RBSE Solutions Class 6 Maths Chapter 3 Whole Numbers Important Questions

Question 1. Predecessor of 500 is
(i) 400
(ii) 499
(iii) 501
(iv) 600
Answer: (ii) 499
In simple words: The predecessor of a number is the number that comes just before it. To find it, you subtract 1 from the original number.

🎯 Exam Tip: The predecessor of any number \( n \) is \( n - 1 \). This concept is fundamental in understanding number sequences.

Question 2. Successor of 812 is
(i) 811
(ii) 800
(iii) 813
(iv) 900
Answer: (iii) 813
In simple words: The successor of a number is the number that comes right after it. To find it, you add 1 to the original number.

🎯 Exam Tip: The successor of any number \( n \) is \( n + 1 \). This helps in understanding the order of numbers.

Question 3. Smallest whole number is
(i) 0
(ii) 1
(iii) 2
(iv) 3
Answer: (i) 0
In simple words: Whole numbers are counting numbers that include zero. They start from 0 and go up (0, 1, 2, 3...). So, zero is the very first and smallest whole number.

🎯 Exam Tip: Remember the difference: whole numbers include 0 (0, 1, 2, ...), while natural numbers start from 1 (1, 2, 3, ...).

Question 4. Number on the left of 9, number line will be
(i) 10
(ii) 9
Answer: (iv)
In simple words: On a number line, numbers get smaller as you move towards the left side. The numbers to the left of 9 would be 8, 7, 6, and so on.

🎯 Exam Tip: Always visualize a number line where numbers decrease from right to left and increase from left to right.

Question 6. Successor and predecessor of 67 will be
(i) 68,66
(ii) 66, 69
(iii) 65, 66
(iv) 65, 69
Answer: (i) 68,66
In simple words: The successor of 67 is 67 + 1 = 68, and its predecessor is 67 - 1 = 66. So, the pair is 68 and 66.

🎯 Exam Tip: Pay attention to the order in which the question asks for successor and predecessor. Successor first, then predecessor, is common.

Question 7. On the number what number line on the right of 13 number will be
(i) 12
(ii) 13
(iii) 14
(iv) 15
Answer: (iii) 14
In simple words: On a number line, numbers get larger as you move towards the right side. The number that comes immediately after 13 is 14.

🎯 Exam Tip: Moving right on a number line means increasing value, while moving left means decreasing value.

Question 8. Smallest natural number is
(i) 0
(ii) 1
(iii) 2
(iv) 3
Answer: (ii) 1
In simple words: Natural numbers are the basic counting numbers. They start from 1 and go up (1, 2, 3...). So, one is the first and smallest natural number.

🎯 Exam Tip: Always remember that natural numbers begin with 1, unlike whole numbers which begin with 0.

Very Short Answer Type Questions

Question 9. Complete the following statements:
(i) Zero (0) is a ________ number
(ii) ________ Number has no predecessor
(iii) Natural numbers are ________
(iv) (40 + 10) + 50 = ________ + (10 + 50)
(v) 18 x ________ = 90 x 18
Answer:
(i) whole
(ii) 0
(iii) infinite
(iv) 40
(v) 90
In simple words: (i) Zero is known as a whole number. (ii) Zero is unique because it is the only whole number that does not have a number before it within the set of whole numbers. (iii) Natural numbers are unending, meaning there is no largest natural number. (iv) This shows that in addition, the way numbers are grouped does not change the total sum. (v) This means that changing the order of numbers in multiplication still gives the same answer.

🎯 Exam Tip: Understand the properties of numbers (whole, natural) and mathematical operations (commutative, associative) to fill in these types of blanks accurately.

Question 10. By multiplying and 1 to any number result obtained is
Answer: When 0 is multiplied by any number, the result is always 0. When 1 is multiplied by any number, the result is the number itself. For example, \( 5 \times 0 = 0 \) and \( 5 \times 1 = 5 \).
In simple words: Multiplying any number by zero always gives zero. Multiplying any number by one always gives the same number back.

🎯 Exam Tip: Remember the 'zero property' (multiplication by 0) and the 'identity property' (multiplication by 1) as they are crucial for calculations.

Question 11. Show 4 + 4, 4 - 4 and 4 × 4 on number line.
Answer:
For \( 4 + 4 = 8 \)
For \( 4 - 4 = 0 \):

For \( 4 \times 4 = 16 \):

In simple words: To show operations on a number line, we start at zero. For adding 4, we move 4 steps to the right. For subtracting 4, we move 4 steps to the left from the current position. For multiplying 4 by 4, we make 4 jumps of 4 steps each from zero.
🎯 Exam Tip: Ensure that arrows clearly indicate the direction and magnitude of each operation on the number line. Labels are important too.

Question 12. Is division and subtraction of whole numbers follows commutativity and Associativity
Answer: No.
Division and subtraction of whole numbers do not follow commutativity or associativity. For example, \( 5 - 3 \neq 3 - 5 \) and \( (10 - 5) - 2 \neq 10 - (5 - 2) \). Similarly, \( 6 \div 3 \neq 3 \div 6 \).
In simple words: For whole numbers, you cannot change the order of numbers when dividing or subtracting and expect to get the same answer. Also, how you group numbers in division or subtraction changes the final result.
🎯 Exam Tip: Remember that commutative property means \( a \cdot b = b \cdot a \) and associative property means \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \). These typically hold for addition and multiplication, but not for subtraction and division.

Question 13. Which operations of whole numbers follows commutativity and associativity ?
Answer: Addition and multiplication of whole numbers follow commutativity and associativity. For example, for any whole numbers \( a, b, c \):
Commutativity: \( a + b = b + a \) and \( a \times b = b \times a \).
Associativity: \( (a + b) + c = a + (b + c) \) and \( (a \times b) \times c = a \times (b \times c) \).
In simple words: Only addition and multiplication work in a way that you can change the order of numbers or how they are grouped, and you will still get the same answer.
🎯 Exam Tip: Clearly state both addition and multiplication as operations that satisfy both commutative and associative properties for whole numbers.

Short/Long Answer Type Questions

Question 14. Find addition and multiplication by arranging in suitable order.
(i) 72 + 44 + 94
(ii) 51 x 63 x 47
Answer:
(i) We solve this by grouping numbers to make addition easier, using the associative property:
\( 72 + 44 + 94 \)
\( = (70 + 2) + (40 + 4) + (90 + 4) \)
\( = (70 + 40 + 90) + (2 + 4 + 4) \)
\( = 200 + 10 \)
\( = 210 \)
(ii) We use the associative and distributive properties to arrange for easier multiplication:
\( 51 \times 63 \times 47 \)
\( = 51 \times (60 + 3) \times 47 \)
\( = (51 \times 60 + 51 \times 3) \times 47 \)
\( = (3060 + 153) \times 47 \)
\( = 3213 \times 47 \)
\( = 3213 \times (40 + 7) \)
\( = (3213 \times 40) + (3213 \times 7) \)
\( = 128520 + 22491 \)
\( = 151011 \)
In simple words: For addition, we group numbers to make sums of tens or hundreds easier to add. For multiplication, we break down numbers into parts (like \( 63 \) into \( 60+3 \)) and multiply each part separately, then add the results to get the final answer.
🎯 Exam Tip: Smart grouping (associative property) and breaking down numbers (distributive property) can simplify complex calculations, especially in multiple-step problems.

Question 15. Solve the following
(i) 62 x 48
(ii) 40 x 72
Answer: We solve these by using the distributive method, which breaks down multiplication over addition.
(i) \( 62 \times 48 \)
\( = 62 \times (40 + 8) \)
\( = (62 \times 40) + (62 \times 8) \)
\( = 2480 + 496 \)
\( = 2976 \)
(ii) \( 40 \times 72 \)
\( = 40 \times (70 + 2) \)
\( = (40 \times 70) + (40 \times 2) \)
\( = 2800 + 80 \)
\( = 2880 \)
In simple words: We can multiply big numbers by splitting one of them into easier parts, like tens and ones. Then, multiply the other number by each part separately and add those results together.
🎯 Exam Tip: The distributive property is a powerful tool to simplify multiplication, especially when one of the numbers can be easily broken into multiples of 10.