Multiplication of 2 numbers that are near to 100 or 1000

This tip is suitable for multiplying two numbers that are near to 100. For example, 103 x 104 and 97 x 98.

Example 1:

To calculate 103 x 104:

1. Add the the ones from the multiplicand to the multiplier.
   103 + 4 = 107.


2. Multiply the ones from the multiplier with the ones from the multiplicand.
   3 x 4 = 12.


3. Concatenate the results from step 1 and 2. Therefore, 103 x 104 = 10712.

Example 2:

To calculate 1005 x 1002:

1. Add the the ones from the multiplicand to the multiplier.
   1005 + 2 = 1007.


2. Multiply the ones from the multiplier with the ones from the multiplicand. Prepend a zero to the result.
   5 x 1 = 010.


3. Concatenate the results from step 1 and 2. Therefore, 1005 x 1002 = 1007010.

Example 3:

To calculate 97 x 98:

1. Subtract from 10, the ones from multiplicand.
   10 - 8 = 2.


2. Subtract from multiplier, the result from step 1.
   97 - 2 = 95.


3. Subtract from 10, the ones from multiplier.
   10 - 7 = 3.


4. Multiply the result from step 3 with the result from 1. Prepend a zero.
   2 x 3 = 06.


5. Concatenate the results from step 2 and step 4. Therefore, 97 x 98 = 9506.

Example 4:

To calculate 993 x 995:

1. Subtract from 10, the ones from multiplicand.
   10 - 5 = 5.


2. Subtract from multiplier, the result from step 1.
   993 - 5 = 988.


3. Subtract from 10, the ones from multiplier.
   10 - 3 = 7.


4. Multiply the result from step 3 with the result from 1. If you get a one digit number, prepend two zeroes, otherwise prepend just one zero.
   5 x 7 = 035.


5. Concatenate the results from step 2 and step 4. Therefore, 993 x 995 = 988035.

Exercise:

If domain name is cost $9.90 each, what is the cost if you want to buy 92 domain?

Multiplication of any number by a number near 100

It is easy to multiply any number by 100. We just need to append two zeroes to the end of that multiplicand number. For example, 100 x 23 = 2300. But, what if the multiplier is a number that is near to 100, such as 101, or 99?

To multiply a number, a, by a number, b, that is near to 100, here are the steps.

1. Multiply the multiplicand by 100.
   c = 100 x b


2. Subtract 100 from the multiplier.
   d = b - 100


3. Multiply multiplicand, a with the result from step 3, d.
   e = d x a


4. Finally, add the result from steps 1 and 3.

In simple words, we could write it as

( 100 x multiplicand ) + ( (multiplier - 100) x multiplicand )

Example:

1. 101 x 23 = (100 x 23) + ( (101 - 100) x 23 ) = 2300 + (1 x 23) = 2300 + 23 = 2323


2. 99 x 23 = (100 x 23) + ( (99 - 100) x 23 ) = 2300 + (-1 x 23) = 2300 - 23 = 2277

Now, you can try to do it on larger numbers such as 101 x 297, or even slightly larger or smaller than 100 multiplier, such as 103 x 74.

Multiply a number by 11

Multiplying a one digit number by 11, is easy. For example, 2 x 11 = 22. We just repeat the number back twice.

What if we have 1334 x 11? This strategy could help us to multiply any greater than 2 digits number by 11.



The best way to explain this strategy is by using examples.

Example 1: 243 x 11.

1. 2 _ _ 3   (3 digits - put extra 2 blanks in the middle)


2. 2 2+4 _ 3   (add the 1st 2 numbers)


3. 2 6 4+3 3   (add the last 2 numbers)


4. 2 6 7 3

Therefore, 243 x 11 = 2673

Example 2: 1435 x 11.

1. 1 _ _ _ 5  (4 digits - put extra 3 blanks in the middle)


2. 1 1+4 4+3 3+5 5 = 15785

Therefore, 1435 x 11 = 15785

Note:

If the addition of the 2 numbers would gives 2 digits number, add that number's left digit to the left digit of the original number.

Example 3: 99x 11.

Wrong: 99 x 11 = 9 9+9 9 = 9189

Note that 9 + 9 = 18 (a 2 digits number).

1. 9 _ 9


2. 9 9+9 9


3. 9 18 9 ---> 9 + 1 8 9


4. 1089

Example 4: 46 x 11.

46 x 11 = 4 4+6 6 = 4 10 6 = 4 +1 0 6 = 506

As a conclusion, to multiply a number by 11, add the digits of a 2 digits number, and place the sum between them. If the addition produce a more than 1 digit number, carry the tens column to the left.

Product of a single digit number with 9

This algorithm is useful for kids that are lazy enough to memorize the multiplication table of 9.

The algorithm works like this:

Suppose you want a product of n and 9, you can do

1. n - 1


2. 10 -n


3. The answer is (n-1) as the first digit and (10 - n) as the second digit.

Example:

4 x 9 =36

First digit: 4 - 1 = 3

Second digit: 10 - 4 = 6

Note: This trick only works on multiplication of any single digit number with 9.

Box multiplication

The box multiplication technique is suitable for people that has problem with numbers, since it will organized all the number in place.

Example 1:

13 × 23 = 299 First, draw a box for each number. Divide each box diagonally, with a straight line. Then multiply diagonally to the right. For example, 3 × 2 = 6. Put 0 inside the left triangle and 6 inside the right triangle, and so on.

After we have fill in all the numbers inside the triangle, add all the numbers diagonally to the left. For example 6 + 0 + 3 = 9, 0 + 2 + 0 = 2. Write the addition at the end. Follow the arrow.

Example 2:

79 × 85 = 6715 In this example, when we add 2, 4 and 5, we get 11. So, we write 1 and carry 1 (just write it in bracket). Next, when we want to add 7, 6 and 3, add the carry number as well. So, it will become 7 + 6 + 3 + 1 = 17. The same thing goes here. Write 7 and carry 1. The last one is 5 + 1 = 6.

note: The box multiplication technique could also be applied to the numbers that are more than two digits, such as 234 × 346 and 342 × 34.

Multiply two 3 digits numbers in your head

This article will show how to do multiplication of two three digits numbers from right to left. Consider 234 × 456.

Step 1: Multiply the last digits. Write 2, carry 4.

Step 2: Cross multiply the one and the tenth, and add them together. We get 53. Add the 4 that we carry to 53. We get 57. Write 7, carry 5.

Step 3: Multiply all digits, like in the figure below. We get 55. Add the 5 that we carry to 55. We get 60. Write 0, carry 6.

Step 4: Finally, multiply the two left digits. We get 22. Add the 6 that we carry to 22. Write 2, carry 2.

Step 5: Finally, multiply the left digits. Add the 2 that we carry to 8. We get 10. Write both numbers.

Therefore, the answer is 108072.

Easy Multiplication I

This technique of multiplication will do the multiplication from right to left. Let’s look at an example. 23 x 12 = 276

Step 1: Multiply the last digits.

Step 2: Cross multiply both sets of numbers and add them together.

Step 3: Finally, multiply the left digits.