Multiply a 2-digit number by 9 (An Alternative)

9 is an interesting number. It is the last number in the series of single digits. It is revered in Hinduism as it is considered as a complete, perfected and divine number because it represents the end of the cycle in decimal system.

There are many significant facts about 9 in various fields.

Let us not delve into all those aspects.

Back to main topic:

Take a simple 2-digit number: 12

12x9= 108, this is simple math as you may have known this answer without even calculating it due to day-today usage.

How is it calculated in a traditional way:

12

x 9 .............................Step 1: you proceed from right to left. 9x2=18.

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8 ..............................carry over 1

..............................Step 2: 9x1=9 carry over 1 is added to this...so we get 10

Hence the final answer is 108

12x9=108

Let us look at an alternative way of doing this:

1)12x9

Step1: The 2-digit number is 12. So, do this simple subtraction by subtracting the 2 from 12: 12-2=10

Note: the subtracted digit 2 comes from this: Extract the 1st digit i.e., 1 of 12. Add 1 to it.

Step2: Take the last digit of 12:2. As we know 9x2 yields 18, whose last digit is 8. Consider this 8 as an answer of this step.

Step3: Combine the answers of Step1 and Step2. We get: 108

2) 14x9

Step1: The 2-digit number is 14. So, do this simple subtraction by subtracting the 2 from 14: 14-2=12

Note: the subtracted digit 2 comes from this: Extract the 1st digit i.e, 1 of 14. Add 1 to it.

Step2: Take the last digit of 14: 4. As we know 9x4 yields 36, whose last digit is 6. Consider this 6 as an answer of this step.

Step3: Combine the answers of Step1 and Step2. We get: 126.

3) 67x9

Step1: The 2-digit number is 67. So, do this simple subtraction by subtracting the 7 from 67: 67-7=60

Note: the subtracted digit 7 comes from this: Extract the 1st digit i.e., 6 of 67. Add 1 to it.

Step2: Take the last digit of 67: 7. As we know 9x7 yields 63, whose last digit is 3. Consider this 3 as an answer of this step.

Step3: Combine the answers of Step1 and Step2. We get: 603

4)99x9

Step1: The 2-digit number is 99. So, do this simple subtraction by subtracting the 10 from 99: 99-10=89

Note: the subtracted digit 10 comes from this: Extract the 1st digit i.e., 9 of 99. Add 1 to it.

Step2: Take the last digit of 99: 9. As we know 9x9 yields 81, whose last digit is 1. Consider this 1 as an answer of this step.

Step3: Combine the answers of Step1 and Step2. We get: 891

You can take any 2-digit number(except the ones ending with 0) and try this out. This method may seem cumbersome in the beginning. But as you practise it, you will find it so simple. You may actually find it easier to use this method than the traditional way of multiplying.