Multiplication of 2 numbers whose last digit adds to 10

 

In this tutorial, we are going to learn the shortcut, how to multiply 2 numbers whose last digits adds to 10. The important condition for this shortcut, however is that, the rest of the digits should remain same.

In order to use this short, the following condition should be satisfied.

  1. Last digits should add to 10.
  2. The remaining digits should remain same.

For example, this shortcut can be used to multiply the numbers such as 72 x 78, 53 x 57, 81 x 89 etc.

Let’s say, we want to multiply 72 x 78. This satisfies the condition, as the unit digits add to 10 ( 2+8=10) and the remaining digits remain same i.e., 7.

The entire steps are illustrated in the following figure.

 

Multiply 2 numbers whose last digits add to 110

 

Step 1 :  Break the number such that unit digits  is on the right and the rest of the digit ( i.e., 7 in this case) is on the left.

Step 2 :  Multiply the unit digits(2×8) . This forms the second part of the answer.

Step 3 :  Take the rest of the digit on the left and multiply by the next higher digit that follows it. In our case, we need to multiply 7 by 8 which gives us 56 which forms the first part of the answer.

 

Similarly, can you compute what is 107 x 103 ?

 

multiply_add_10_1

 

Exception :  Let’s say we need to multiply the numbers 71 x 79. It satisfies both the condition. When you use the same technique, you notice that the answer is wrong.

 multiply_add_10_2

 

This is because, the right hand side of the answer should always be 2-digits and multiplying 1 and 9 results in 9. So we have to convert 9 to 09.

 

multiply_add_10_3

Exercise : Can you mentally multiply ?

  • 89 x 81
  • 124 x 126
  • 1003 x 1007
  •  54 x 56

 

Please contact me if some point in the tutorial is not clear. I would be glad to help.

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