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Published on March 31st, 2013 In category Division and Multiplication tricks | Maths

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# Shortcut to multiply by 111, 101 and 1001

this article we will learn to multiply any numbers ( even with digits as large as , 7, 8 , or 12)

Trick to Multiply by 111

Suppose we have a number 748634 to be multiplied by 111. The rule is as follows

1. The first digit of the number will be same i.e. 7
2. The second digit will be 7 + 4 = 11 Since it is a 2 digit number 1 will carried to preceding number 1. So first digit will be 8 and second digit will 1 upto this stage
3. The third digit will be 7 + 8 + 4 = 19 , keep 9 and take 1 to preceding digit so we have first 3 digits as 829
4. The fourth digit will be (pl note this step) 4 + 8 + 6 (2nd + 3rd + 4rth) = 18, so now the first 4 digit will be 8308 as the 1 is carried forward and added to the 9 that become 1o and again 1 is carried forward
5. The fifth digit will be 8 + 6 + 3 = 17 , 1 will be carried over and 5 digit will 83097
6. The sixth digit will be 6 + 3 + 4 = 13, 1 will be carried forward and sixth digit will become 830983
7. The seventh digit will be 3 + 4 = 7
8. The eigth digit will be 4 itself so the answer will 83098374 You can check this will calulator itself, the solution looks tricky but it is quite simple

Summary of Trick: Keep the first digit and last digit same, keep adding the numbers in group of 3 except the ten digit number. Don’t forget to carry forward the numbers and add to the preceding numbers when it is more than 9 thats all. It will need a little bit of practice

Trick to Multiply by 101

Suppose we have same number 748634 to be multiplied by 101. The rule is as follows

1. The first 2 digits in the answer is same 74
2. The last 2 digit in the answer is same 34
3. For the 3rd digit onward add the numbers to alternate numbers 7-4-8-6-3-4 , so add 7 + 8 = 15, 4 + 6 = 10, 8 + 3 = 11, 6 + 4 = 10
4. For the third digit 7 +8 = 15, keep 5 and carry forward 1 so first 2 digit becomes 75 and 3 digits are 755
5. For fourth digit use 4 +6= 10, keep 0 and carry forward 1 so 4 digit now becomes 7560
6. For fifth digit take 8 +3 = 11, keep 1 and carry forward 1 then answer becomes 75611
7. For sixth digit take 6 +4 =10 and carry forward 1 then answers becomes 756120