- Rafia Shabbir

# What Is Mental Math? Find 12 Mind Blowing Mental Math Tricks

Updated: Aug 21, 2021

Technology especially digital calculators have made calculations much quicker and easier. Now, we utilize them even for simpler arithmetic calculations such as addition, subtraction, multiplication, and division. But do you know relying on technology for every calculation is affecting our brain?

Well, today in this article we will discuss why you should focus on developing mental math skills and what are some of the mind-blowing tricks to do so? First, let us define what mental math or mental calculation is.

Mental math refers to solving basic arithmetic questions using the human brain only, without the aid of external devices such as calculators.

**Fun Mental Math Strategies for Faster Mental Calculations**

The following math tricks are quite useful in mental math calculations. You can surprise everyone around you by coming up with instant answers without a calculator and gain a reputation of a math genius in your circle. 😊

**1. Percentages can be Switched**

Do you know that you can switch the percentages? It means that if you are given a % of b, then you can write it as b% of a. In both cases, the answer will be the same.

**Example**

Suppose you have to find 2% of 50. Instead of grabbing the calculator, you can write it as 50% of 2 which is equal to 1.

**2. Divisibility by 3**

This is a very common and popular mental math technique. To see either a large number is divisible by 3 or not, add the digits of the number. If the sum of digits is divisible by 3, then the number will also be divisible by 3.

**Example**

To check whether 13467 is divisible by 3 or not add the digits like this:

=1 + 3 + 4 + 6 + 7

= 21

Is 21 divisible by 3? Certainly, yes because 3 into 7 is equal to 21. So, the number 13467 is also divisible by 3.

**3. Look for the Complements**

The complement of a single-digit number is any other number which will make the sum of the number and its complement equal to **10**. It means that the complement of 1 is 9, 2 is 8, 3 is 7, 4 is 6 and so on.

When you are presented a list of numbers, the fastest way to add them in your head is to find the complements in the list.

**Example**

Consider the following list of numbers:

2 + 3 + 5 + 7 + 4 + 1 + 8 + 9 + 5 + 7 + 6 + 5 + 3

Well, this is a long list of addition. To solve it faster, rearrange the digits by writing the numbers and their complements together. The numbers which are left can be written in the end.

2 + 8 + 3 + 7 + 3 + 7 + 5 + 5 + 4 + 6 + 1 + 9 + 5

The complements have their sum equal to 10:

=10 + 10 + 10 + 10 + 10 + 10 + 5

=65

Teach this trick by presenting problems using addition worksheets. Set the time, so that students are compelled to apply these tricks and come up with the answers instantly.

**4. Addition and Subtraction**

When you are adding the large numbers round them off to the nearest ten, hundred or thousand. If the rounded number is greater than the original number, then subtract the additional number from the answer and vice versa.

**Example**

Add number 387 and 415. To add it quickly in your head, round off the number 387 to 400 and 415 to 400. Adding these two numbers will give us 800. Now, subtract 13 from 800 to get 787 and add 15 to get 802.

**5. Subtracting Large Number from 1000**

When you are dealing with a problem in which you must subtract a large number from 1000, then use the following strategy:

Subtract first and the second digit from 9 separately

Subtract the last digit from 10.

**Example**

Subtract 786 from 1000. To answer this without the use of the calculator and even pencil or paper, use the steps explained above. Subtracting 7 from 9 gives us 2. The subtraction of 8 from 9 will yield 1. Finally, subtracting the last digit 6 from 10 will give us 4. Hence, the final answer will be 214.

**6. Divisibility by 5**

To determine whether a number is divisible by 5 or not, see its last digit. If it contains 0 or 5, then we can say that the number is divisible by 5.

**Example**

The numbers 234675 and 9865430 are both divisible by 5 because their last digits are 5 and 0 respectively.

**7. Multiplication by 11**

If you are asked to multiply a two-digit number by 11, you can do it faster in your head and come up with the answer instantly. Surprised? Well, consider examples below to learn about this mind-blowing trick.

**Examples**

**Multiply 72 by 11.**

The first and last digit of the resulting number will be the same, i.e. 7 and 2. To calculate the mid digit add 7 and 2 together.

7+ 2 = 9

The resulting answer will be 792.

Be careful if the sum of the number has a 2 digits and includes 1 because it will be done differently. Consider another example below.

** 2. Multiply 68 by 11**

Add 6 and 8 together to get the following:

6 + 8 = 14

Now, add the 1 of 14 to 6 and place 4 in the middle. The last digit will be the same, i.e. 8. The answer will be 748. It is surely one of the coolest division facts that you will ever come across.

**8. Multiplying by 5**

If you need to multiply a large number by 5, then do it instantly by taking half of the number and multiplying it by 10.

**Examples**

**Multiply 48 by 5**

Half of 48 is 24 and when it is multiplied by 10 we get 240. Hence, the answer is 240.

**Multiply 75 by 5**

Half of 75 is 37.5. Multiplying it by 10 will give us 375 which is the correct answer.
**9. Square Root **

Do you know that you can calculate the square root of a number by following simple steps?

Consider an example below to know how to do it.

**Example**

Find the square root of 41. Most people will say that it is impossible to find the answer without a calculator, but the truth is this can be done in few seconds following these steps.

Take the next lower perfect square. In the case of 41, the next lower perfect square is 36.

Add it to the number. By adding 36 and 41, we get 77.

Now, divide it by the square root of 36. In the case of 77, we will divide it by 6 to get 12.8.

Now divide the answer by 2 to get the square root of the number. When 12.8 is divided by 2, we get 6.4 which is the square root of 41.

**10. Divisibility by 8**

If you are given a large number and you want to check whether it is divisible 8 or not, then see its last 3 digits. If the last 3 digits are divisible by 8, then the whole number is divisible by 8. Isn’t this a cool division math skill?

**Example**

For example, consider the number 456789064

The last three digits 064 are divisible by 8, so the whole number is divisible by 8.

**11. Divisibility by 4**

To check whether a number is divisible by 4 or not, look at its last two digits. If they are divisible by 4, then the whole number is also divisible by 4.

**Example**

The number 1654380 is divisible by 4 because the last two digits are 80 which are divisible by 4.

**12. Order of Operations**

The arithmetic operations should be executed in order to reach the answer to a complex question which involves multiple operations. The order of operations is PEMDAS which is the acronym for:

*P: Parentheses*

*E: Exponents*

*M D: Multiplication or division*

*A S: Addition or subtraction*

**Example**

Consider an expression below:

This order is very helpful in solving algebraic expressions. Consider an example below:

Solve (2 + 7) – 7 x 6 ÷ 3

To solve the above expression first solve the term inside the parenthesis.

2 + 7 is equal to 9, so the resultant expression will be written as:

9 – 7 x 6 ÷ 3

Now, apply the division operation by solving 6 ÷ 3 which is equal to 2.

9 – 7 x 2

The next step is to multiply 7 and 2 to get 14. The final step involves subtracting 14 from 9 to get the answer -5.

**Benefits of Mental Math **

**Make Math Learning Fun and Exciting**

Teachers can use math flashcards and worksheets to teach these simple yet powerful math tricks to the students. It will improve the basic math skills of the students and make math education fun and exciting in the class. The best thing about these math facts is that they can be memorized easily. Teaching math concepts through interactive math lessons and hands-on math activities is the best way to drive greater student engagement.

**Helps in Daily Life**

Mental math enhances your cognitive and problem-solving skills. Without knowing mental math strategies, it would be very difficult for you to understand complex concepts and perform daily life activities. These cool math tricks will train your brain to improve its concentration skills. Help your child to practice math facts by presenting math puzzles and fun math games. It will also increase their number sense.

**May Improve Emotional Health**

According to a study published in the journal Clinical Psychological Science, stimulating a certain part of the brain while solving mental math problems may be beneficial for the emotional health of the person. We use the dorsolateral prefrontal cortex to solve memory-based math problems. This part of the brain is also linked with depression and anxiety. Higher math activity can stimulate this part of the brain and may help in combating these mental disorders.

**Helps in Boosting the Self - Confidence**

Memory-based math games and activities also help children in boosting their self-confidence. When math teaching is coupled with math riddles, worksheets, workbooks, puzzles and games, it sparks off student’s interest in mathematics and gives them more confidence in his math skills. If you are a math teacher, you can avail number of printable math worksheets templates and other math resources available online to teach these math concepts.

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**About Us**

Hope you liked the article. We at Educationise are passionate about education and you can contact us if you want us to develop educational materials especially customized according to your needs. We have wide range of experience of working on educational projects and we aim to deliver the highest quality output.