CBSE Class 6 Mathematics Whole Numbers Assignment Set 06

Question 1. Divide 45679 by 11 and verify the result by division algorithm which states that Dividend = Quotient x Divisor + Remainder.
Answer: On dividing 45679 by 11:
\( 45679 \div 11 \)
We get:
Quotient = 4152
Remainder = 7

Verification using the division algorithm:
Dividend = Quotient \( \times \) Divisor + Remainder
Right-hand side = \( 4152 \times 11 + 7 \)
= \( 45672 + 7 \)
= \( 45679 \)
= Left-hand side (Dividend)
Hence, the division algorithm is verified.
In simple words: Divide 45679 by 11 to get 4152 with 7 left over. Multiplying 4152 by 11 and adding 7 gives back 45679.
Exam Tip: Always write down both the division steps and the formula check clearly to get full credit.

Question 2. Divide and check the algorithm theorem
(i) 48329 by 19
(ii) 461256 by 925
Answer:
(i) Dividing 48329 by 19:
Quotient = 2543
Remainder = 12
Verification:
Dividend = Quotient \( \times \) Divisor + Remainder
= \( 2543 \times 19 + 12 \)
= \( 48317 + 12 \)
= \( 48329 \) (Equal to Dividend)

(ii) Dividing 461256 by 925:
Quotient = 498
Remainder = 606
Verification:
Dividend = Quotient \( \times \) Divisor + Remainder
= \( 498 \times 925 + 606 \)
= \( 460650 + 606 \)
= \( 461256 \) (Equal to Dividend)
In simple words: Divide to find the quotient and remainder. Then multiply the quotient by the divisor and add the remainder to confirm the start number.

Exam Tip: Check that the remainder is always strictly smaller than the divisor before starting your verification step.

Question 3. Find the value of the following
(i) 5245 - 300 x (900 ÷ 75)
(ii) 325 + (975 ÷ 975)
Answer:
(i) \( 5245 - 300 \times (900 \div 75) \)
First, calculate the value inside the brackets:
\( 900 \div 75 = 12 \)
Now, perform multiplication:
\( 300 \times 12 = 3600 \)
Next, subtract:
\( 5245 - 3600 = 1645 \)

(ii) \( 325 + (975 \div 975) \)
First, solve the bracket:
\( 975 \div 975 = 1 \)
Now add:
\( 325 + 1 = 326 \)
In simple words: Always work out the part inside brackets first. After that, do multiplication or division before adding or subtracting.

Exam Tip: Follow the order of operations (BODMAS) step by step rather than combining multiple steps at once.

Question 4. Find the number which when divided by 45 gives the quotient 15 and the remainder 50
Answer: Given:
Divisor = 45
Quotient = 15
Remainder = 50

Using the division formula:
Dividend = Divisor \( \times \) Quotient + Remainder
= \( 45 \times 15 + 50 \)
= \( 675 + 50 \)
= \( 725 \)
Hence, the required number is 725.
In simple words: Multiply 45 by 15 and add 50 to get the missing number.

Exam Tip: State the division algorithm formula clearly before substituting the given values.

Question 5. The cost of 24 T.V. sets is Rs 37440 Find the cost of 5 T.V. sets.
Answer: Cost of 24 TV sets = Rs. 37440
Cost of 1 TV set = \( 37440 \div 24 = \text{Rs. } 1560 \)
Cost of 5 TV sets = \( 1560 \times 5 = \text{Rs. } 7800 \)
Therefore, the cost of 5 TV sets is Rs. 7800.
In simple words: Find the price of one TV set by dividing. Then multiply that price by 5.

Exam Tip: Always show the cost of a single unit first when using the unitary method.

Question 6. Find the least number of 5 digits which is exactly divisible by 65
Answer: The smallest 5-digit number is 10000.
Dividing 10000 by 65:
\( 10000 = 65 \times 153 + 55 \)
Here, Quotient = 153 and Remainder = 55.
To make 10000 completely divisible by 65, the number to be added is:
\( 65 - 55 = 10 \)
Required number = \( 10000 + 10 = 10010 \).
In simple words: Divide 10000 by 65 to see what is left over. Then add the missing part so it divides evenly.

Exam Tip: For the least number of given digits, add (Divisor - Remainder) to avoid dropping down to a 4-digit number.

Question 7. Find the largest 4 digit number which is divisible by 15.
Answer: The greatest 4-digit number is 9999.
Dividing 9999 by 15:
\( 9999 = 15 \times 666 + 9 \)
Here, the remainder is 9.
Subtracting this remainder from 9999 gives a number perfectly divisible by 15:
Required number = \( 9999 - 9 = 9990 \).
In simple words: Divide 9999 by 15 and remove the extra remainder to find the biggest 4-digit multiple.

Exam Tip: For the largest number of given digits, subtract the remainder from the greatest number.

Question 8. On dividing 59761 by a number, the quotient is 189 and the remainder is 37. Find the divisor.
Answer: Given:
Dividend = 59761
Quotient = 189
Remainder = 37

According to the division algorithm:
Dividend = Divisor \( \times \) Quotient + Remainder
\( 59761 = \text{Divisor} \times 189 + 37 \)
\( \text{Divisor} \times 189 = 59761 - 37 \)

\( \implies \text{Divisor} \times 189 = 59724 \)

\( \implies \text{Divisor} = 59724 \div 189 = 316 \)
Thus, the divisor is 316.
In simple words: Subtract 37 from 59761 first. Then divide that result by 189 to find the divisor.

Exam Tip: Remember to subtract the remainder from the dividend before doing the division step.

Question 9. What least number must be added to 1200 to get a number exactly divisible by 23
Answer: Dividing 1200 by 23:
\( 1200 = 23 \times 52 + 4 \)
Here, the remainder is 4.
The least number that must be added is:
Divisor - Remainder = \( 23 - 4 = 19 \).
(Check: \( 1200 + 19 = 1219 \), and \( 1219 \div 23 = 53 \)).
In simple words: Divide 1200 by 23 to get the remainder 4. Subtract 4 from 23 to find what needs to be added.

Exam Tip: When a problem asks what must be added, find (Divisor - Remainder), not just the remainder.

Question 10. What least number must be subtracted from 13256 to get a number exactly divisible by 67.
Answer: Dividing 13256 by 67:
\( 13256 = 67 \times 197 + 57 \)
The remainder obtained is 57.
Therefore, the least number that must be subtracted from 13256 is 57.
(Check: \( 13256 - 57 = 13199 \), which is \( 67 \times 197 \)).
In simple words: Divide 13256 by 67. The leftover remainder 57 is the number you need to take away.

Exam Tip: When a question asks what must be subtracted, the answer is directly equal to the remainder.

Question 11. 19625 trees have been equally planted in 157 rows. Find the number of trees in each row.
Answer: Total number of trees = 19625
Total number of rows = 157
Number of trees planted in each row = \( 19625 \div 157 = 125 \).
Hence, there are 125 trees in each row.
In simple words: Divide the total trees by the number of rows to get the count in one row.

Exam Tip: Always state what the calculated number represents by including units such as "trees".

Question 12. The product of two numbers is 167910. If one of the two numbers is 965, find the other.
Answer: Product of the two numbers = 167910
One number = 965
Other number = Product \( \div \) Given number
= \( 167910 \div 965 \)
= \( 174 \)
Therefore, the other number is 174.
In simple words: Divide the total product by the known number to find the second number.

Exam Tip: Write down the relationship: Product = First number \( \times \) Second number before dividing.