MULTIPLYING TWO, TWO DIGIT NUMBERS

 In this blog we shall see a simple method to mentally multiply two two digit numbers which meet the following conditions:

1. The number in the units place in the two numbers must add up to 10.

2. The number in the tens place in both the numbers must be the same.

Let us see a few examples.  

Let us take two numbers 17 and 13. 

Note that the numbers in the unit's place in the two numbers are 7 and 3, and they add up to 10. The number in the ten's place is   1 and 1.

Let us take two other numbers 38 and 32. 

Note that the numbers in the unit's place in the two numbers are 8 and 2, and they add up to 10. The number in the ten's place is   3 and 3.

Hope you have understood how to check the numbers to see whether they meet the  two conditions, stated above.

Now let us take up multiplying the numbers.

Example 1 

The numbers we take up are 17 and  13.

The numbers satisfy both the conditions.

Step1. Multiply 7x3 to get 21. Write this number 21, which is part of the answer.

Step 2. Now take 1 which is in the ten's place. The next higher number to 1 is  2.. 1x2 = 2.

Write this 2 to the left of 21. The final answer is 221 !

 

 

Example   2

The numbers we take up are 38 and  32.

The numbers satisfy both the conditions.

Step1. Multiply 8x2  to get 16. Write this number 16, which is part of the answer.

Step 2. Now take 3 which is in the ten's place. The next higher number to 3 is  4.  3x4=12.

Write this 12 to the left of 16. The final answer is 1216 !

                                                -0O0- 

 

SQUARE OF A NUMBER WITH 5 IN ITS UNITS PLACE.

Here is a simple way to mentally calculate the square of numbers like 15,25,35 ....105 ...

EXAMPLE 1

Let us consider 15 :

Step 1. Take 5 from the units place and multiply it by 5 to get 25. 

Write down  25, which a part of the  answer.

Step 2. Take 1 which is to the left of 5.  The next higher number to 1 is 2.

Step 3. Multiply 1x2 to get 2.

Step 4. Write this  2, to the left of 25  which we wrote in step 1, to get 225, which is the final answer. 

15x15=225

 

EXAMPLE 2

Let us consider 25 :

Step 1. Take 5 from the units place and multiply it by 5 to get 25. 

Write down  25, which a part of the  answer.

Step 2. Take 2 which is to the left of 5. The next higher number to 2 is 3.

Step 3. Multiply 2x3  to get 6.

Step 4. Write this  6, to the left of 25  which we wrote in step 1, to get 625, which is the final answer. 

25x25=625

EXAMPLE 3

Let us consider 45 :

Step 1. Take 5 from the units place and multiply it by 5 to get 25. 

Write down  25, which a part of the  answer.

Step 2. Take 4 which is to the left of 5.  The next higher number to 4 is 5.

Step 3. Multiply  4x5  to get 20.

Step 4. Write this  20, to the left of 25  which we wrote in step 1, to get 2025, which is the final answer. 

45x45=2025

EXAMPLE 4

Let us consider 115 :

Step 1. Take 5 from the units place and multiply it by 5 to get 25. 

Write down  25, which a part of the  answer.

Step 2. Take 11 which is to the left of 5.  The next higher number to 11 is 12.

Step 3. Multiply 11x12  to get 132.

Step 4. Write this  132, to the left of 25  which we wrote in step 1, to get 13225, which is the final answer. 

115x115 =13225.

 

Practice frequently with different numbers so that you are able to this with ease.

   

                                                            -0O0-