Some tips for multiplication with 9, 11, 12, 13 with 9: - placed 0 in right side of the number, then subtract the actual number with this. for example - 2345 * 9 = ? step 1 - place 0 at right - 23450 step 2 - Subtract actual number - 2345 ----------- 21105 with - 11: - ex: - 4987 * 11 = ? step 1 - place 0 at left of the digit. like 04987 in our case. step 2- multiply the right most digits of both number i.e. (7* 1) if carry comes then carry over it for the next term . 04987 11 -------- 54857 step 3- now add the ten digit number with unit digit number (8+7=15) write 5 and carry over 1. step 4 - now add hundred digit number with ten digit number (9+8=17 +1 (carry over from previous step)= 1 similarly proceed up to left most digit so we get 54857 with 12 : - it is similar to the method used for 11. only difference is in this we have to multiply with 2 then add with the previous digit . for example :- 4987 * 12 = ? 04987 step 1 - placed 0 in left most. 12 ---------------- 59844 step2 - 7*2 = 14 , write 4 and carry over 1 step3 - 8*2+ 7=23 + 1 = 24 , write 4 and carry over 2. step 4- 9*2 +8 = 26, + 2=28. write 8 , 2 carry over. step5 - 4*2+9=17+2=19, write 9 and carry on 1 step6 - 0*2 + 4 =4+1=5 with 13 - it is similar to 12 but instead of multiplying with 2 here we have to pultiply it with 3. |

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