and 7)

Use this quiz to check your grade 4, 5 and 7 students’ understanding of multiplication and division. 10+ questions with answers covering a range of 4, 5 and 7 grade multiplication and division topics to identify areas of strength and support!

How to solve multiplicative comparison problems

In order to solve multiplicative comparison problems:

Draw a model.

Use multiplication or division to write an equation.

Solve the equation.

Multiplicative comparison examples

Example 1: multiplicative comparison using a bar model with whole numbers.

Maddie has collected 21 stickers. Her friend, Anna, has collected 3 times that amount. How many stickers does Anna have in her collection?

• Draw a model. 

Anna has 3 times the amount of stickers as Maddie. So she has 3 groups of 21.

2 Use multiplication or division to write an equation.

The equation is 3 \times 21= \; ?

3 State the answer.

3 \times 21=63

Anna has 63 stickers.

Example 2: multiplicative comparison using a bar model with whole numbers

Aderonke owns an animal shelter. She has 24 dogs in her shelter and twice as many cats. How many cats are in the shelter?

There are twice as many cats as dogs which means there are two groups of 24.

The equation is 2 \times 24= \; ?

2 \times 24=48

Aderonke has 48 cats in her animal shelter.

Example 3: multiplicative comparison using a bar model

Amani has 18 yards of wire. Austin has a third of that length of wire. How much wire does Austin have?

Austin’s wire is a third of the length of Amani’s wire. So, 18 yards is divided into three equal groups.

The equation is 18 \div 3=\text{ length of Austin's wire}

\cfrac{1}{3} \times 18=\text { length of Austin's wire}

\begin{aligned} & 18 \div 3=6 \\\\ & \cfrac{1}{3} \, \times 18=\cfrac{18}{3} \, =6 \end{aligned}

Austin’s wire is 6 yards long.

Example 4: multiplicative comparison using a bar model

Billy saved \$122 dollars. His sister, Nikki, has saved 4 times that amount. How much money has Nikki saved?

Nikki has 4 times the amount of money saved than Billy, which means she has 4 groups of \$122.

The equation is 4 \times 122=\text{ amount of money Nikki saved}

4 \times 122=488

Nikki saved \$488.

Example 5: multiplicative comparison with decimals

Jerome’s neighbor has 92 yards of fencing. Jerome has a fourth of that amount of fencing. How much fencing does Jerome have?

Jerome’s neighbor has 92.4 feet of fencing. He has a fourth of that amount, which means 92.4 is divided into 4 equal groups.

The equation is 92.4 \div 4=\text { length of Jerome's fence}

92.4 \div 4=23.1

Jerome has 23.1 yards of fencing.

Example 6: multiplicative comparison with fractions

Carl has 5 \, \cfrac{1}{2} \, gallons of paint. Lucy has three times that amount.

How many gallons of paint does Lucy have?

Lucy has three times the amount of gallons of paint than Carl which means there are 3 groups of 5 \, \cfrac{1}{2} .

The equation is 3 \times 5 \cfrac{1}{2}=\text { gallons of paint for Lucy}

\begin{aligned} & 3 \times 5 \, \cfrac{1}{2} \, =3 \times \cfrac{11}{2} \\\\ & 3 \times \cfrac{11}{2} \, =\cfrac{33}{2} \, =16 \cfrac{1}{2} \end{aligned}

Lucy has 16 \, \cfrac{1}{2} \, gallons of paint.

Teaching tips for multiplicative comparison

• Connect visual models to the equations so students can see the visual representation of the abstract equation.
• Math worksheets have their place in a math lesson, but providing students with alternative opportunities to practice such as math games or digital platforms are more engaging.
• Another visual representation that can be used when doing multiplicative comparison word problems is the number line.
• Incorporate projects such as having students create their own multiplicative comparison word problems with answer keys and share them on the Google Classroom.

Easy mistakes to make

• Confusing when to use multiplication versus when to use division For example, when you are given an amount such as 18 and are asked to find 3 times that amount, use multiplication. However, if you are given the amount of 18 and are asked to find a third of that amount, use division.

Related multiplication and division lessons

• Multiplication and division
• Multiplying and dividing integers
• Multiplying and dividing rational numbers
• Multiplication and division within 100
• Multiplying multi digit numbers
• Dividing multi digit numbers
• Understanding multiplication
• Long division
• Understanding division

Practice multiplicative comparison problems

1. Doug has 16 pieces of candy. Dhalia has 3 times that amount. How many pieces of candy does Dhalia have?

Dhalia has 3 times the amount of candy as Doug which means she has 3 groups of 16.

3 \times 16=48

Dhalia has 48 pieces of candy.

2. Danni has 35 pens in her classroom. Jo has 5 times that amount. How many pens does Jo have in her classroom?

Jo has 5 times as many pens as Danni which means she has 5 groups of 35.

5\times 35=175

Jo has 175 pens in her classroom.

3. Coach Tony has 82 students trying out for his volleyball team. Coach Luke has half that amount trying out for his soccer team. Which equation represents the amount of students trying out for Coach Luke’s soccer team?

Coach Luke has half the number of students trying out for his soccer team than Coach Tony which means 82 is divided into 2 equal groups.

82 \div 2=41

4. Devin has \$243.30 in her savings account. Debra has a third of that amount in her savings account. How much money does Debra have?

Debra has a third of the amount of money as Devin. So \$243.30 has to be divided into 3 equal groups.

243.30 \div 3=81.10

Debra has \$81.10 .

5. Julie has 4 \, \cfrac{2}{3} \, feet of yarn. Dylan has 6 times that amount. How much yarn does Dylan have?

Dylan has 6 times the amount of yarn as Julie, which means 6 groups of 4 \, \cfrac{2}{3} \, .

\begin{aligned} & 6 \times 4 \, \cfrac{2}{3} \, = \\\\ & 6 \times \cfrac{14}{3} \, = \cfrac{84}{3}=28 \end{aligned}

Dylan has 28 feet of yarn.

6. Rory planted a vegetable garden. He planted 51 tomato plants and a third the amount of zucchini plants. How many zucchini plants did he plant?

16 zucchini plants

17 zucchini plants

18 zucchini plants

19 zucchini plants

Rory planted a third of the number of tomato plants which means 51 is divided into 3 equal groups.

51 \div 3=17

\cfrac{1}{3} \, \times 51=17

Multiplicative comparison FAQs

No, you do not always have to write an equation. However, writing equations is a skill necessary for secondary mathematics.

The next lessons are

• Types of numbers
• Rounding numbers
• Factors and multiples

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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

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Easy Finger Math Tricks to Help Kids Solve Problems

While using your fingers isn't the fastest way to recall a multiplication fact while doing a problem, finger math tricks can help kids figure out how to answer the problem at hand — and as they work on their math, they will eventually learn all the facts by repetition.

Note that before your child can understand other finger tricks, they must be able to count by 2s, 5s, and 10s and multiply by 2s, 3s, and 4s.

Quick Finger Math Tricks for Threes and Fours

The tricks for multiplying by threes and fours are really a matter of counting out the answer on your fingers. As your children count out the answer repeatedly, they'll memorize it and then be able to move on to larger numbers.

Multiplying by Three

Did you realize that all of your fingers have three segments? Therefore, you can figure out anything from 3 x 1 to 3 x 10 by counting the segments on each finger. To start:

• Hold up the number of fingers you're going to multiply by 3. For example, if the problem is 3 x 4 — hold up four fingers.
• Count each segment on each finger you're holding up, and you should come up with 12 — which is the correct answer.

Multiplying by Four

Multiplying by four is the same as multiplying by two — twice. To start:

• Hold up the number of fingers to correspond with the number you are multiplying by four. For example, if you are multiplying 4 x 6 — hold up six fingers.
• Count each finger by two, moving from left to right. Then count each finger again, continuing to count by twos, until you've counted every finger twice.

Helpful Hack To keep track of the fingers you've counted twice, sometimes it's easier to put your finger down as you count the first time, and back up as you count the second time.

Finger Math Tricks for Multiplying by 6, 7, 8, and 9

While numbers one through five are easy for most kids to remember, six and up often pose a problem. This handy trick will make it a little easier to work those problems out.

Multiplying 6, 7, 8, and 9 by Hand

To begin, assign each finger a number. For example, your thumbs represent 6, your index fingers each represent 7, etc. This will remain the same throughout the finger math hack.

Your left hand will represent the first number that you are multiplying and your right hand will represent the second number you are multiplying. In this example, we are multiplying 7 x 8. 

To Determine the Part of Your Answer:

• On your left hand, put down the finger that represents the number you are multiplying as well as any fingers whose number value is less than this figure. In this example, you are multiplying 7 x 8, so the left hand will represent 7. You will drop your index finger (number 7) and your thumb (number 6).
• Similarly, the right hand will represent eight, so you will drop down your middle finger (number 8), your index finger (number 7), and your thumb (number 6).
• Now, just multiply the fingers that are still pointed upwards. In this case, you will have three fingers on your left hand and two on your right, so you will multiply 3 x 2 to get 6. This is the first part of your answer!

To Determine the Second Part of Your Answer:

• Keeping your fingers in the same positions, count how many fingers are folded down. In the 7 x 8 example, you should have five fingers folded. 
• You will count each of these in quantities of ten. So, 10, 20, 30, 40, 50.
• 50 is your answer.

To Determine Your Final Answer:

• Add your two numbers together. In this example, you would add 6 + 50, which gives you 56!

Another Finger Math Trick Just for Nine

There is a trick that works separately, just for multiplying by the number nine.

• To start, hold up all ten fingers, with your palms facing you.
• Assign each finger a number, starting with your left-hand thumb and ending with your right-hand thumb. The left-hand thumb will be one, the left-hand index finger will be two, and so on until you reach the number 10 for your right-hand thumb.
• To tackle a problem, put down the corresponding finger of the number you're multiplying by nine. For example, if you are multiplying 9 x 8, you'd put down the eighth finger (which will be on your right hand).
• Count all the fingers to the left of the finger you have folded down. This will give you 7. This is the first digit of your answer.
• Count all the fingers to the right of the finger you have folded down. This will give you 2. This is the second digit of your answer.
• Put the numbers together! Your answer is 72.

Finger Multiplication Tricks Can Make Math Easy and Fun

While the hope is that your kids will eventually memorize their multiplication charts , using some quick hand tricks for multiplication and letting them count things out on their fingers is not a bad way to learn. It keeps frustration at bay since the answer is always a fingertip away, and the repetition of having to figure it out will help cement those facts into their brains.