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- 1. Multiplication Shortcuts

2. Multiplication of 2 digit with 2 digit 67 56 Step 1: 7 6 = 42 Step 2: (66) + (57) = 71 +4(carry) = 75 Step 3: 6 5 = 30 + 7(carry) = 37 3. Multiplication of 3 digit with 3 digit 789 123 Step 1: 3 9 = 27 Step 2: (83) + (92) = 42 + 2(Carry) = 44 Step 3: (7 3) + (1 9) + (8 2) = 46 + 4(Carry) = 50 Step 4: (7 2) + (8 1) = 22 + 5(Carry) = 27 Step 5: 7 1 = 7 + 2(Carry) =9 4. Divisibility by 7 5. Find % ending in 0 or 5 6. To find the % of any Number 7. Convert Fractions into % 8. Multiply the Big Numbers 9. How to divide any number by 9 ? Before we proceed to understand this shortcut, we need to remember the reciprocals of 9. Number Fraction Reciprocal 1 1/9 0.1111 2 2/9 0.2222 3 3/9 0.3333 4 4/9 0.4444 5 5/9 0.5555 6 6/9 0.6666 7 7/9 0.7777 8 8/9 0.8888 9 9/9 1 Dividend is a 2-digit number Find 13 / 9 Step 1 : Here 13 is the dividend and 9 is the divisor. In this example, divisor has 1 digit. So, set 1 digit from right as reminder. Step 2 : The quotient is the sum of the digits on left. In our case, it is 1. So, the quotient is 1. Step 3 : The reminder is the sum of all the digits. So, the reminder is 1+3 = 4. So, the quotient is 1 and reminder is 4. From the above table, 4/9 = 0.4444. So 13/9 = 1.4444 10. How to divide any number by 9 ? Find 36 / 9 Step 1 : Here 36 is the dividend and 9 is the divisor. In this example, divisor has 1 digit. So, set 1 digit from right as reminder. Step 2 : The quotient is the sum of the digits on left. In our case, it is 3. So, the quotient is 3. Step 3 : The reminder is the sum of all the digits. So, the reminder is 3+6 = 9. If the remainder is equal or more than 9(divisor), it is carry forward to the quotient just like in multiplication. So, the quotient is 3+1 =4 and reminder is 9-9 = 0. 3 6 3 9 4 0 11. How to divide any number by 9 ? Can you solve the following : 89 / 9 97 / 9 91 / 9 96 / 9 8 9 8 17 1 089 12. How to divide any number by 9 ? Dividend is a 3-digit number or more When the dividend is a 3-digit number or more, there is a slight variation in the division steps. Find 425 / 9 Step 1 : Here 425 is the dividend and 9 is the divisor. In this example, divisor has 1 digit. So, set 1 digit from right as reminder. Step 2 : The quotient is the successive sum of the digits on left i.e., 4/4+2 = 46 Step 3 : The reminder is the sum of all the digits i.e., 4+2+5 = 11. Notice, that the reminder is greater than 9. If the remainder is equal or more than 9(divisor), it is carry forward to the quotient just like in multiplication. So, the quotient is 46+1 =47 and reminder is 11-9 = 2. So, 421 /9 = 47.222 13. Can you solve the following : 12389 / 9 933347 / 9 1931 / 9 3631 / 9 How to divide any number by 9 ? 14. How to divide a number by 99 ? Before we proceed to understand this shortcut, we need to remember the reciprocals of 99. Number Fraction Reciprocal 1 1/99 0.010101 2 2/99 0.020202 9 9/99 0.090909 10 10/99 0.101010 13 13/99 0.131313 56 56/99 0.565656 78 78/99 0.787878 89 89/99 0.898989 15. How to divide a number by 99 ? Dividend is a 3-digit number Find 732 / 99. Step 1 : Here 732 is the dividend and 99 is the divisor. In this example, divisor(99) has 2 digit. So, set 2 digit from right as reminder. Group the digits on the left into groups of 2. Step 2 : The quotient is just the digit on the left. In our case, it is 7. So, the quotient is 7. Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 7+32 = 79. So, the quotient is 7 and reminder is 39. From the above table, 39/99 = 0.393939. So 732/99 = 7.393939 16. How to divide a number by 99 ? Find 498 / 99 Solution : Step 1 : Here 498 is the dividend and 99 is the divisor. In this example, divisor has 2 digit. So, set 2 digit from right as reminder. Step 2 : The quotient is just the digit on the left. In our case, it is 4. So, the quotient is 4. Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 4+98 = 102. If the remainder is equal or more than 99(divisor), the difference is carry forward to the quotient just like in multiplication. So, the quotient is 4+1 =5 and reminder is 102-99 = 3. From the above table, 3/99 = 0.030303. So 498/99 = 5.030303. 17. How to divide a number by 99 ? Dividend is a 4-digit number Find 5342 / 9 Solution : Step 1 : Here 5398 is the dividend and 99 is the divisor. In this example, divisor has 2 digit. So, set 2 digit from right as reminder. Step 2 : The quotient is just the digit on the left. In our case, it is 53. So, the quotient is 53. Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 53+98 = 151. Since 151 is greater than 99(divisor), the difference is carry forward to the quotient just like in multiplication. So, the quotient is 53+1 =54 and reminder is 151-99 = 52. From the above table, 52/99 = 0.525252 So 5392/99 = 54.5252 18. How to divide a number by 99 ? Can you solve the following : 898 / 99 2947 / 99 9451 / 99 9634 / 99 19. How to divide a number by 99 ? Dividend is a 5-DIGIT OR MORE Example 4 : Find 777745 / 99 Solution : Step 1 : Since we are dividing the number by 99(2 digit), set 2 digit from right as the remainder. In our case it is 45. Step 2 : The quotient is the successive sum taking 2- digits at a time. So, the quotient was obtained by taking the successive sum taking 1-digit on the right at a time. So, the quotient after the carry-forward is 7854. Step 3 : The reminder is the sum of all the digits taking 2-digits at a time. i.e., 77 +77 + 45 = 199 Notice, that the reminder is greater than 99. If the remainder is equal or more than 99(divisor), the carry forward to the quotient is just like in multiplication. So, the quotient is 7854+2 =7856 and reminder is 199-99(2) = 1. So, 777745 / 99 = 7856.0101 20. Find 3214675 / 99 Reminder = 115 So, the quotient is 32470+1 =32471 and reminder is 115-99 = 16. So, 3214675 / 99 = 32471.161616 How to divide a number by 99 ? 21. Can you solve the following : 4564564 / 99 679543 / 99 345346 / 99 45643 / 99 How to divide a number by 99 ? 22. Squaring a number ending in 5 352 =? The successor of 3 is 4 Multiply 3 and 4 Put the answer 12. Suffix 25. The answer is 1225. 23. Squaring the number beginning in 5 562 = ? Always Add 25 with the number in units digit 25+6 = Suffix the square of the unit digit = 31 36 24. Numbers ending in 6 662 =_________. a) Write down 6. b) 2 x (6 + 1) + 1 = 15. Write 5, carry *1. c) 6 x (6 + 1) = 42 + *1 = 43. Write 43. d) The answer is 4356. 862 =_________. a) Write down 6. b) 2 x (8 + 1) + 1 = 19. Write 9, carry *1. c) 8 x (8 + 1) = 72 + *1 = 73. Write 73. d) The answer is 7396. 25. How to divide the number when the divisor ends in digit 9? 87129 =? The first step is to round the denominator to the next digit. Long Division Method Shortcut Technique 26. Divide the following : 47/89 12/69 132/179 123/189 27. Divide 95159. Reduce 95159 as follows : Now divide 9.5 by 16 like normal division, instead of putting a zero in each step, you replace it with the last quotient to continue the division. 28. Divide 436159. Reduce 436159 as follows : Now, there is a small difference compared to the previous 2 examples. In the previous 2 examples, the numerator was less than the denominator. However, in this case, we have the numerator which is greater than the denominator. In this division, we need to add the quotient with the rest of the digit (6) and put this digit next to the reminder. 29. Divide 3462179. Notice that numerator is greater than the denominator. There is a slight variation compared to the previous example Notice the carry-forward in step 2 of the division. So, therefore, 30. Divide the following : 4347/149 1222/239 1349/179 2323/249 31. Multiplication by 12 Lets understand this method by taking an example. 345 12 Step 1: Write 345 as 0345. Step 2: Multiply each and every digit with 2 and add it to its right neighbour. This process is started from right. Multiply 5 with 2 and add it to its right neighbour. 5 has no right neighbour so add the multiplication to 0. This gives 10 as a result. So 0 is written down and 1 is carried forward. 32. Step 3: Multiply 4 with 2 and add it to 5. Carry 1 is added to the result. This gives 14 as a result. 4 is written down and 1 is carry forwarded. 33. Step 4: Multiply 3 with 2 and add it to 4. Carry 1 is added to the result. This gives 11 as a result. 1 is written down and 1 is carry forwarded. 34. Step 5: Multiply 0 with 2 and add it to 3. Carry 1 is added to the result. This gives 4 as a result. 35. MULTIPLICATION BY SIX Practice what is half of ? To each number add half of the neighbour; plus 5 if it is odd 6 5 4 8 7 2 3 2 2 4 3 1 0 6 2 2 0 8 4 x 6 4052373 1 0 4 4 3 0 5 2 x 6 2138562 1

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