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

Q1: Finding the division of 3 or more digit number when the divisor is 9.
(i) 102 ÷ 9

Ans: 
STEP 1:
Splits the digit 102 into 2 parts as a divisor has only one digit as 2 goes in remainder part and rest all digits will goes in Quotient part i.e.
Q       R
1 0 ǀ  2
STEP 2:
To find the 1st digit of a quotient put 1 as it is i.e.
Q       R
1 0 ǀ  2
↓
1
STEP 3:
(i) To find the 2nd digit of a quotient, add quotient and dividend digit i.e.
(1 + 0 = 1)
(ii) To find the remainder, add remainder and quotient i.e.(2 + 1 = 3) i.e.
Q        R
1 0 ǀ  2
↓
1 1 ǀ  3
Ans: 
Quotient = 11
Remainder =   3

(ii) 1232 ÷ 9 

Ans: 
STEP 1:
Split the digit 1232 into 2 parts as a divisor has only one digit as 2 goes in remainder part and rest all digits will goes in Quotient part i.e.
Q          R
123 ǀ 2
STEP 2:
Q           R
123 ǀ  2
↓
1
STEP 3:
(i) To find the 2nd digit of a quotient add quotient and the divident i.e.(1 + 2 = 3) ,
(ii) To  find the  3rd digit of a quotient add 2nd digit of quotient with the divident digit i.e. (3 + 3 = 6)
(iii) To find the remainder add 3rd digit of quotient with  remainder i.e. (6 + 2 = 8) i.e.
Q            R
1 2 3  ǀ     2
↓
1 3  6  ǀ    8    
Ans: 
Quotient = 136
Remainder = 8

Q2: Division method when divisor is closer and smaller than power of 10.
(i) 234 ÷ 87

Ans: Lets us consider the value
234 ÷ 87
STEP 1:
Splits the digit 234 into 2 parts as a divisor has two  digit as 34 goes in  remainder part and rest all digits will goes in Quotient part i.e.
Q          R
2 ǀ 34
STEP 2:
Apply Nikhilam formula on 87 and we will get the compliment 13 (i.e. 9 - 8 = 1, 10 - 7 = 3)
                  Q           R
                     2 ǀ  34
13               ↓
                     2
STEP 3:
(i) Multiply 2 with individual digit of 13  i.e.
                   Q      R
                   2   ǀ  3 4
13               ↓   ǀ  2 6
                    2  ǀ  6 0          
Ans: 
Quotient = 2
Remainder = 60

(ii) 113401 ÷ 997

Ans: Lets us consider the value
113401÷997
STEP 1:
Splits the digit 113401 into 2 parts as a divisor has three digit so remainder will also have 3 digit, as 401 goes in remainder part and rest all digits will goes in Quotient part i.e.
Q          R
113 ǀ 401
STEP 2:
Apply Nikhilam formula on 997 and we will get the compliment 003
(i.e. 9 - 9 = 0, 9 - 9 = 0, 10 - 7 = 3)
                     Q           R
                    113 ǀ  401
003          ↓
                   1
STEP 3:
(i) Multiply 1 with individual digit of 003  i.e.
                         Q      R
                  1 1 3  ǀ  401
 003         ↓ 0 0 ǀ  3
                       1 1     ǀ
(ii) Multiply 2nd quotient with individual digit of 003, and add the third column, to get 3rd quotient
                         Q      R
                    1 1 3  ǀ  401
003         ↓ 0 0  ǀ   3
                      0  ǀ  0 3
                     1 1 3  ǀ
(iii) Multiply 3rd quotient with individual digit of 003, and add the 4th, 5th and 6th column, to get the  remainder.
(Note: Have to repeat the function till we get the number in last column)
                             Q      R
                       1 1 3  ǀ  4  0   1
003         ↓ 0 0  ǀ  3
                           0  ǀ  0  3
                                ǀ  0  0    9
                    1 1 3 ǀ   7  3  (10)  (1 is carried forward)
                     1 1 3 ǀ   7  4   0
Ans: 
Quotient = 113
Remainder = 740

Q3: Finding cube of 3 digit number using vedic maths.
(i) (153)³

Ans: STEPS:
(i) Split the given digits into two part
15     3
(ii) consider the 1st part i.e. 15 from left to right go on reducing power i.e
15³    15²    15
(iii) Next consider the 2nd part i.e. 3 from right to left go on reducing the power i.e.
15³    15².3   15.3²   3³
(iv) Find the values and write in 2nd Row
15³          15².3         15.3²           3³
3375        675           135             27
(v) Multiply middle terms by 3 i.e.
15³         15².3         15.3²         3³
3375     675           135             27
                   ×3            ×3
3375       2025       405            27
(vi) To get the final answer   we are going to keep unit digit as it is rest other digit are carried forward
15³           15².3         15.3²          3³
3375        675           135             27
                      ×3            ×3
3375       2025          405             27
(206)        (40)             (2)                              (CARRIED FORWARD)
 3581         5                   7                 7
Ans:
(153)³ = 35,815,77

Q4: Fill in the Blanks
(i) In Vedic Mathematics, division is based on the concept of ________.

Ans: proportion and distribution
Explanation: Vedic division involves dividing numbers by breaking them down into parts and distributing them proportionally.

(ii) The main tool used in Vedic division is called the ________.

Ans: nikhilam sutra
Explanation: The nikhilam sutra is a rule or formula used in Vedic Mathematics for division. It helps simplify the division process.

(iii) The process of dividing numbers using Vedic Mathematics is ________ compared to traditional long division.

Ans: faster
Explanation: Vedic division methods often involve mental calculations and can be quicker than the step-by-step approach of long division.

(iv) The Vedic division method is based on ________ and ________ principles.

Ans: proportion and distribution
Explanation: Vedic division uses the principles of proportion and distribution to break down numbers and divide them efficiently.

(v) The Vedic Mathematics approach to division is known for its ________ and ________.

Ans: efficiency and simplicity
Explanation: Vedic division methods provide shortcuts and techniques that simplify the division process, making it more efficient and easier to understand.

Q5: True or False
(i) The Vedic division method can only be applied to two-digit numbers.

Ans: False
Explanation: The Vedic division method is not limited to two-digit numbers and can be used for longer or shorter numbers as well.

(ii) The Vedic division method involves complex calculations and is not suitable for quick mental calculations.

Ans: False
Explanation: Vedic division methods often involve mental calculations and can be quicker than traditional long division.

(iii) The Vedic division method provides a more intuitive and visual approach to division.

Ans: True
Explanation: Vedic division methods often involve visual representations and patterns, making them easier to understand and visualize.

(iv) The Vedic division method can be used to find the remainder of a division problem.

Ans: True
Explanation: The Vedic division method allows for the calculation of both the quotient and the remainder in a division problem.

(v) The Vedic division method is an ancient technique that has no practical applications in modern mathematics.

Ans: False
Explanation: The Vedic division method is still relevant and useful in modern mathematics, particularly for mental calculations and quick estimations.