SOME TRICKS USING VEDIC MATHEMATICS MAGIC WITH 11

SOME TRICKS USING VEDIC MATHEMATICS

MAGIC WITH 11 Multiplication by 11 is very interesting and fast in itself. in many cases the answer can be given at a glance. Example 1: 25 * 11 Step 1: Write 2 and 5 of 25 as it is. Step 2: Write the sum of 2 and 5 (i. e. 7) in between. 25 * 11 2 7 add Similarly, 71 * 11 = 781 5

Example 2: 42631 * 11 In longer calculations like this, we first write the border numbers, i. e. 4 and 1 as it is and then write the sum of next successive pairs in between as shown below: i. e. 42631 * 11 4 6 8 9 4 1 4 and 1 as it is, as two border numbers. Then, starting from the left side, we keep writing the sum of the two digits: 4+2=6 || 2+6=8 || 6+3=9 || 3+1=4 So the answer is 468941. This system of ‘calculation at a glance’ is more comfortable when the addition of numbers do not require carry over. When it needs carry over, we make use of the formula known as “only the last two”. In such a case, we simplify the calculation by making it as a Dot Sandwich, i. e. one dot on both the sides of the number.

Example 3: 4573 * 11 First we convert it into a dot sandwich like: . 4573. ( where the value of dot is zero ) and then keep adding the last two digits, starting from the right dot as shown below: Step 1: . 4 5 7 3. 3+0=3 3 Step 2: . 4 5 7 3. 1 03 Step 3: . 4 5 7 3. 1 303 Step 4: . 4 5 7 3. 1 7 + 3 = 10 ( 1 is carried to next step ) 0303 Step 5: . 4 5 7 3. 50303 5 + 7 = 12 12 + 1(carry) = 3 ( 1 is carried to next step ) 1 4+5=9 9 + 1(carry) = 0 ( 1 is carried to next step ) 1 0+4=4 4 + 1(carry) = 5 So, the answer is 4573 * 11 = 50303

MULTIPLICATION WITH 9999… In the whole number series, 9 is the most interesting number, and so multiplication by 9 is also very interesting in itself. The formula used for these calculations are: 1. By one less than the one before. 2. All from nine and last from ten. When two numbers are multiplied, any one of them is the multiplicand the other is the multiplier. e. g. 23 * 99, here, we consider 23 as the multiplicand the other number, i. e. 99 as multiplier.

TYPE 1: MULTIPLICAND DIGITS = MULTIPLIER DIGITS The answer comes in two parts; LHS and RHS. 1. For LHS, we apply the formula: by one less than the one before, i. e. subtract one from the multiplicand. 2. For RHS, we write the complement of the multiplicand, by using the formula: “all from nine and last from ten”. Example 1: 389 * 999 LHS = 389 – 1 = 388 RHS = (complement of 389) 1000 – 389 = 611 Answer = LHS / RHS 388 / 611 So, 389 * 999 = 388611

Example 2: 942678 * 999999 LHS = 942678 – 1 = 942677 RHS = (complement of 942678) 1000000 – 942678 = 057322 Answer = LHS / RHS 942677 / 057322 So, 942678 * 999999 = 942677057322.

TYPE 2: MULTIPLICAND DIGITS < MULTIPLIER DIGITS 1. The same formula will be applied as in type 1, but with a little modification. 2. Make the number of digits in the multiplicand equal to the number of 9’s by adding required 0’s, before the multiplicand. Example 1: 67 * 999 Since, the multiplier here has three 9’s, so convert the multiplicand 67 also into a 3 digit number, by adding a 0 in front of it. So it becomes: 067 * 999 LHS = 067 – 1 = 066 RHS = (complement of 067) 1000 – 067 = 933 Answer = LHS / RHS 066 / 933 So, 67 * 999 = 66933.

Example 2: 243 * 9999 Since, the multiplier here has four 9’s, so convert the multiplicand 243 also into a 4 digit number, by adding a 0 in front of it. So it becomes: 0243 * 9999 LHS = 0243 – 1 = 0242 RHS = (complement of 0243) 10000 – 0243 = 9757 Answer = LHS / RHS 0242 / 9757 So, 243 * 9999 = 2429757

TYPE 3: MULTIPLICAND DIGITS > MULTIPLIER DIGITS Example 1: 378 * 99 In this case we do multiplication in three steps: STEP 1: Divide the multiplicand into two parts, such that the number of digits on RHS of the multiplicand is equal to the number of 9’s in the multiplicand. i. e. 3 / 78 * 99 STEP 2: Add 1 to the LHS of the multiplicand subtract the number obtained from whole of the multiplicand to get the LHS of the answer. i. e. 3 + 1 = 4; subtract 4 from 378 to get 374 STEP 3: For RHS part answer, write the complement of RHS of the multiplicand. i. e. (complement of 78) 100 – 78 = 22 So, the answer is 378 * 99 = 374 / 22 = 37422

Example 2: 4276 * 999 Step 1: Divide multiplicand 4276 in 2 parts, as shown: 4 / 276 * 999 3 digits three 9’s Step 1: Add 1 to the LHS of the multiplicand subtract the number obtained from whole of the multiplicand to get the LHS of the answer. i. e. 4267 – 1 = 4271 Step 3: For RHS part answer, write the complement of RHS of the multiplicand. i. e. 1000 – 276 = 724 So, the answer is 4276 * 999 = 4271 / 724 = 4271724