how to solve multiplication problems in your head

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You don’t have to be a math teacher to know that a lot of students—and likely a lot of parents (it’s been awhile!)—are intimidated by math problems, especially if they involve large numbers. Learning techniques on how to do math quickly can help students develop greater confidence in math , improve math skills and understanding, and excel in advanced courses.

If it’s your job to teach those, here’s a great refresher.

Fast math tricks infographic

10 tricks for doing fast math

Here are 10 fast math strategies students (and adults!) can use to do math in their heads. Once these strategies are mastered, students should be able to accurately and confidently solve math problems that they once feared solving.

1. Adding large numbers

Adding large numbers just in your head can be difficult. This method shows how to simplify this process by making all the numbers a multiple of 10. Here is an example:

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 644 becomes 650 and 238 becomes 240.

Now, add 650 and 240 together. The total is 890. To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.

650 – 644 = 6 and 240 – 238 = 2

Now, add 6 and 2 together for a total of 8

To find the answer to the original equation, 8 must be subtracted from the 890.

890 – 8 = 882

So the answer to 644 +238 is 882.

2. Subtracting from 1,000

Here’s a basic rule to subtract a large number from 1,000: Subtract every number except the last from 9 and subtract the final number from 10

For example:

1,000 – 556

Step 1: Subtract 5 from 9 = 4

Step 2: Subtract 5 from 9 = 4

Step 3: Subtract 6 from 10 = 4

The answer is 444.

3. Multiplying 5 times any number

When multiplying the number 5 by an even number, there is a quick way to find the answer.

For example, 5 x 4 =

• Step 1: Take the number being multiplied by 5 and cut it in half, this makes the number 4 become the number 2.
• Step 2: Add a zero to the number to find the answer. In this case, the answer is 20.

When multiplying an odd number times 5, the formula is a bit different.

For instance, consider 5 x 3.

• Step 1: Subtract one from the number being multiplied by 5, in this instance the number 3 becomes the number 2.
• Step 2: Now halve the number 2, which makes it the number 1. Make 5 the last digit. The number produced is 15, which is the answer.

4. Division tricks

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

• 10 if the number ends in 0
• 9 when the digits are added together and the total is evenly divisible by 9
• 8 if the last three digits are evenly divisible by 8 or are 000
• 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3
• 5 if it ends in a 0 or 5
• 4 if it ends in 00 or a two digit number that is evenly divisible by 4
• 3 when the digits are added together and the result is evenly divisible by the number 3
• 2 if it ends in 0, 2, 4, 6, or 8

5. Multiplying by 9

This is an easy method that is helpful for multiplying any number by 9. Here is how it works:

Let’s use the example of 9 x 3.

Step 1 : Subtract 1 from the number that is being multiplied by 9.

3 – 1 = 2

The number 2 is the first number in the answer to the equation.

Step 2 : Subtract that number from the number 9.

9 – 2 = 7

The number 7 is the second number in the answer to the equation.

So, 9 x 3 = 27

6. 10 and 11 times tricks

The trick to multiplying any number by 10 is to add a zero to the end of the number. For example, 62 x 10 = 620.

There is also an easy trick for multiplying any two-digit number by 11. Here it is:

Take the original two-digit number and put a space between the digits. In this example, that number is 25.

Now add those two numbers together and put the result in the center:

2_(2 + 5)_5

The answer to 11 x 25 is 275.

If the numbers in the center add up to a number with two digits, insert the second number and add 1 to the first one. Here is an example for the equation 11 x 88

(8 + 1)_6_8

There is the answer to 11 x 88: 968

7. Percentage

Finding a percentage of a number can be somewhat tricky, but thinking about it in the right terms makes it much easier to understand. For instance, to find out what 5% of 235 is, follow this method:

• Step 1: Move the decimal point over by one place, 235 becomes 23.5.
• Step 2: Divide 23.5 by the number 2, the answer is 11.75. That is also the answer to the original equation.

8. Quickly square a two-digit number that ends in 5

Let’s use the number 35 as an example.

• Step 1: Multiply the first digit by itself plus 1.
• Step 2: Put a 25 at the end.

35 squared = [3 x (3 + 1)] & 25

[3 x (3 + 1)] = 12

12 & 25 = 1225

35 squared = 1225

9. Tough multiplication

When multiplying large numbers, if one of the numbers is even, divide the first number in half, and then double the second number. This method will solve the problem quickly. For instance, consider

Step 1: Divide the 20 by 2, which equals 10. Double 120, which equals 240.

Then multiply your two answers together.

10 x 240 = 2400

The answer to 20 x 120 is 2,400.

10. Multiplying numbers that end in zero

Multiplying numbers that end in zero is actually quite simple. It involves multiplying the other numbers together and then adding the zeros at the end. For instance, consider:

Step 1: Multiply the 2 times the 4

Step 2: Put all four of the zeros after the 8

200 x 400= 80,000

Practicing these fast math tricks can help both students and teachers improve their math skills and become secure in their knowledge of mathematics—and unafraid to work with numbers in the future.

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Mental Multiplication Tricks & Tips To Do Mental Math Faster In Your Head

The mental multiplication tricks and tips in this post will let you do mental math faster than a calculator entirely in your head. There are many mental strategies for multiplication, but the mental multiplication strategies covered here can be applied to multiply any set of numbers. Learning the mental multiplication tips in this post will be like learning to ride a bicycle. Once you learn it, it is really very hard to forget it.

Prerequisite For These Multiplication Tricks

Before we proceed, you must have mastered single-digit multiplication. It is a prerequisite that you know your single-digit multiplication tables from 1 x 1 to 9 x 9 before you do mental multiplication of large numbers. If you are a little rusty, bookmark this post now and make sure you memorize your single digit multiplication tables first. If you are strong in your single digit multiplication, you can read on.

This post is the second part of a Mental Math Tricks series. It is highly advised you read the first post of this series – Mental Math Tricks for Speed Math , before you proceed with learning how to do mental math in multiplication.

The Secret of Mental Multiplication Tricks

In the first part of Mental Math Tricks , we learnt that mental math becomes harder to do when you calculate from right to left. Therefore, the secret of mental math is to do the opposite and calculate from left to right instead. By solving from left to right, you will start calling out the answer, before you finish the full calculation. Calculating from left to right might feel a bit weird at first, but it will feel natural with a little practice. In this post, we will see how to apply this to mental multiplication.

What is a Multiplicand and a Multiplier?

Before we get into multiplication tricks to do mental math, let us quickly define what a multiplicand and a multiplier is. Take for example, the multiplication problem 43 x 23. Here the number 43 is the multiplicand – the number being multiplied. The number 23 is the multiplier – the number which is multiplying the first number.

There are several multiplication tricks for mental math in this post. Each mental multiplication method will have two examples. The first example, visible to everybody, will introduce you to the multiplication trick. The second example, visible only to logged-in users, will have variations not covered in the first example. So log in or sign up for free to access the entire content.

Multiplication Tricks for 1 Digit Number

General mental multiplication for 1 digit multiplier.

The general mental multiplication method is to multiply from left to right. Though the general method can be applied for any number, it works best when the numbers don’t end with 7, 8 and 9. We have a separate technique for numbers ending with 7, 8 and 9. For now, let us apply the mental multiplication method to multiply 5321 x 4.

The rule is simple. Multiply from left to right. One digit at a time.

Left to right multiplication is faster because you have to remember fewer numbers to recall and use later. You will immediately start calling out the answer from the very first step of the calculation.

Now try multiplying 7142 x 6. The procedure is the same as before and you can find it below:

Mental Multiplication With Rounding Up for 1 Digit Multiplier

Using mental multiplication tricks after rounding up is useful when the numbers end in 7, 8 or 9. It greatly simplifies the multiplication. Let us see how to apply this with an example. Multiply 68 x 3.

1. Round up the number

2. Multiply from left to right

3. Multiply the amount you rounded up

4. Subtract the numbers from the previous two steps

If you try doing this the way you normally do it on paper, you will realize that it takes more time than what it takes you now to do it in your head. If you don’t have the speed yet, don’t worry. It will come with practice. There are mental multiplication practice exercises and worksheets at the end that you can download and practice.

Now you try multiplying 96 x 7. The procedure is the same as before and you can find it below:

Mental Multiplication of 2 Digit Numbers

General multiplication tricks.

Let us now look at how to do mental multiplication for 2 digit numbers now. The multiplication tricks we saw earlier needs to be slightly modified. Let us see how to do that with an example. Multiply 36 x 32.

1. Break the multiplicand

3. Add the individual answers together to get the final answer

You can solve the same problem by breaking the multiplier instead of the multiplicand. Your choice will depend on which gives you the simpler addition process in Step 3. Try to select the number that has the smaller one’s digit because that will usually result in you adding smaller numbers, in most cases.

Now you try multiplying 26 x 23. The procedure is the same as before and you can find it below:

Rounding Up for 2 Digit Multiplier

Just like with one digit multipliers, rounding up and multiplying is useful when the numbers end in 7, 8 or 9. Let us look at how to do it with an example. Multiply 87 x 99:

1. Round up a number

2. Multiply the rounded-up value and the amount rounded up from left to right

3. Subtract the two numbers

Now you try multiplying 41 x 57. The procedure is the same as before and you can find it below:

Mental Multiplication Using Factors

Like rounding up, one of the multiplication tricks is to factor the number before multiplying it. Let us look at how to do that by trying to multiply 45 x 22.

1. Factor the number

2. Multiply the number with the first factor (left to right)

4. Multiply the product with the second factor (left to right)

In the multiplication tricks we saw earlier, you will have to remember the product of the first digit to add/subtract with the product of the second digit. However, in mental multiplication using factors you just multiply the second factor with the first product, so you don’t have to remember so many numbers as you calculate.

Now you try multiplying 21 x 63 using the factor method. The procedure is the same as before and you can find it below:

Mental Multiplication Tricks Practice Worksheets

Below you can download the PDF mental multiplication practise worksheets to apply the multiplication tricks covered.

Becoming A Human Calculator

You have learnt the basic multiplication tricks. But We have only scratched the surface and there is so much more to cover. If you really want to become a human calculator and take your mental math skills to the next level, then watch this video . In the video I will share the story of how I actually struggled with math and how I got to where I am today. You will learn the secret that will shorten your learning curve and speed up your journey to mental math mastery. To watch the video click here .

Post your questions, clarifications and feedback in the comments. It will take practice before applying the multiplication tricks becomes easy and effortless. You will find it hard initially to remember all the number in your head as you calculate. But practice will help you improve your short term memory for numbers. Force yourself to do mental calculation from left to right for your everyday calculation, and use a calculator only to double-check your numbers. Your speed and ability will improve the more you practice.

16 thoughts on “Mental Multiplication Tricks & Tips To Do Mental Math Faster In Your Head”

Your animations for the last two examples are in the wrong order.

Thanks for letting me know. Fixed it.

In the example you have shown 68 x 3 but initially you hv mentioned 68 x 2.

It was good to read all

Thanks for the comment fixed it.

Thanks. Fixed the Typo

Can you do a similar post for 3 digit number multiplication to 3 digit number?

Yes will do that.

Wow! This has really helped me

Glad it helped.

it helped but still need to learn it

i realy need the same thing as sashank

Practice, learning and thinking again about the steps are great idea for mathematic prectice. Thanks for this informative article on this, and subscribed your blog.

Is there an existing tool in assessing if the learner mastered multiplying two digits mentally

Yes. You can use the website mathtrainer.org to practice

Wow I enjoyed it ,it was so interesting (I love mathematics)

Thank u for maths tricks. Its a great blog

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October 9, 2013

5 Tips for Faster Mental Multiplication

The Math Dude: Quick & Dirty Tips to Make Math Simpler

By Math Dude Jason Marshall

Now that we've learned the basics of lightning fast mental addition,   mental subtraction , and mental multiplication , it's time to turn our attention to a few tips that will help you take your skills to the next level.

Today we're going to kick things off by learning 5 tips that will help you multiply numbers quickly in your head and become the mental math wizard in your family.

Tip #1: Multiplying by Powers of 5 There are times in life when you just get lucky. It turns out that one of those lucky little moments occurs each and every time you need to multiply one number by another number that happens to be a power of 5. For example, let's say you need to find 36 x 5 (which, of course, fits the bill since 5 is the first power of 5). The trick is to recognize the fact that 5 = 10 / 2. Why is that helpful? Because it means that we can find 36 x 5 by instead finding 36 x 10 (which is easy) and then dividing the result by 2. In this case, 36 x 10 = 360, and 360 / 2 = 180. Impressively speedy, right?

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But we're not done! What if we instead need to solve the problem 36 x 25? Well, this trick is all about multiplying by powers of 5 …and 25 = 5^2 is certainly that. So how does it work in this case? The trick here is to recognize that 25 = 100 / 4. And in general, the trick with powers of 5 is to recognize that they are always some multiple of 10 divided by an integer. This tells us that 36 x 25 = 36 x 100 / 4. Since we can quickly figure out that 36 x 100 = 3,600, it's easy to find that 36 x 25 = 3,600 / 4 = 900.

Tip #2: Squaring Numbers Ending in 5 Our fun with 5s doesn't end there. We talked about how to square numbers in your head before, but it turns out that things get a whole lot easier when squaring a two-digit number that ends in 5. Here's the trick: Any time you square a two-digit number that ends in 5, the last digits of the answer will be 25 and the digits before that are given by multiplying the first digit of the number by the number that's one greater.

> Continue reading on QuickAndDirtyTips.com

How to multiply in your head

Part of Maths Multiplying and dividing Year 3 Year 4

Watch: Multiplying in your head

When multiplying by 10 in our heads, we can move each number a place value column to the left and add a zero.

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What is 6 x 40?

• 6 x 40 is equal to 6 x 4 x 10
• 6 x 4 is equal to 6 x 2 x 2
• 6 x 2 x 2 = 24
• 24 x 10 = 240
• This means 6 x 40 = 240

Break down the calculation as much as you need to. If you know 6 x 4 = 24, you don't have to break it down into 6 x 2 x 2.

What is 0.2 x 10 ?

More on Multiplying and dividing

Find out more by working through a topic

How to work out division with remainders

• count 35 of 36

Using written methods for short division

• count 36 of 36

Multiplication sentences using the × symbol

• count 1 of 36

How to multiply and divide by 0, 1, 10 and 100

• count 2 of 36

Multiplication by Heart: Mastering Mental Math

Imagine being able to effortlessly solve complex multiplication problems in your head, without relying on a calculator or pen and paper. Multiplication by heart, also known as mental math, is a valuable skill that can significantly enhance your mathematical abilities. In this article, we will explore the importance of mastering mental multiplication and provide effective strategies to help you become a mental math whiz.

1. Introduction

In today's fast-paced world, having strong mental math skills is essential. Multiplication is one of the fundamental operations in mathematics, and being able to quickly and accurately perform multiplication calculations can streamline problem-solving and decision-making processes. By mastering mental multiplication, you can improve your overall math proficiency and gain a competitive edge in various academic and professional endeavors.

2. The Importance of Mental Math Skills

Mental math skills go beyond mere calculations. They sharpen your analytical thinking, enhance problem-solving abilities, and boost your confidence in handling numerical data. Additionally, mental math allows you to make estimations, perform calculations on the go, and tackle math-related challenges efficiently. Whether you're a student, professional, or simply an individual looking to improve your cognitive abilities, mastering mental math is a worthwhile endeavor.

3. Benefits of Learning Multiplication by Heart

Learning multiplication tables by heart offers numerous advantages. Firstly, it eliminates the need for reliance on external aids such as calculators, saving you time and improving your overall efficiency. Additionally, mental math helps develop a deeper understanding of number relationships, paving the way for advanced mathematical concepts. Moreover, mental multiplication enables you to solve problems quickly, which can be particularly useful in time-sensitive situations such as exams or job interviews.

4. Strategies to Master Multiplication Tables

Understanding number patterns.

One effective strategy for mastering multiplication tables is to recognize number patterns. For example, understanding the concept of doubling and halving can help you quickly determine the product of numbers. By identifying patterns and relationships, you can reduce the mental effort required for calculations.

Using Multiplication Tricks and Shortcuts

There are several tricks and shortcuts that can simplify multiplication. For instance, the distributive property allows you to break down complex multiplication problems into simpler ones. Additionally, techniques like the "9 times" trick or using powers of 10 can speed up your calculations. Familiarize yourself with these tricks to expedite mental math.

Memorization Techniques

Memorizing multiplication tables forms the foundation of mental math. Develop personalized mnemonic devices or visual associations to help you remember the multiplication facts. Practice regularly and gradually increase the range of numbers you can recall effortlessly.

5. Practice and Reinforcement

Flashcards and quiz games.

Using flashcards and engaging in quiz games are effective ways to reinforce multiplication skills. Create flashcards with multiplication problems and their answers, and practice them regularly. Additionally, there are numerous online platforms and mobile apps that offer interactive multiplication quizzes to make learning engaging and fun.

Real-Life Applications

Apply multiplication to real-life scenarios whenever possible. Calculate the cost of groceries, determine the total time spent on daily activities, or estimate distances based on speed and time. By incorporating multiplication into your daily life, you reinforce your mental math skills and enhance their practicality.

Online Resources and Apps

Take advantage of the abundance of online resources and apps dedicated to mental math. These platforms provide structured lessons, practice exercises, and interactive tools to facilitate learning. Find reputable sources that align with your learning style and make the most of technology to sharpen your multiplication skills.

6. Overcoming Challenges

Building confidence.

Many individuals struggle with mental math due to a lack of confidence. Overcoming this challenge requires a positive mindset and regular practice. Celebrate small victories and acknowledge progress to build confidence gradually. Remember that everyone learns at their own pace, and with determination, you can conquer mental multiplication.

Breaking Down Complex Problems

Complex multiplication problems can be intimidating, but they can be broken down into smaller, more manageable steps. Identify common factors, use approximation techniques, or simplify numbers to ease the calculations. Breaking down problems not only simplifies the process but also enhances your problem-solving abilities.

Seeking Help and Support

If you encounter difficulties while learning mental multiplication, don't hesitate to seek help and support. Reach out to teachers, tutors, or fellow learners who can provide guidance and clarification. Collaborating with others can offer new perspectives and accelerate your learning progress.

7. Maintaining and Expanding Mental Math Skills

Regular practice.

Consistency is key to maintaining and expanding mental math skills. Dedicate regular practice sessions to reinforce multiplication tables and improve your speed and accuracy. Set aside a specific time each day or week for mental math exercises to ensure continuous progress.

Applying Multiplication to Other Math Concepts

Multiplication is interconnected with various other mathematical concepts. Apply your mental multiplication skills to areas like division, fractions, ratios, and percentages. By understanding how multiplication relates to these concepts, you deepen your mathematical understanding and broaden your problem-solving capabilities.

Exploring Advanced Techniques

Once you have mastered the fundamentals of mental multiplication, consider exploring advanced techniques. Look into topics like Vedic mathematics or mental math strategies used by mathematicians and mental math champions. These techniques can further enhance your mental math abilities and open doors to exciting new challenges.

8. Conclusion

Mastering mental multiplication, or multiplication by heart, is a valuable skill that empowers individuals in various aspects of life. By dedicating time and effort to learning and practicing mental math, you can improve your mathematical abilities, enhance problem-solving skills, and gain confidence in handling numerical data. Embrace the strategies outlined in this article, and unlock the potential of mental math in your daily life.

Q: Is it necessary to learn multiplication tables by heart? A: While calculators and digital devices are readily available, learning multiplication tables by heart offers numerous benefits, including improved efficiency, deeper understanding of numbers, and quick problem-solving abilities.

Q: How can I make memorizing multiplication tables easier? A: Employ mnemonic devices, visual associations, or repetition techniques to make memorization more manageable and engaging.

Q: Can mental math be challenging for everyone? A: Mental math can be challenging for some individuals initially, but with consistent practice, anyone can improve their mental math skills.

Q: Are there any online resources to help me practice mental math? A: Yes, there are several online platforms and mobile apps that offer interactive exercises, quizzes, and tutorials to facilitate mental math practice.

Q: Can mental math be useful outside of academic or professional settings? A: Absolutely! Mental math has practical applications in everyday life, such as calculating expenses, estimating distances, and making quick decisions based on numerical data.

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Mental Math

Calculating things in your head can be a difficult task. If you can't remember what you've worked out or simply don't know how to solve a problem then it can be very challenging and frustrating. I'm going to try and give a few tips on how to do it more easily. My own mental calculation skills are below my general math ability due to problems with short term memory, but with a few shortcuts I can often calculate things scarily fast.

A useful trick when adding lots of small numbers is to clump together the ones that add up to multiples of 10. For example, if you have to add 2 + 3 + 5 + 7 + 9 + 11 + 8, that can be rearranged as (3 + 7) + (9 + 11) + (2 + 8) + 5 = 10 + 20 + 10 + 5 = 45.

Subtraction

A useful trick when subtracting numbers is to begin with the smaller value and mentally skip your way up the difference, with jumping points at recognizable boundaries, such as powers of 10. For example, to subtract 67 from 213 I would start with 67, then add 3 + 30 + 100 + 13. Try this once and you see how easy it is. Sounding out your thoughts it would be "three, thirty-three, one hundred thirty-three plus the remaining 13 is one hundred forty-six".

Multiplication

When multiplying it is very important to pick the correct sums to do. If you multiply 251 by 323 straight off it can be very difficult, but it is actually a very easy sum if approached in the right way. 251x3 + 251x20 + 251x300 is a scary prospect, so you have to work out the simplest method.

One of the first things to do is to look if the numbers are near anything easy to work out. In this example there is, very conveniently, the number 251, which is next to 250. So all you have to do is 323x250 + 323 - much easier, but 323x250 still doesn't look too simple. There is, however, an easy way of multiplying by 250 which can also apply to other numbers. You multiply by 1000 then divide by 4. So 323x1000 = 323,000, divide by two and you get 161,500, divide by 2 again and you get 80,750. Now this may not seem easy, but once you've got used to it dividing by four (or other low numbers) in that way becomes natural and takes only a fraction of a second. 80,750+323 = 81,073 , so you've got the answer with a minimum of effort compared to what you would otherwise have done. You can't always do it this easily, but it is always useful to look for the more obvious shortcuts in this style.

An even more effective way in some circumstances is to know a simple rule for a set of circumstances. There are a large number of rules which can be found, some of which are explained below.

If you recognize that one or both numbers are easily divisible, this is one way to make the problem much easier. For example, 72 x 39 may seem daunting, but if taken as 8 x 9 x 3 x 13, it becomes much easier.

First, rearrange the numbers in the hardest to multiply order. In this case, I'd go with 13 x 8 x 9 x 3. Then multiply them one at a time.

• 13 x 8 = 10 x 8 + 3 x 8 = 80 + 24 = 104
• 104 x 9 = 936
• 936 x 3 = 2808

Same First Digit, Second Digits Add to 10

Let's say you are multiplying two numbers, just two two-digit numbers for now (though the rules could be adapted for others) which start with the same digit and the sum of their unit digits is 10. For example, 87x83. You multiply the first digit by one more than itself (8x9 = 72). Then multiply the second digits together (7x3 = 21). Then stick the first answer at the start of the second to get the answer (7221). If you want to know how this works it is proved (and plenty of other techniques given)here.

Squaring a Number That Ends with 5

This is a special case of the previous method. Discard the 5, and multiply the remaining number by itself plus one. Then tack on a 25 (which as in the previous section, is 5x5). For example, 45x45. Discarding the 5 leaves us with 4. Multiplying 4 by itself plus one gives us 20 (4x5 = 20). Tacking on a 25 yields 2025, so 45x45=2025.

Just Over 100

This trick works for two numbers that are just over 100, as long as the last two digits of both numbers multiplied together is less than 100. For example, for 103 x 124, 3 x 24 = 72 100, so it will not.

If the first test works, then the answer is:

• 108 x 109 = 1[8+9][8x9] = 1[17][72] = 11,772
• 105 x 115 = 1[5+15][5x15] = 1[20][75] = 12,075
• 132 x 103 = 1[32+3][32x3] = 1[35][96] = 13,596

This trick works for numbers just over 200, 300, 400, etc. with one simple change:

• 215 x 204 = [2x2][(15+4)x2][15x4] = [4][19x2][60] = [4][38][60] = 43,860

For numbers just over 1000, 2000, etc., use the following:

• 2008 x 2009 = 4,034,072

For each order of magnitude (x10), add two zeroes to the middle.

Again there are many possible techniques, but you can make do with the following or research your own. All numbers are the products of primes (you can make them by multiplying together prime numbers). If you are dividing you can divide by all the prime products of the number you are dividing by to get the answer. This means that 100/24 = (((100/2)/2)/2)/3. Although this means you have a lot more stages to do they are all much simpler. 100/2 = 50 , 50/2 = 25 , 25/2 = 12.5 , 12.5/3 = 4 5 / 30 = 4 1 / 6 = 4.166666666recurring

Also, another helpful trick is, when you have to muliply and then divide by a number, always divide first, until you've reached numbers that are relatively prime, and then multiply. This keeps numbers from being too large. For example, if you must do (18 * 115)/15, it is much easier to divide 115 by 5 and 18 by 3, and then multiply them together to get 23 * 6 = 138.

Multiply by the Reciprocal

Division is equivalent to multiplying by the reciprocal. For instance, division by 5 is the same as multiplication by 0.2 (1/5=0.2). To multiply by 0.2, simply double the number and then divide by 10.

Division by 7

Division by 9

The fraction 1/9 and its integer multiples are fairly straight forward - they are simply equal to a decimal point followed by the one-digit the numerator repeating to infinity:

To solve a problem such as 367/9, we reduce it to

The best way to make estimation quickly in mental math is to round to one or two significant digits (that is, round it to the nearest place of the highest order(s) of magnitude), and then proceed with typical operations. Thus, 1241 * 15645 is approximately equal to 1200 * 16000 = 19200000, which is reasonably close to the correct answer of 19415445. In certain cases, one can even round to simply the nearest power of ten (which is useful when making estimations with much error and large numbers).

Other mental math

Perhaps one of the more useful tricks to mental math is memorization. Although it may seem an annoyance to need to memorize certain math facts, such as perfect squares and cubes (especially powers of two), prime factorizations of certain numbers, or the decimal equivalents of common fractions (such as 1/7 = .1428...). Many are simple, such as 1/3 = .3333... and 2^5 = 32, but speed up your calculations enormously when you don't have to do the division or multiplication in your head. For example, trying to figure out 1024/32 is much easier knowing that that is the same as 2^10/2^5, or which, subtracting exponents, gives 2^5, or 32. Many of these are memorized simply by frequent use; so, the best way to get good is much practice.

I haven't got time to write any more at the moment (hopefully some other people will be able to contribute though) so I wont add any more for now, but the ideas I have shown can often be applied to more areas and help in most mental math.

I haven't mentioned addition or subtraction, which seem to be strange things to overlook, but there are much fewer shortcuts for these activities. If anyone edits this I suggest that is the first thing to talk about.

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How to Do Long Multiplication

Last Updated: May 15, 2024 Fact Checked

This article was reviewed by Grace Imson, MA . 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 7 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 2,355,167 times.

Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large. If you take it step by step, though, you'll be able to do long multiplication in no time. Get ready to ace those math quizzes by going to Step 1 below to get started.

Doing Standard Long Multiplication

• You will essentially begin by multiplying the 2 in 32 by each of the numbers in 756, and then multiplying the 3 in 32 by each of the numbers in 756. But let's not get ahead of ourselves.
• The "bigger" number means the one with the most digits (numbers).

Taking a Shortcut

Practice Problems and Answers

Community Q&A

• Don't forget to carry your tens along, or else it'll all mess up. Thanks Helpful 2 Not Helpful 0
• Make sure you get your numbers in the right columns! Thanks Helpful 1 Not Helpful 1
• Practice on short, easy numbers first. Thanks Helpful 1 Not Helpful 2

You Might Also Like

• ↑ https://www.mathsisfun.com/numbers/multiplication-long.html
• ↑ https://www.khanacademy.org/math/arithmetic-home/multiply-divide/multi-digit-mult/v/multiplication-6-multiple-digit-numbers
• ↑ https://mathworld.wolfram.com/LongMultiplication.html
• ↑ https://www.homeschoolmath.net/teaching/md/multiplication_algorithm.php
• ↑ https://www.splashlearn.com/math-vocabulary/multiplication/multiplication
• ↑ https://amsi.org.au/teacher_modules/multiplication_and_division.html
• ↑ https://www.mathsisfun.com/multiplication-tips-tricks.html

About This Article

To do long multiplication quickly, start by splitting up the tens and ones place in the smaller number. For example, if the number was 12, you would end up with 10 and 2. Next, multiply the bigger number by both the tens number and the ones number. Finally, add the 2 products together to get your final answer. To learn how to write out a long multiplication problem by hand, keep reading! Did this summary help you? Yes No

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