CBSE Class 6 Mathematics Whole Numbers Assignment Set 09

Question 1. Rearrange the digits of the number 20057034 to get the smallest and the largest number of 8 digits.
Answer: Given number has 8 digits: 2, 0, 0, 5, 7, 0, 3, 4.
To form an 8-digit number, the first digit (at the ten-thousands / millions place) cannot be 0.
Smallest 8-digit number: Arrange the given digits in ascending order, placing the smallest non-zero digit first = 2,000,3457
Largest 8-digit number: Arrange the given digits in descending order = 7,543,2000
In simple words: To make the smallest number, put the smallest non-zero digit first and then write the remaining digits in increasing order. To make the largest number, write all digits in decreasing order.

Exam Tip: Never start a whole number with zero when asked to form a number of a specific digit count, because a leading zero is not counted.

Question 2. How many whole numbers are there between 7983005 and 7983015. Write them.
Answer: To find the number of whole numbers between two numbers \(a\) and \(b\) (where \(b > a\)), the formula is \(b - a - 1\).
Number of whole numbers = \(7983015 - 7983005 - 1 = 10 - 1 = 9\)
The whole numbers between 7983005 and 7983015 are: 7983006, 7983007, 7983008, 7983009, 7983010, 7983011, 7983012, 7983013, 7983014.
In simple words: Count the whole numbers that lie strictly between the two given numbers, excluding the two endpoints.

Exam Tip: When finding numbers "between" two given numbers, subtract 1 from their difference.

Question 3. Write True (T) or False (F) for the following statements.
(i) Zero is the smallest natural number.
(ii) One is the smallest whole number.
(iii) Ten arabs is the largest whole number.
(iv) Zero is less than every natural number.
(v) The smallest 5-digit number is the successor of the largest 4-digit number.
(vi) Every whole number has its successor.
(vii) 1 Arab = 100 Crores = 1,00,00,00,000 = \(10^9\)
Answer:
(i) False (F) - 1 is the smallest natural number, whereas zero is the smallest whole number.
(ii) False (F) - 0 is the smallest whole number.
(iii) False (F) - There is no largest whole number as numbers are infinite.
(iv) True (T) - Natural numbers start from 1, and 0 is less than all of them.
(v) True (T) - The largest 4-digit number is 9999, and its successor is \(9999 + 1 = 10000\), which is the smallest 5-digit number.
(vi) True (T) - Every whole number has a successor (\(n + 1\)).
(vii) True (T) - 1 Arab equals 100 Crores, which is written as 1,00,00,00,000 or \(10^9\).
In simple words: Check each statement against basic number properties. Natural numbers start from 1, whole numbers start from 0, and there is no end to numbers.

Exam Tip: Remember that natural numbers start at 1 and whole numbers start at 0.

Question 4. Name the property used in whole numbers. If \(a, b\) are two whole numbers then \((a+b)\), \(ab\) are also whole numbers. Prove by taking any example of your choice.
Answer: Name of the property: Closure Property.
Proof / Verification:
Let \(a = 5\) and \(b = 7\) (both are whole numbers).
Addition: \(a + b = 5 + 7 = 12\), which is also a whole number.
Multiplication: \(a \times b = 5 \times 7 = 35\), which is also a whole number.
In simple words: The closure property means when you perform an operation on two whole numbers, the result is always another whole number.

Exam Tip: Closure property holds true for addition and multiplication of whole numbers, but not always for subtraction and division.

Question 5. If \(a, b\) are any two whole numbers. If (i) \(a+b = b+a\) and (ii) \(ab = ba\), what name will you give for this property. Verify also by taking any example of your choice.
Answer: Name of the property: Commutative Property.
Verification:
Let \(a = 4\) and \(b = 6\).
(i) Addition: \(a + b = 4 + 6 = 10\) and \(b + a = 6 + 4 = 10\). Thus, \(4 + 6 = 6 + 4\).
(ii) Multiplication: \(a \times b = 4 \times 6 = 24\) and \(b \times a = 6 \times 4 = 24\). Thus, \(4 \times 6 = 6 \times 4\).
In simple words: The commutative property means changing the order of numbers during addition or multiplication does not change the final answer.

Exam Tip: Commutative property applies to addition and multiplication, but does not apply to subtraction and division.

Question 6. State the following property in whole numbers. If \(a, b, c\) are three whole numbers then (i) \(a+(b+c) = (a+b)+c\) (ii) \(a\times(b\times c) = (a\times b)\times c\). Verify by taking any example of your choice.
Answer: State of property: Associative Property.
Verification:
Let \(a = 2\), \(b = 3\), and \(c = 4\).
(i) Associative Property of Addition:
\(a + (b + c) = 2 + (3 + 4) = 2 + 7 = 9\)
\((a + b) + c = (2 + 3) + 4 = 5 + 4 = 9\)
Thus, \(2 + (3 + 4) = (2 + 3) + 4\).
(ii) Associative Property of Multiplication:
\(a \times (b \times c) = 2 \times (3 \times 4) = 2 \times 12 = 24\)
\((a \times b) \times c = (2 \times 3) \times 4 = 6 \times 4 = 24\)
Thus, \(2 \times (3 \times 4) = (2 \times 3) \times 4\).
In simple words: The associative property means when adding or multiplying three numbers, changing the grouping of the numbers does not change the result.

Question 7. Distributive Property in the set of whole numbers states for any three whole numbers \(a, b, c\): \(a \times (b + c) = (a \times b) + (a \times c)\). i.e. If \(a = 5\), \(b = 4\), \(c = 3\) then \(5 \times (4 + 3) = 5 \times 4 + 5 \times 3\). Write two more such examples.
Answer: Example 1:
Let \(a = 2\), \(b = 6\), \(c = 5\).
\(2 \times (6 + 5) = 2 \times 11 = 22\)
\((2 \times 6) + (2 \times 5) = 12 + 10 = 22\)
Thus, \(2 \times (6 + 5) = (2 \times 6) + (2 \times 5)\).

Example 2:
Let \(a = 7\), \(b = 2\), \(c = 8\).
\(7 \times (2 + 8) = 7 \times 10 = 70\)
\((7 \times 2) + (7 \times 8) = 14 + 56 = 70\)
Thus, \(7 \times (2 + 8) = (7 \times 2) + (7 \times 8)\).
In simple words: The distributive property lets you multiply a number by a sum by distributing the multiplier to each addend individually.

Exam Tip: Distributive property links multiplication over addition to make mental calculations much easier.

Question 8. Add 273, 343 and 127. Is the result a whole no.?
Answer: Sum = \(273 + 343 + 127\)
First, combine convenient numbers: \(273 + 127 = 400\)
Then, \(400 + 343 = 743\)
Yes, the result 743 is a whole number.
In simple words: Add the three given numbers together. Since the answer is a counting number starting from zero, it is a whole number.

Exam Tip: Look for pairs of numbers that add up to multiples of 10 or 100 to simplify addition quickly.

Question 9. Add the greatest number of 5 digits to the least number of 5 digits.
Answer: Greatest number of 5 digits = 99999
Least number of 5 digits = 10000
Sum = \(99999 + 10000 = 109999\)
In simple words: Find the biggest 5-digit number (all nines) and the smallest 5-digit number (one followed by zeros) and add them together.

Exam Tip: The greatest \(n\)-digit number is formed by writing \(n\) nines, and the least \(n\)-digit number is 1 followed by \(n-1\) zeros.

Question 10. Find the sum using most convenient combinations:
(i) 414, 486, 550
(ii) 2098, 3002, 3050
Answer:
(i) \(414 + 486 + 550\)
Notice that \(414 + 486 = 900\)
Now add 550: \(900 + 550 = 1450\)

(ii) \(2098 + 3002 + 3050\)
Notice that \(2098 + 3002 = 5100\)
Now add 3050: \(5100 + 3050 = 8150\)
In simple words: Group numbers that add up to clean round numbers (like multiples of 100 or 1000) first to make addition fast and easy.

Exam Tip: Always check the units digits to find which numbers pair up to make 10 or multiples of 10.