Worksheet Solutions: Multiplication | Improve Your Calculations: Vedic Maths (English) - Class 6 PDF Download

Revision of Basic Concepts

This practice worksheet deals with the methods derived from Vedic Maths sutras that help in multiplying numbers whose sum of unit place is equal to 10. 

What is the Multiplication (Sum of 10) method?

This multiplication method is only applicable if it fulfils below 2 preconditions. First, the sum of unit place digits of 2 numbers should be 10, and remaining digits from numbers should be the same.  This method is derived from the ancient mathematical methods by vedas. This method is considered to be one of the easiest methods in multiplication. 

How to use the method?

For example, if you want to perform 36 x 34. You can see that this multiplication fulfils both preconditions. So we can apply the method for these numbers. For a solution, one has to follow the given steps. First multiply unit digits from both the numbers and write the multiplication in the answer. Now, the remaining digit is 3.  Next digit in the number series after 3 is 4. And multiply this 3 with 4. Final answer will be 1224.  This method is also applicable to more than 2 digits.

Q1: Solve the following questions using the Multiplication (Sum of 10) method.
(i) 18 x 12 = 216
(ii) 25 x 25 = 1025
(iii) 47 x 63 = 2961
(iv) 45 x 55 = 2475
(v) 99 x 11 = 1089
(vi) 23 x 77 = 1771
(vii) 145 x 165 = 23,925
(viii) 143 x 147 = 21,021
(ix) 194 x 196 = 38,024
(x) 207 x 903 = 1,86,921

Multiplication by Nikhilam Sutra

The Vedic sutra – “Nikhilam Navatascaraman Dasatah” means “all from nine and the last from ten ”
Let us take an example of 1-digit number 7 × 9, both the numbers are close to 10. 7 is 3 less than 10 and 9 1 less than 10.

• 7 | – 3, 7 is 3 less than 10
• 9 | –1, 9 is 1 less than 10
• Take either 7 – 1 = 6 or 9 – 3= 6, this will make the first part of the product
• Multiply (-3) by (-1), –3 × ( –1) = 3

∴ 7 × 9 = 63

Any number can be multiplied by this sutra with few modifications, let us take another example 13 × 7

• 13 | + 3, 13 is 3 more than 10
• 7 | – 3, 7 is 3 less than 10
• Take either 13 – 3 = 10 or 7 + 3 = 10 as the first half of the product
• Now 3 × ( –3) = –9, since the other half is negative number
  • Multiply the half of the product by 10, 10 × 10 = 100
  • Subtract 9 from it, 100 – 9 = 91

∴ 13 × 7 = 91

If numbers are bigger and closer to 100, for example 98 × 91

• 98 | –02, 98 is two less than 100
• 91 | –09, 91 is 9 less than 100
• Take 98 – 09 = 89 or 91 – 02 = 89, as the first half of the number
• (–02) × (–09) = 18. This is the other half of the number

∴ 98 × 91 = 8918.

Q2: Solve the following using Nikhilam sutra:
(i) 12 × 13

Ans: 12 × 13
12 | +2
13 | +3
Taking 12 + 3 = 15
3 × 2 = 6
∴ 12 × 13 = 156.

(ii) 9 × 8

Ans: 9 × 8
9 | –1
8 | –2
Taking 9 – 2 = 7
–1 × –2 = 2
∴ 9 × 8 = 72.

(iii) 16 × 11

Ans: 16 × 11
16 | +6
11 | +1
Taking 16 + 1 = 17
6 × 1 = 6
∴ 16 × 11 = 176

Q3: Solve the following using Nikhilam sutra:
(i) 97 × 89

Ans: 97 × 89
97 | –03
89 | –11
Taking 89 – 03 = 86
–03 × –11 = 33
∴ 97 × 89 = 8633

(ii) 91 × 92

Ans: 91 × 92
91 | –09
92 | –08
Taking 91 – 08 = 83
–9 × –8 = 72
∴ 91 × 92 = 8372

(iii) 99 × 101

Ans: 99 × 101
99 | –01
101 | +01
101 – 01 = 100
–1 × 1 = –1
100 × 100 = 10000
10000 – 1 = 9999
∴ 99 × 101 = 9999.