SHORT TRICKS ON MULTIPLICATION.

✓MULTIPLYING WITH 15. Rule: Add one-half the first digit to itself to obtain the first answer digit (or digits). Continue this process until the units digit is reached. Add an extra 5 if the digit to the left of the given digit is odd. If any of the sums is more than 9, record the units digit and add the tens digit to the preceding answer digit. Ignore any fractions that may occur. If the units digit of the given number is even, the units digit of the answer is 0. If the units digit of the given number is odd, the units digit of the answer will be 5. For instance, multiply 738 by 15. Add 7 to one-half itself, ignoring the fraction. 7 + 1/2(7)  =10 These are the first two answer digits. Next, add 3 to one half itself. 3 + 1/2(3) = 4 The number to its left is 7, which is odd. Therefore add 5. 4+5=9 This is the third answer digit. 10 9 The next digit is 8, and there is an odd digit to its left. 8 + 1/2(8) + 5 = 17 Record the 7 and add the 1 to the preceding 9, which becomes 10. Record 0 and add 1 to the answer digit preceding it. 0 +1 = 1. The answer digits are now 1107 The units digit of given number is even; therefore, the units digit of the answer is 0. 11,070     Answer. ✓MULTIPLYING BY 25. RULE: Move the decimal point of given number two places to the right and divide by 4. What is being done here is to substitution multiplication of two digit number which division by a single digit 4. Multiply 649372 by 25. First, move the decimal point two places to the right. 649,372.00 becomes 64,937,200. Next divide the result by 4. 64,937,200 ÷ 4 = 16,234,300   Answer ✓MULTIPLYING BY 52. RULE: Move the decimal point of the given number two places to the right and divide by 2.  Add twice the original number to the result. Suppose we wanted to find the yearly salary of someone earning rupees 117 per week. Since there are 52 weeks in a year, the problem becomes      117 × 52 Move the decimal point of the given number two places to the right.             117.00 becomes  11,700 Divide by 2. 11,700 ÷ 2 =5,850. To this add twice the original number.       2 × 117 = 234;        5,850 + 234 = 6,084 Thus the yearly salary of someone earning rupees 117 a week is rupees 6084. ✓MULTIPLYING A TWO DIGIT NUMBER BY 95. RULE: Subtract 5 from the given number and affix two zeros to the result. This will be called the partial product. Next subtract the given number from 100 and multiply the result by 5 add this product to the partial product to obtain the final answer. This can be best demonstrated by trying the example: 95 × 73.   First subtract 5 from the given number and affix two zeros to the result.        6,800 Next subtract the given number from 100. 100 - 73 = 27 Multiply by 5. 27 × 5 = 135 Finally add this product to the previously determined partial product. 6,800 + 135 = 6,935   Answer. ✓MULTIPLYING BY 125. RULE: move the decimal point of the given number three places to the right and divided by 8.

Dividing by it may not seems to be much of a shortcut at first but a simple application of the method will prove its worth. Multiply 1,483 by 125. The usual multiplication process would require table multiplication steps  plus Many  steps in addition. The shortcut method using one step in division. First, move the decimal point of the given number three places to the right. 1,483.000 becomes 1,483,000. Next, divide by 8. Division by 8 can be simplified by dividing the given number by 2, then dividing the quotient by 2, and finally dividing  the second quotient by 2, This third quotient is the final answer Thus 1,483,000 ÷ 2 = 741,500. 741,500 ÷ 2 = 370,750. 370,750 ÷ 2 = 185,375. Hence 1,483,000 ÷ 8 = 185,375 Answer ✓MULTIPLYING TWO TWO-DIGIT NUMBERS WHEN BOTH END IN 5 AND ONE TENS DIGIT IS ODD WHILE THE OTHER IS EVEN. RULE: to the product of the tens digit add one half there some ( ignoring the fraction 1/2 ). Affix 75 to the result. This rule will be tried with the numbers 75 and 45. The product of the tens digit is 7 × 4 = 28 One-half the sum of tens digits (neglecting 1/2 ) is 1/2(7+4)= 5 The sum of these two numbers is 33. Affix 75 to the result. Thus 75×45=3,375. A word of caution about "affixing a number."this merely means the number is attached or tagged on at the beginning or end of a group of numbers; it does not mean the number is to be added to the another number. ✓MULTIPLYING TWO 2 DIGIT NUMBERS WHOSE TENS DIGITS ARE BOTH 5 AND WHOSE UNITS ARE BOTH ODDS OR BOTH EVEN. RULE: ADD ONE HALF THE SUM OF THE UNITS DIGIT TO 25. AFFFIX THE PRODUCT OF THE UNITS DIGITS TO THE RESULT. IF THE PRODUCT IS LESS THAN 10 PROCEED IT WITH A ZERO. If we are asked to multiply 52 by 58 we see that the units digits are both even and therefore this rule can be used. The sum of the units digits is 10 and one-half this is 5.          25+5=30 Multiply the units digits.        2×8=16. Affix this to the 30 obtained above.        3,016  Answer. ✓MULTIPLYING TWO TWO-DIGITS NUMBERS WHICH TENS DIGITS ARE BOTH 5 AND THE ONE UNIT DIGIT IS ODD WHILE THE OTHER IS EVEN. Rule: Add one-half the sum of the units digit to 25, ignoring the fraction 1/2. Addd the product of the units digit to 50 and affix the result to the sum obtained in the first step. In this case we need not worry whether the product of the units digits is greater or less than 10 since it is eventually added to 50. Let us find the product of 54 and 59. One units digits is odd, while the other one is even. One-half the sum of the units digit is 6-1/2. Ignoring the fraction and adding this to 25. We obtain,               25+6=31 The product of the units digit is 36. This is added to 50 and the sum affixed to 31.            50+36=86.            3,186  Answer ✓MULTIPLYING TWO TWO DIGIT NUMBERS WHOSE TENS DIGITS ARE BOTH 5 AND THE WHOSE UNITS DIGIT ADDED TO 10 Rule: affix the product of the units digit to 30. If the product is less than 10 precede it with a zero. Multiply 53 by 57. The units digits, 3 and 7, total 10 so that this rule can be used. The first two digits of the answer are 30. The product of the units digit is            3×7=21 Affix this to 30. Thus 3,021 is Answer