How to Improve Mental Math Skills

Plus, learn what mental math is and why it’s so helpful!

You may find yourself in a situation where you need to do some math, but you don’t have a calculator or even a pen and paper. So, what do you do? This is where mental math comes in. Mental math is the process of solving math problems in your head. It may seem hard, but it’s actually pretty easy (as long as you know the right tricks). We spoke with math teachers and tutors to bring you the best advice on how to improve your mental math skills and get better at doing math in your head. Whether you’re a stressed-out student or a math wizard looking for even faster tricks, there’s something for everyone to learn!

The Best Ways to Improve Mental Math Skills

1. Break addition and subtraction problems into easy parts.
2. Round up numbers to make multiplication, addition, and subtraction easier.
3. Multiply from left to right, instead of from right to left.
4. Remove zeros from the end of numbers to add and subtract quickly.

Steps

Tricks for Doing Math In Your Head

1. Break addition and subtraction problems into parts. Treat each group of hundreds, tens, and ones as a separate problem. As math tutor Kevin Wang explains, this makes it easier and faster to add or subtract values.^[1] For example:
   
   • 712 + 281 → "700 + 200," "10 + 80," and "2 + 1"
   • 700 + 200 = 900, then 10 + 80 = 90, then 2 + 1 = 3
   • 900 + 90 + 3 = 993.
   • Thinking in "hundreds" or "tens" instead of single digits makes it easier to keep track when digits sum to more than ten. For example, for 37 + 45, think "30 + 40 = 70" and "7 + 5 = 12". Then add 70 + 12 to get 82.
2. Change the problem to make round numbers. Round numbers are faster to work with. So, try rounding up each number to find a quick estimate. Keep note of the changes you’ve made, just in case you need an exact answer later.^[2] Check out these examples:
   
   • Addition: For 596 + 380, realize that you can add 4 to 596 to round it to 600, then add 600 + 380 to get 980. Undo the rounding by subtracting 4 from 980 to get 976.
   • Subtraction: For 815 - 521, break it up into 800 - 500, 10 - 20, and 5 - 1. To turn the awkward "10 - 20" into "20 - 20", add 10 to 815 to get 825. Now solve to get 304, then undo the rounding by subtracting 10 to get 294.
   • Multiplication: For 38 x 3, you can add 2 to 38 to make the problem 40 x 3, which is 120. Since the 2 you added got multiplied by three, you need to undo the rounding by subtracting 2 x 3 = 6 at the end to get 120 - 6 = 114.
3. Learn to add many numbers at once. Reorder the numbers to make convenient sums. An addition problem is the same no matter what order you solve it in! Look for numbers that add up to 10 or other round numbers that you can easily work with.^[3]
   
   • For example, 7 + 4 + 9 + 13 + 6 + 51 can be reorganized to (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.
4. Multiply from left to right. On paper, most people multiply the ones place first, going from right to left. But in your head, it can be easier to go the other way: from left to right.^[4] Take a look at these examples to see what we mean:
   
   • For 453 x 4, start with 400 x 4 = 1600, then 50 x 4 = 200, then 3 x 4 = 12. Add them all together to get 1812.
   • If both numbers have more than one digit, you can break them into parts. Each digit has to be multiplied by each other digit, so it can be tough to keep track of it all. 34 x 12 = (34 x 10) + (34 x 2), which you can break down further into (30 x 10) + (4 x 10) + (30 x 2) + (4 x 2) = 300 + 40 + 60 + 8 = 408.
5. Simplify problems with numbers ending in zero. If the numbers end in zeroes, you can ignore them until the end—just add them on later! Here’s a more detailed breakdown:^[5]
   
   • Addition: If all numbers have zeroes at the end, you can ignore the zeroes they have in common and restore them at the end. 850 + 120 → 85 + 12 = 97, then restore the shared zero: 970.
   • Subtraction works the same way: 1000 - 700 → 10 - 7 = 3, then restore the two shared zeroes to get 300. Notice that you can only remove the two zeroes the numbers have in common, and must keep the third zero in 1000.
   • Multiplication: Ignore all the zeroes, then restore each one individually. 3000 x 50 → 3 x 5 = 15, then restore all four zeroes to get 150,000.
   • Division: Remove all shared zeroes, and the answer will be the same. 60,000 ÷ 12,000 = 60 ÷ 12 = 5. Don't add any zeroes back on.
6. Combine numbers between 11 and 19. This fast multiplication trick is best for solving problems for numbers 11 through 19. It may seem a little tricky at first, but once you get the hang of it, you’ll be adding long equations in your head in no time! Here’s what you have to do:^[6]
   
   • Let’s start with the equation 13 x 15.
   • Subtract 10 from the second number, then add your answer to the first: 15 - 10 = 5, and 13 + 5 = 18.
   • Multiply your answer by ten: 18 x 10 = 180.
   • Next, subtract 10 from both sides and multiply the results: 3 x 5 = 15.
   • Add your two answers together to get the final answer: 180 + 15 = 195.
   • Careful with smaller numbers! For 13 x 8, you start with "8 - 10 = -2", then "13 + -2 = 11". If it's hard to work with negative numbers in your head, try a different method for problems like this.
   • For larger numbers, it’s easier to use a "base number" like 20 or 30 instead of 10. If you try this, make sure you use that number everywhere that 10 is used above.^[7] For example, for 21 x 24, you start by adding 21 + 4 to get 25. Now multiply 25 by 20 (instead of 10) to get 500, and add 1 x 4 = 4 to get 504.
7. Multiply two-digit numbers by 11 with addition. This is called the 11s trick, and it can be super handy. All you have to do is add the two digits together, then put the result in between the original digits. Here’s an example:^[8]
   
   • What is 72 x 11?
   • Add the two digits together: 7 + 2 = 9.
   • Put the answer in between the original digits: 72 x 11 = 792.
   • If the sum is more than 10, place only the final digit and carry the one: 57 x 11 = 627, because 5 + 7 = 12. The 2 goes in the middle, and the 1 gets added to the 5 to make 6.
8. Play around with percentage signs to make problems easier. Some percentages are easier to calculate in your head than others. Because of this, it may be easier to swap which number in the problem has the percentage sign or play around with decimal signs. Here are some ways to quickly calculate percentages in your head:^[9]
   
   • Say you need to find 79% of 10. 79% of 10 is the same as 10% of 79. This is true of any two numbers. If you can't find the answer to a percentage problem, try switching it around.
   • To find 10% of a number, move the decimal one place to the left (10% of 65 is 6.5). To find 1% of a number, move the decimal two places to the left (1% of 65 is 0.65).
   • Use these rules for 10% and 1% to help you with more difficult percentages. For example, 5% is ½ of 10%, so 5% of 80 = (10% of 80) x ½ = 8 x ½ = 4.
   • Break percentages into easier parts: 30% of 900 = (10% of 900) x 3 = 90 x 3 = 270.
9. Memorize square charts. Square charts give you a new way to multiply. Memorizing your multiplication tables from 1 to 9 makes single-digit multiplication automatic. But for larger numbers, instead of trying to memorize hundreds of answers, memorize just the squares instead (each number times itself). With a little extra work, you can use these squares to find the answer to other problems. We recommend memorizing the squares from 1 to 20.^[10]
   
   • To multiply two numbers, first find their average (the number exactly between them). For example, the average of 18 and 14 is 16.
   • Square this answer. Once you’ve memorized the squares chart, you'll know that 16 x 16 is 256.
   • Next, look at the difference between the original numbers and their average: 18 - 16 = 2. (Always use a positive number here.)
   • Square this number as well: 2 x 2 = 4.
   • To get your final answer, take the first square and subtract the second: 256 - 4 = 252.
10. Convert 4, 5, 8, or 16 with 2 and 10. Did you know you can easily multiply by 4, 5, 8, or 16 with 2s and 10s? You can convert these numbers by doubling. Here’s how:
    
    • To multiply by 5, instead multiply by 10 and then divide by 2.
    • To multiply by 4, double the number and then double it again.
    • For 8, 16, 32 (or even higher powers of 2), keep doubling. For example, 13 x 8 = 13 x 2 x 2 x 2, so double 13 three times: 13 → 26 → 52 → 104.

What is mental math?

1. Mental math is when you perform math calculations in your mind. Also known as mental arithmetic, mental calculation, or quick math, mental math is the process of doing math in your head—no note taking, no calculators, just your mind. For example, if you read the equation 6 + 4 and know the answer immediately, you’ve done mental math!^[11]
   
   • There are different levels of mental math. Everyone does basic mental math day to day (counting money, figuring out sale prices, etc.), but some individuals challenge themselves to solve complex math problems mentally.
   • Does mental math take long? It depends on the problem! Simple addition or subtraction problems can take seconds, while a lengthy multiplication or division problem may take longer to think through.
   • What are the benefits? Being able to do mental math can help you in everyday situations, whether that’s quickly solving a problem on a test or calculating how much your groceries cost.

How to Practice Mental Math

1. Memorize multiplication and division tables with flashcards. If you want to get better at quickly knowing the product or quotient of a problem, math teacher Joseph Meyer suggests using flashcards.^[12] Make flashcards of common problems and equations, or use an online generator to test your knowledge.
   
   • Meyer also recommends using tactile tricks if you’re a hands-on learner. He advises practicing your tables by counting physical objects, like buttons. This way, you can see and feel the math.^[13]
2. Play math games. There are thousands of math games online that you can play. These games are designed to be fun—they don’t feel like you’re learning! Simply search “online math games” on a web browser or in an app store. As tutor Ronitte Libedinsky says, “The best way to improve mental math is by repetition.”^[14]
   
   • We recommend trying out CoolMathGames.com and DoodleMath.
3. Add up your total while shopping. You may not realize it yet, but there are numbers all around you—math is a part of your everyday life! Practice your mental math skills while shopping by adding up your total in your head before going to the register, or finding how much an item is after a sale.
   

Mental Math FAQs

1. Is it better to do math in your head? Being able to do math in your head has its advantages, but it isn’t necessarily better than using a calculator. Mental math comes in handy in everyday situations. For instance, being able to quickly know what an item will cost at 25% off can be a superpower. But if you have to use a calculator, it isn’t the end of the world.
   • Mental math is something many teachers encourage students to learn, as being able to mentally arrange numbers and solve problems is considered a life skill.^[15]
2. Is mental math hard for those with ADHD? Yes, mental math can be more difficult for those with ADHD.^[16] Studies show that people with Attention Deficit Hyperactivity Disorder (ADHD) have a greater chance of developing dyscalculia, a math learning disability.^[17] Because of this, it can be harder to perform mental calculations quickly.
   • Dyscalculia is a math learning disability that makes it harder to keep track of numbers and understand mathematical concepts. It becomes more difficult to focus on numbers, leading to frustration and anxiety.^[18]
3. Is mental math hard? Mental math can be hard, but it doesn’t have to be! Think of mental math as a skill to improve. Everyone has to start from somewhere—there are beginners and there are experts. The more you work on improving your skills, the better you’ll be.^[19]
   • Keep in mind that mental math comes easier for some, and that’s okay! For some people, math is a second language, something they can easily pick up. Everyone can learn mental math, but it’s okay if more advanced problems leave you stumped.^[20]

Practice Problems and Answers

Sample Mental Math Practice Problems

Sample Mental Math Practice Problems

Sample Mental Math Practice Answers

Sample Mental Math Practice Answers

Video

Tips

• In the real world, you don't always need to know the exact answer. If you're at the grocery store and trying to add 7.07 + 8.95 + 10.09, you could round to the closest whole numbers and estimate that the total is roughly 7 + 9 + 10 = 26.
• Some people find it easier to think in money than abstract numbers. Instead of 100 - 55, try thinking of a dollar minus a 50¢ coin and a 5¢ coin.

References

Quick Summary

1. ↑ [v163150_b01]. 27 August 2024.
2. ↑ http://gizmodo.com/10-tips-to-improve-your-mental-math-ability-1792597814
3. ↑ https://www.3plearning.com/blog/mental-math-strategies/
4. ↑ https://www.3plearning.com/blog/mental-math-strategies/
5. ↑ https://www.3plearning.com/blog/mental-math-strategies/
6. ↑ https://youtu.be/Rgw9Ik5ZGaY?t=95
7. ↑ https://youtu.be/SV1dC1KAl_U?t=110
8. ↑ https://youtu.be/1JW9BA57aR8?t=43
9. ↑ http://www.wired.co.uk/article/master-mental-maths
10. ↑ http://gizmodo.com/10-tips-to-improve-your-mental-math-ability-1792597814
11. ↑ https://worldmentalcalculation.com/what-is-mental-math/
12. ↑ [v162481_b01]. 30 November 2023.
13. ↑ [v162481_b01]. 30 November 2023.
14. ↑ [v161428_b01]. 26 May 2020.
15. ↑ https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Cathy-Seeley/Do-the-Math-in-Your-Head!/
16. ↑ https://pmc.ncbi.nlm.nih.gov/articles/PMC9649814/
17. ↑ https://pmc.ncbi.nlm.nih.gov/articles/PMC3664565/
18. ↑ https://www.theminiadhdcoach.com/living-with-adhd/adhd-and-dyscalculia
19. ↑ https://worldmentalcalculation.com/what-is-mental-math/
20. ↑ https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Cathy-Seeley/Do-the-Math-in-Your-Head!/

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