Math Tricks for Fast Calculation: There are several ways to solve a Mathematics problem. Just knowing the ways is not enough at all times. There are times when students need to solve Maths questions swiftly. Say, when they have ten more minutes for the exam bell to ring. Especially when a student appears for competitive exams, all the complex questions are required to be answered within a limited time. At such times, fast calculation tricks become extremely helpful.

Contrary to popular belief, developing a fast and accurate mental math ability is not difficult, and it definitely does not take years. It’s possible to increase your mental math speed by more than 100% by learning a few easy math tricks. Those basic tricks look at mathematical properties that can be checked under specific circumstances. Mathematics tricks and tips differ in length depending on the mathematical operation and the numbers involved, and learning one takes no more than 10 minutes.

Best Maths Tricks for Fast Calculation

As per research, a simple maths trick can solve complex problems in record time. Sometimes, knowing the trick to solve a mathematical problem makes a huge difference in the result of an exam. There are mathematical tricks for addition, subtraction, multiplication, squares, powers, logarithms, etc. Let’s start the list of best maths tricks and shortcuts with multiplication by 11.

Trick 1: Multiply Any Number By 11

Suppose you want to solve 58 x 11. Can you solve it in less than 5 seconds? Probably you can’t. That’s because you don’t know one little trick for multiplication by 11. The math trick for multiplying by 11 goes like this:

Imagine a problem like N x 11. Now follow the steps:

1. The last digit of the answer is the second digit of N.
2. The middle digit of the answer is the last digit of the sum of both digits of N.
3. The first digit of the answer is the first digit of N plus the carry if there’s one.

Now let’s apply the steps with our previous example of 58 x 11:

1. Last digit: 8.
2. Middle digit: 3. The sum of the digits 58 is 5 + 8 = 13.
3. First digit: 5 + 1 = 6. Notice that we have a carry because in the previous step we found that the sum of the digits of N is bigger than 10.

So, we conclude that 58 x 11 = 638

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Trick 2: Squaring Two-digit Numbers

Take for example that you want to square 56. Follow the steps given below to solve it in seconds:

• Step 1: Add the last digit of the number you are trying to square to the entire number itself, creating your sum. So, we have 56 + 6 = 62.
• Step 2: Multiply the sum (Step 1) by the first digit of the base number. So, we get 62 times 5 which is equal to 310.
• Step 3: Square the last digit of the base number. So, we get 6² = 36.
• Step 4: Append the square number (Step 3) to the product calculated above (Step 2).

Hence, our answer will be 3136.

Note: If you calculate the squared value in step 3 and the result is a double-digit number, don’t fret. Just like when you were in elementary school, you have to carry the one, and add it on!

Trick 3: Multiplication By 9, 99, 999

There is a simple yet powerful trick to multiply any number by 9, 99, and 999. The trick is given below:

Multiplying a number by 9 is just like multiplying it by (10-1).

For example, multiplying 9 × 9 is 9(10-1) whose result is 90-9 = 81

Another example:

9 × 68 = 68 (10-1)
= 680 – 68
= 612

Finger Method for Multiplication Table of 9:

A simple way to do the “9” multiplication table is to place both hands in front of you with fingers and thumbs extended. To multiply 9 by a number, fold down that number finger, counting from the left.

Examples: To multiply 9 by 5, fold down the fifth finger from the left. Count fingers on either side of the “fold” to get the answer. In this case, the answer is 45.

To multiply 9 times 6, fold down the sixth finger, giving an answer of 54.

To multiply a number by 99 is the same as by (100-1)

47 multiplied by 99
= 47 (100-1)
= 4700 – 47 = 4653

Multiplying a number by 1000 means the same as multiplying the same by (1000-1)

Therefore, 55 multiplied by 1000 is the same as 55(1000-1)
= 55000 – 55
= 54945

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Trick 4: How to Tell The Day for Any Date?

Can you tell the day for any date without a calendar at hand? Is that really possible? It is actually a simple skill that anyone can learn. It is also very practical as you may always consider your availability for an activity or an event or you just need to know the day of anyone’s birthday.

Trick: You may need to memorize some codes to learn this trick, but they are very easy to remember.
First, we assign a code number every day of the week.

1. Monday – 1
2. Tuesday – 2
3. Wednesday – 3
4. Thursday – 4
5. Friday – 5
6. Saturday – 6

Second, we assign a code number for every month of the year. These month codes are used for every year with two exceptions. In a leap year, the month code for January is 5 and for February is 1. The month codes with the corresponding mnemonics are as follows:

1. January – 6 (WINTER has 6 letters)
2. February – 2 (2nd month)
3. March – 2 (You march with 2 feet)
4. April – 5 (APRIL has 5 letters)
5. May – 0 (MAY0 for mayonnaise)
6. June – 3 (JUN has 3 letters)
7. July – 5 (JULIE has 5 letters)
8. August – 1 (August begins with an A, the 1st letter)
9. September – 4 (SEPT has 4 letters)
10. October – 6 (Maths ‘TRICKS’ has 6 letters)
11. November – 2 (2nd last month)
12. December – 4 (XMAS has 4 letters)

Third, we assign a code number for every year. For example, the year code for 2011 is 6.

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Formula to calculate the day:

Day of the week = (Month code + Date + Year Code) mod 7

Note: mod 7 indicates the remainder you get when you divide by 7.

Let’s understand this trick with an example:

Example 1: What is the day of July 16, 2011?

⇒ Day of the week = (Month code + Date + Year Code) mod 7

Day of the week = (5 + 16 + 6) mod 7 = 27 mod 7 = 6 (Therefore, it’s a Saturday)

Example 2: What is the day for December 25, 2011?

⇒ Day of the week = (Month code + Date + Year Code) mod 7

Day of the week = (4 + 25 + 6) mod 7 = 35 mod 7 = 0 (Therefore, it’s a Sunday)

Note: It is one of the most useful tricks for competitive exams.

Trick 5: Memorize The Value Of Pi

If you are also the one who always gets confused about the value of pi (who wouldn’t since pi is a never-ending number!), there is a neat trick to memorize the initial 7 digits. The trick is given below:

To remember the first seven digits of pi, count the number of letters in each word of the sentence:

“How I wish I could calculate pi.”

This becomes 3.141592.

Trick 6: Divisibility Rules

Many times we want to know if a number is divisible by 2, 3, 4, 5, etc. We can use these simple divisibility rules to know for sure if the number will be divided exactly or not.

Take the number 210. We check if it is divisible or not by following the divisibility rules given below:

1. Divisible by 2 if the last digit is a multiple of 2 (210 is divisible by 2 since the last digit i.e. 0 is a multiple of 2).
2. Divisible by 3 if the sum of the digits is divisible by 3 (210 is divisible by 3 since the sum of the digits which is 3 is divisible by 3).
3. Divisible by 4 if the last two digits are divisible by 4 (210 is not divisible by 4 because 10 is not divisible by 4).
4. Divisible by 5 if the last digit is 0 or 5 (210 is divisible by 5 since the last digit is 0).
5. Divisible by 6 if it passes the rules for both 2 and 3 (210 is divisible by 6 since it passes both rule 2 and rule 3).
6. Divisible by 9 if the sum of the digits is divisible by 9 (210 is not divisible by 9 since 2 + 1 + 0 = 3 is not divisible by 9).
7. Divisible by 10 if the number ends in a 0 (210 is divisible by 10 since the last digit is 0).
8. Divisible by 12 if the rules for divisibility by 3 and 4 apply (210 is not divisible by 12 since it is not divisible by both 3 and 4).

Trick 7: Multiplying Large Numbers If One Of Them Is Even

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

30 x 150

• Step 1: Divide the 30 by 2, which equals 15. Double 150, which equals 300.
• Step 2: Multiply your two answers together.
  So, 15 x 300 = 4500

The answer to 30 x 150 is 4500

Trick 8: 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:
726 + 233

While these numbers are hard to contend with, rounding them up will make them more manageable. So, 726 becomes 730 and 233 becomes 240.
Now, add 730 and 240 together. The total is 970.

To find the answer to the original equation, it must be determined how much we added to the numbers to round them up.
730 – 726 = 4 and 240 – 233 = 7
Now, add 4 and 7 together for a total of 11.

To find the answer to the original equation, 11 must be subtracted from the 970.

So, 970 – 11 = 959
So the answer to 726 + 233 is 959.

Trick 9: Find Percentage Easily

Suppose we have to find 5% of 475. Using the long method, you can calculate it by writing 5/100 then multiplying it by 475 and calculating it. However, that is a time-consuming process and every second matters in a competitive exam. So, follow the steps given below to calculate this percentage in a pinch.

1. For the given number, move the decimal point over by one place. 475 becomes 47.5
2. Then divide the number 47.5 by 2, we get 23.75.
3. 23.75 is the solution to the given problem.

Trick 10: Calculate Square Of Numbers Ending In 5

Let’s see some simple tricks for kids. Suppose we have to find the square of 75 (ends in 5). Follow the steps given below to calculate it quickly.

1. Start writing the answer to the last two digits number that is 25 because any number that ends with 5 is 25.
2. Take the first digit of the number 75. That is 7 and take the number that follows 7 is 8.
3. Now, multiply 7 and 8, and we get the number 56.
4. Finally, write the number 56 in the prefix and combined with 25 what we already wrote.
5. So, the answer is 5625.

Formula: Squares Ending in 5:  n5 = n(n+1)5² = n(n+1)25 , where n is the first digit.

Bonus Trick: Adding & Subtracting Fractions Using Butterfly Method

There are clean maths tricks for fast calculation for adding and subtracting simple fractions without needing any pen and paper. Suppose we have to add 5/7 and 2/5. Use the trick given below to add it quickly:

The steps are listed below:

• 1st Step: Multiply the numerator of the first fraction with the denominator of the second fraction and write the product on the top left.
• 2nd Step: Multiply the numerator of the second fraction with the denominator of the first fraction and write the product on the top right.
• 3rd Step: Multiply the denominator of the first fraction with the denominator of the second fraction and write the product on the bottom.
• 4th Step: Add the two products at the top and write the sum.
• 5th Step: The sum that you got will be the numerator of the fraction and the product from Step 3 will be the denominator.

To subtract fractions, only the 4th Step will be changed. Instead of adding the two products, we will subtract them.

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Frequently Asked Questions on Math Tricks and Formulas

Here are some of the frequently asked questions on maths fast calculation tricks:

Q1. How can I add large numbers quickly?
Ans: To add any two numbers quickly, follow the below steps:
(i) Firstly, round up both the numbers by adding or subtracting small numbers.
(ii) Add the numbers.
(iii) Now subtract or add those values to get the final result.
For example, Add 796 and 292.
Round up 796 to 796+4 = 800 and 292 to 292+8 = 300
800+300 = 1100
Now subtract the added numbers from 1100,
1100-4-8 = 1100-12 = 1088.

Q2. How can I do maths faster?
Ans: You can refer to the tricks on Mathematics provided on this page to solve mathematical problems faster and in an easy way.

Q3. What is the benefit of learning these tricks?
Ans: Learning tricks to solve math problems help us to do calculation fast. It saves time and increases the chances of scoring more marks in the exams.

Q4. How to find if a number is divisible by 13?
Ans: If a number N is given, then multiply the last digit of N with 4 and add it to the rest truncate of the number. If the outcome is divisible by 13, then the number N is also divisible by 13.
For example, 650 is divisible by 13 because;
65+0*4=65
Hence, 65 is divisible by 13.

Q5. What is the trick to multiplying quickly?
Ans: To multiply two numbers, we can split the numbers and then multiply them. For example, multiply 81 and 24.
⇒ Splitting the number 81 = 8 x 9
⇒ Multiply 24 by 8, 24 x 8 = 192
⇒ Now multiply 192 x 9 = 1728
Hence, multiplication the number by one digit number is easier.

Q6. What are some of the tricks to remember while dividing two numbers?
Ans: You can be mindful of the following tips:
– When a number ends with an even digit, it is divisible by 2.
– If the sum of the digits in a number is divisible by 9, the whole number can be divided by 9. Similarly, if the sum of the digits in a number is divisible by 3, the whole number can be divided by 3. In addition, any number that can be divided by 9, can be divided by 3
– A number that can be divided by both 2 and 3, can be divided by 6
– If the last two digits of a number are divisible by 4, the whole number can be divided by 4. Similarly, if the last three digits of a number can be divided by 8, the whole number can be divided by 8.
– A number that ends with 0, can be divided by 10. If it ends with 0 or 5, it can be divided by 5.

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Hope you learned some new maths tricks with answers and apply them to mathematical calculations. We hope you had fun along with learnings reading this article. However, if you have further questions on maths tricks and shortcuts, do not hesitate, just let us know through the comments section and we will provide you with an update. Stay tuned to Embibe for the latest news and updates on how to solve Mathematics problems in the fastest manner.