Multiplication Tricks

Multiplication tricks are used to reduce the time it takes to calculate long multiplication problems with accuracy. Multiplication is one of the fundamental operations of arithmetic. The multiplication of the whole numbers can be conceived as repeated addition which means the multiplication of two numbers is equivalent to adding as many copies of one of them as the quantity of the multiplier. There are two terms needed to be understood- multiplicand and multiplier. The Multiplicand is the number that is being multiplied and Multiplier is the number that is multiplying the first number. 

Key Takeaways: Multiplication, Multiplication Tricks, Multiplicand, Multiplier.

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What is Multiplication?

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Multiplication is one of the fundamental operations of arithmetic, which gives the result of combining groups of equal sizes. Multiplication operation is often represented by the signs cross “X” or dot “.’ Or asterisks “*” symbols. The multiplication of the whole numbers can be conceived as repeated addition which means the multiplication of two numbers is equivalent to adding as many copies of one of them as the quantity of the multiplier.

Read More: Arithmetic Progression

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How to Multiply fast?

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Here are some of the multiplication tricks that can be used for different numbers.

Multiplication by 2

It refers to a double number.

For instance, 6X2, here we have to double the number 6, so we can use the addition method.

So, 6+6= 12

Multiplication by 3

It denotes three times a number.

For example, 6X3= 6+6+6= 18

Multiplication by 4

It refers to double of a double number.

For instance, 6X4: first, double of 6 is 12. After that double the number 12 and thus we get 24.

Multiplication by 5

When a number is to be multiplied by 5, a simple technique can be employed where we first divide the number by 2 and multiply by 10.

For example, 6X5: 6 divided by 2, we get 3, now 3 is multiplied by 10, 3X10=30. Thus, we get 30 as the answer.

Multiplication by 8

Here the simple trick is to double the three times consecutively.

For example: 6X8: 6+6= 12; 12+12=24; 24+24=48

Multiplication by 9

Another interesting trick can be applied to do multiplication by 9. At first, +1 is to be added to 9 and minus the number with itself, which is to be multiplied.

Example: 6X9: (9+1 X 6)-6=60-6=54

Multiplication by 10

It is arguably the simplest. Zero is to be put after the number that is to be multiplied by 10.

For example, 14X10= 140

Multiplication by 11

This method works wonderfully for multiplying numbers up to 9 by 11, here the number is simply repeated once for the result.

Example: 6X11= 66.

Multiplication by 12

To multiply a number by 12, the number has to be multiplied by 10 first and then add the number to the double of it.

For example, let us consider 4X12. Multiply the number 4 by 10 first which gives 40 and then add 40 to the double of this number which is 4X2=8. Thus, the number becomes 40+8=48.

Multiplication by 15

When a number is to be multiplied by 15, it is to be multiplied by 10 first and then half to it to get the final answer.

For example, 4X15. Multiplying 4 by 10 we get 40 and adding the half 20 to it gets us 60.

4X15= (4X10) + (40/2)

= 40+ 20

= 60

Multiplying by 20

Multiplying a number by 20 is simple. Here, just multiply the number by 10 and then double it.

Let us consider 20X8, multiplying 8 by 10 gives us 80 and then doubling it we get 160.

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Multiplication by 5ⁿ (5, 25, 125 and so on)

1. As many zeroes o be added at the end of the given number as there is a power of 5
2. Divide the resultant number by 2? to the result.

Example: 94X 125

Here, 125= 5³. Thus, the power of 5 is 3.

Now, as per the steps mentioned above, 3 zeroes are to be added at the end of 94 and hence it becomes 94000. In the second step 94000 is to be divided by 23=8.

Thus, the final number becomes 94000/8= 11750.

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

1. The unit digits of the numbers are to be multiplied.
2. Now the digits that are the same are to be multiplied with their consecutive number.
3. Finally, the result from step I is appended to the right of the result obtained in step II.

Example: 22X28

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

1. The unit digits are multiplied: 2X8= 16
2. Multiply the digit 2 with its consecutive number: 2 X (2+1)=2X3=6
3. Append 16 to the right of 6. Hence, the number becomes 616.

Thus, 22X28=616.

Multiplication of a number by 9ⁿ (9, 81, 729 and so on).

1. The power of 9 is to be identified first in such a way that step II can be performed based on the result obtained.
2. Then the given number is multiplied by 10 and then subtract the given number from the result obtained.

Example: 232X 81

Here, 81= 92

Hence, step 2 has to be performed twice.

(232X10)-232= 2088

(2088X10)-2088= 18792

Thus, the product of 232 and 81 is 18792.

Read More: Relation Between HCF and LCM

Multiplication of a number by a number whose unit digit is 9

• The second number is to be split in such a way that it should be equal to the given number.
• Now the distributive property of multiplication over addition or subtraction is to be applied as per the requirement.
• Simplify the arithmetic problem.

Example: 142X49

Here, the second number is split as follows

142X (50-1)

= (142X50)- (142X1)……( using the distributive property)

= 7100- 142

= 6958

Therefore, 142X49= 6958

Multiplication of a number by another number that contains all digits as 9

1. The multiplier is to be split in the form of (10n-1).
2. Now, the distributive property of multiplication over subtraction is applied.
3. Simplify the arithmetic problem.

Example: 436X 999

1. 999 is written as (1000-1).
2. Now the problem can be written as

436X (1000-1)= (436X1000)- (436X1)

= 436000-436

= 435564

Thus, the product of 436 multiplied by 999 is 435564.

Rounding up Method for Multiplication

It is the method in which the number is rounded up to make the multiplication easier.

Example: Multiplication for a two-digit number

68X2

Rounding up the number 68 to 70,

70X2= 140

Multiplying the rounded amount itself

2X2= 4

Subtracting 140-4= 136

Therefore, the final answer is 136.

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Things To Remember

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• Multiplication is one of the fundamental operations of arithmetic besides addition, subtraction and division, giving the result of combining groups of equal sizes.
• Multiplication operation is often represented by the signs cross “X” or dot “.’ Or asterisks “*” symbols.
• Multiplicand- It is the number that is being multiplied
• Multiplier- It is the number which is multiplying the first number

• The multiplication method is designed to form tables of different numbers. It is used to memorize the products of different numbers.

Read More: Heights and Distances

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