Multiplication Tricks

Multiplication tricks are required to calculate long and difficult multiplication problems. For single digit, 2-digit and even for 3-digit numbers, it is easy to do the multiplication. But for larger numbers which have more digits such as 4, 5, 6, 7,etc., it takes a long time to solve it. Therefore, we will learn here some magic maths tricks for fast calculation. These tricks can also be used to prepare for competitive exams.

In Maths, there is a number of arithmetic calculations or operations which includes multiplication and division, addition, subtraction, differentiation, integration, etc. Each calculation has its own method to calculate the relation between the numbers based upon the operation performed on them. Along with the methods, it is always useful to learn some multiplication tricks to save time.

What are Multiplicand and Multiplier?

It is necessary to know, what are the numbers called when we apply multiplication operation in them.

• The multiplicand is the number which is being multiplied
• The multiplier is the number which is multiplying the first number.

For example: In this operation, 45 × 20, 45 is the multiplicand and 20 is the multiplier.

How to Multiply Fast?

Here are some tips and tricks with the help of which, you can easily solve multiplication problems. These tricks you can use in competitive exams as well. Students can by-heart multiplication tables to calculate fats. Let check the multiplication tricks for different numbers.

Multiplication by 2: It denotes to double a number.

For example; 5 × 2, here we have to double the number 5, so we can use addition method here, i.e.

5 + 5 = 10

Multiplication by 3: It denotes triple times of a number.

Example: 5 × 3 = 5 + 5 + 5 = 15

Multiplication by 4: It denotes double of a double number.

Example: 5 × 4: double of 5 is 10. Thus double of 10 is 20(10+10)

Multiplication by 5: If a number is multiplied by 5, then divide the number by 2 and multiply by 10.

Example: 8 × 5: 8 divide by 2 = 4, multiply 4 by 10, 4 × 10 = 40.

Multiplication by 8: Double → Again Double → Again Double

Example: 5 × 8: 5 + 5 = 10; 10 + 10 = 20; 20 + 20 = 40

Multiplication by 9: Add +1 to 9 and minus the number with itself, which is to be multiplied.

Example: 5 × 9: 9+1 × 5-5 = 10 × 5 – 5 = 50 -5 = 45

Multiplication Table

Multiplication method is basically designed to form tables of different numbers. It is always suggested for students to learn by heart the tables from 2 to 20 at least, which will help to solve multiplication problems very easily.

Let us create a table for multiplication of 2 to 10 numbers, which will help you to memorize the table.

With this table, you can see each number is appearing twice. There is a duplicate for each number inside the table. For example, 3 × 6 = 18 but also 6 × 3 = 18.

Learning from the table is the general trick of multiplication. Now let us learn about multiplying tricks of 4 digit numbers along with the general method and rounding up method.

Also, learn:

General Method for Multiplication

In this method, we apply the simple procedure of multiplication.

For example 6780

× 2

————–

13560

So you can see there are only one digit multiplier and 4 digit multiplicand. Easily with the help of a table, you can solve such problems.

List of Important Multiplication Tricks

Case 1: Multiplication of the given number by 5ⁿ. (5, 25, 125, …)

Step 1: Add as many zeroes at the end of the given number, as there is a power of 5

Step 2: Divide the resultant number by 2^{(Power of 5)}, to get the result.

Example: 

Multiply 94 by 125

Solution:

Given: 94 ×125

Here 125 = 5³. The power of 5 is 3.

Step 1: Now, add 3 zeros at the end of 94, and hence it becomes 94000

Step: Now, divide 94000 by 2³. Hence, it becomes 

= 94000/8

= 11750

Therefore, 94 ×125 is 11750

Case 2: In the multiplication of two numbers, if the sum of whose unit digit is 10, and the remaining digits are the same in both the numbers.

Step 1: Multiply the unit digits of the numbers

Step 2: Now multiply the digit (which are same) with its consecutive number

Step 3: Finally, append the result obtained in step 1 to the right of the result obtained in step 2.

Example: 

Multiply 22 by 28

Solution:

Given: 22 × 28

Here, the sum of the unit digit is 10 (2+8 = 10)

Step 1: Multiply unit digits: 2 × 8 = 16

Step 2: Multiply the digit 2 with its consecutive number 2 × (2+1) = 2 x 3 = 6

Step 3: Append 16 to the right side of 6. Hence, it becomes 616.

Therefore,  22 × 28 is 616.

Case 3: Multiplication of the given number by 9ⁿ. (9, 81, 729)

Step 1: Identify the power of 9, such that step 2 has to be performed based on the power of 9.

Step 2: Multiply the given number by 10, and then subtract the given number from the result obtained.

Example: 

Multiply 232 by 81.

Solution:

Here the power of 9 is 2. (9² = 81)

Hence, step 2 has to be performed twice.

• (232 × 10) – 232 = 2088
• (2088 × 10) – 2088 = 18792

Therefore, the product of 232 and 81 is 18792.

Case 4: Multiplication of a number by a given number whose unit digit is 9

Step 1: Split the second number, such that it should be equal to the given number

Step 2: Now, apply distributive property of multiplication over addition or subtraction, as per the problem requirement

Step 3: Simplify the arithmetic operation

Example: Multiply 142 by 49

Step 1: Split the second number, and hence it becomes 142 × (50-1)

Step 2: Now, apply the distributive property of multiplication over subtraction.

= (142×50)-(142×1)

= 7100 -142

= 6958

Therefore, 142× 49 =  6958

Case 5: Multiplication of a number by a given number which contains all the digits a 9

Step 1: Split the given number (multiplier) in the form of (10ⁿ – 1)

Step 2: Now, apply the distributive property of multiplication over subtraction

Step 3: Simplify the arithmetic operations

Example:

Multiply 436 by 999

Solution: 

Step 1: 999 can be written as (1000-1). Hence, the given problem is written as 436×(1000-1)

Step 2: Now, apply the distributive property of multiplication over subtraction.

436×(1000-1) = (436×1000) – (436×1)

436×(1000-1) = 436000 – 436

436×(1000-1) = 435564

Therefore, the product of 436 and 999 is 435564.

Case 6: Multiplication of the given numbers which are close to the powers of 10. (10¹, 10², 10³, …)

Step 1: Write down the two numbers with the difference from the base number

Step 2: Now take the sum of two numbers, which are obtained in step 1 (Considering the sign also) along with either of the two diagonals. This should be the first part of the answer)

Step 3: Now, take the product of two numbers (numbers obtained from step 1), with the consideration of the symbols. This should be the second part of the answer.

Step 4: Combine the first part (result from step 2) and the second part (result from step 3) of the solution together to get the final solution.

Example:

Multiply 93 by 94

Solution:

Step 1:

93 = (93 – 100) = -7

94 = (94 -100) =  -6 

Step 2: 

Take the sum of two numbers along either of two diagonals (Consider the sign also)

Diagonal sum ⇒ 93 + (-6) = 94 +(-7) = 87

Therefore, the first part of the solution is 87

Step 3: Take the product of two numbers: -7 ×-6 = 42

Therefore, the second part of the solution is 42

Step 4: Combine the first and second part of the solution together, and hence it becomes 8742

Therefore, 93 × 94 = 8742.

Rounding Up Method for Multiplication

In this method, we round up the complex numbers in the simple form to make the multiplication easier. Let us explain to you with example problems.

Multiplication Tricks for a 2-digit number

Example 1

58 ×2

Rounding the number 58 to 60,

60×2=120

Multiplying the rounded amount to itself;

2×2=4

Subtracting 120-4=116

So, 116 is the final answer.

Example 2

26 × 22

If we right, 22 as 20+2 and then multiplying them separately,

26×20 and 26×2 and adding them.

26     26

×20 + ×2

—— ——

520  +   52     = 572

—— ——

So the answer for 26×22 is 572.

In the same way, you can practice more of multiplication problems by using these simple multiplication tricks.