Mental math is a set of abilities that enable people to do math “in their heads” rather than using a pencil and paper or a calculator. Mental math is useful in both school and daily life.
You’ll eventually find yourself in a situation where you need to solve a math problem without the aid of a calculator. Trying to imagine a pen and paper in your head isn’t always helpful. Fortunately, there are faster and easier ways to do mental calculations—and they frequently break down a problem in a way that makes more sense than what you learned in school. There’s something for everyone to learn, whether you’re a stressed-out student or a math wizard looking for even faster tricks.
Mental math can assist children in better understanding math concepts and arriving at an answer more quickly. One of these abilities is the ability to recall math facts such as 8*5 = 40. Other abilities include number rounding and estimating calculations.
In this article, we’ll learn some tips, tricks, and techniques that will help you to improve your mental math skills.
Partition Addition and Subtraction Problems
Separately add the hundreds, tens, and ones places. Consider each group as a separate issue:
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” rather than single digits will help you keep track when the sum of the digits exceeds ten. For example, for 37 + 45, think “30 + 40 = 70” and “7 + 5 = 12”. Then add 70 + 12 to get 82.
Change the Problem So That the Numbers Are Round
Adjust to get round numbers, then correct after you’ve finished the problem. Most of us work much faster with round numbers. Keep a mental note of the changes you made so you can fine-tune your answer at the end. As an example:
- 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 four from 980 to get 976.
- Subtraction: For 815-521, divide it into 800-500, 10-20, and 5-1. To convert the awkward “10 – 20” to “20 – 20,” multiply ten by 815 to get 825. Now solve for 304, then subtract 10 to get 294.
- Multiplication: For the problem 38 x 3, add 2 to 38 to make the problem 40 x 3, which equals 120. Because the two you added were multiplied by three, you must undo the rounding at the end by subtracting 2 x 3 = 6 to get 120 – 6 = 114.
Learn How to Add Multiple Numbers at Once
Rearrange the numbers to make more convenient sums. An additional problem is the same regardless of the order in which it is solved. Look for numbers that add up to ten or other nice, round figures:
7 + 4 + 9 + 13 + 6 + 51, for example, can be reorganized as (7 + 13) + (9 + 51) + (6 + 4) = 20 + 60 + 10 = 90.
Multiply from Left to Right
Keep track of the locations in the hundreds, tens, and ones. On paper, most people multiply the ones place first, working their way left to right. However, in your mind, it is easier to go the other way:
- Begin with 400 x 4 = 1600, then 50 x 4 = 200, and finally 3 x 4 = 12. Add them all up to get 1812.
- If both numbers have more than one digit, you can divide them. Each digit must multiply with every other digit, making it difficult to keep track of everything. 34 x 12 = (34 x 10) + (34 x 2), which can be further subdivided into (30 x 10) + (4 x 10) + (30 x 2) + (4 x 2) = 300 + 40 + 60 + 8 = 408.
Try a Quick Multiplication Trick That Works Best for Numbers 11 Through 19
Try this method for dividing a difficult problem into two smaller ones. This is yet another method for segmenting a problem. It can be difficult to remember at first, but once you get the hang of it, it can make multiplication much faster. This is easiest when multiplying two numbers between 11 and 19, but you can learn to use it for other problems as well:
- Let’s take a look at some numbers that are close to ten, such as 13 x 15. Subtract 10 from the second number, then add your result to the first: 15 – 10 = 5, and 13 + 5 = 18.
- Multiply your answer by ten: 18 x 10 = 180
- Subtract ten from both sides and multiply the results: 3 x 5 = 15.
- Add your two answers together to get the final answer: 180 + 15 = 195
- When it comes to smaller numbers, be cautious! For 13 x 8, start with “8 – 10 = -2,” then “13 + -2 = 11.” If working with negative numbers in your head is difficult for you, try a different method for problems like this.
- It will be easier to use a “base number” like 20 or 30 instead of 10 for larger numbers. If you try it, make sure to use that number everywhere ten is mentioned above.  For example, to get 25 from 21 x 24, add 21 + 4 together. Now, instead of ten, multiply 25 by 20 to get 500, and add 1 x 4 = 4 to get 504.
Simplify Problems Involving Numbers That End in a Zero
You can ignore numbers that end in zeros until the end:
- Addition: If all numbers end in zeroes, you can ignore the zeroes they share and restore them at the end. If 850 + 120 = 85 + 12 = 97, then the shared zero is 970.
- Subtraction: operates in the same manner: 1000 – 700 10 – 7 = 3, then add back the two shared zeroes to get 300. You should keep in mind that you can only remove the two zeroes that the numbers share and that the third zero in 1000 must be retained.
- Multiplication: ignore all zeros before restoring each one individually. 3000 x 50 3 x 5 = 15, then add back all four zeroes to get 150,000.
- Division: you can remove all shared zeroes and still get the same answer. 60,000 12,000 = 60,000 12 = 5 Don’t add any more zeroes.
Simply Multiply By 4, 5, 8, or 16 to Get the Answer
You can simplify these problems by only using 2s and 10s. Here’s how it works:
- Instead of multiplying by 5, multiply by 10, then divide by 2.
- Instead of multiplying by 4, double the number, then double it again.
- Simply keep doubling for 8, 16, 32, or even higher powers of two. For example, 13 x 8 = 13 x 2 x 2 x 2, so multiply 13 by three: 13 26 52 104.
The 11s Trick Should Be Memorized
A two-digit number can be multiplied by 11 with little effort. Add the two digits and insert the result between the original digits:
- What is 72 x 11 =?
- Adding the two digits together yields the following result: 7 plus 2 equals 9
- Fill in the blanks with the answer: 792 is the product of 72 x 11.
- If the total exceeds ten, only use the last digit and carry the one: Because 5+7=12, 57 x 11 = 627. The two are placed in the center, and one is added to the 5 to form the number 6.
Make Percentages Into Simpler Problems
Determine which percentages are simpler to calculate in your head. There are a couple of useful tips to be aware of:
- Seventy-nine percent often equals 10 percent of 79. This applies to any two numbers. If you can’t figure out a percentage problem, try flipping it around.
- To find 10% of a number, shift the decimal one place to the left (10 percent of 65 is 6.5). To find one-tenth of a percent of a number, move the decimal two places to the left (1 percent of 65 is 0.65).
- Use these rules for 10% and 1% to assist you with more difficult percentages. For example, 5 percent is 12 of 10%, so 5 percent of 80 = (10 percent of 80) x 12 = 8 x 12 = 4.
- Divide the percentages into manageable chunks: 30% of 900 = (10% of 900) x 3 = 90 x 3 = 270.
For Specific Problems, Memorize Advanced Multiplication Shortcuts
These tricks are effective, but they are limited. They can transform a seemingly impossible mental math task into a quick task, but they will only work on a small percentage of problems. If you’re already pretty good at mental math and want to approach “mathematician” levels of speed, learn these:
- For problems such as 84 x 86, where the tens place is the same, and the ones place digits add up to exactly 10, the first digits of the answer are (8 + 1) x 8 = 72, and the last digits are 4 x 6 = 24, yielding a result of 7224. That is, if B + C = 10, the solution to the problem AB x AC begins with A(A+1) and ends with BC. This also applies to larger numbers if all digits except the one’s place are the same.
- The powers of five (5, 25, 125, 625,…) can be rewritten as powers of ten divided by an integer (10 / 2, 100 / 4, 1000 / 8, 10000 / 16,…). As a result, 88 x 125 becomes 88 x 1000 8 = 88000 8 = 11000.
Remember the Squares Charts
Squares charts provide a new method of multiplying. Remembering your multiplication tables from 1 to 9 automates single-digit multiplication. However, for larger numbers, rather than memorizing hundreds of answers, it is more efficient to memorize just the squares (each number times itself). You can use these squares to solve other problems with a little extra effort:
- Memorize the squares numbered 1 to 20 (or higher if you’re feeling ambitious). (For example, 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, and so on.)
- Find the average of two numbers before multiplying them (the number exactly between them). The average of 18 and 14 is, for example, 16.
- This answer should be squared. You’ll know that 16 x 16 is 256 once you’ve memorized the squares chart.
- Next, consider the difference between the original and average numbers: 18 minus 16 equals 2. (Always use a positive number in this case.)
- This number can also be squared: 2 x 2 = 4.
- Take the first square and subtract the second to get your final answer: 256 – 4 = 252.
Find Practical Ways to Improve Your Mental Math Skills
A little bit of practice every day will make a big difference.
Make an effort to use your mental math skills at least twice or three times per day if you want to improve your confidence and speed. These suggestions will assist you in making this practice more effective:
- Flashcards are excellent for memorizing multiplication and division tables, as well as for practicing tricks for specific types of problems. Write the problem on one side and the answer on the other, and quiz yourself every day until you’ve mastered them all.
- Online math quizzes are another way to put your skills to the test. Look for a well-reviewed app or website created by a learning program.
- Practice in real-life situations. To calculate the total cost, add the total of items purchased while shopping or multiply the gas cost per volume by the size of your car’s tank. The more this becomes a habit, the easier it will be.
Using the above methods, you can improve your mental math skills. Through this article, we tried to provide you with easy and helpful tricks, and we hope that you will get better at it!