RBSE Solutions Class 6 Maths Chapter 3 Whole Numbers More Ques

Rajasthan Board RBSE Class 6 Maths Chapter 3 Whole Numbers In Text Exercise

 

Question 1. Complete the following table for closure property.

Answer:
In simple words: The table shows if a math operation on whole numbers always gives another whole number as the result. Addition and multiplication always do, but subtraction and division sometimes give answers that are not whole numbers.

🎯 Exam Tip: Remember that for closure property, if even one pair of numbers doesn't result in a whole number, then the operation is not closed for whole numbers.

 

In multiplication, associativity occurs.

 

Think And Tell

 

Question 1. 6- 6 = .... or 5 - 5 = .... or 10 - 10 = ....
Answer: When any number is subtracted from itself, the result is always zero. This is a basic property of subtraction. For example, \( 6 - 6 = 0 \), \( 5 - 5 = 0 \), and \( 10 - 10 = 0 \).
In simple words: When you take a number away from itself, you always get zero.

🎯 Exam Tip: Understanding that subtracting a number from itself always yields zero is fundamental for solving many basic equations.

 

Question 1. Fill in the blanks with suitable numbers

Answer: Completing the table:
In simple words: The predecessor of a number is the number just before it (minus 1). The successor is the number just after it (plus 1).

🎯 Exam Tip: Remember that for natural numbers, the number 1 has no predecessor within the set of natural numbers, as 0 is not a natural number.

 

Question 1. From the following line, can you tell which number is bigger?
Answer: Yes, we can tell which number is bigger from a number line. Numbers increase as you move from left to right on the number line. For example, 10 is bigger than 9 because 10 is to the right of 9, and 2 is bigger than 1 because 2 is to the right of 1. Any number on the right side of another number on the line is always greater.
In simple words: On a number line, numbers get bigger as you go to the right. So, the number more to the right is always the larger one.

🎯 Exam Tip: Visualizing numbers on a number line helps in understanding their relative magnitudes, especially for comparing positive and negative integers.

 

Question 2. Think, number on left side of any number on number line will be smaller or greater.
Answer: A number on the left side of any other number on a number line will always be smaller. This is because numbers decrease in value as you move from right to left. For instance, 3 is to the left of 5, which means 3 is smaller than 5.
In simple words: A number to the left on the number line is always smaller.

🎯 Exam Tip: The number line is a fundamental tool; always remember the left means smaller, and the right means larger.

 

Question. Looking at the following table find out true or false.

Answer:
In simple words: The table checks if numbers are positioned correctly on a number line (right means greater, left means smaller) and if the greater/lesser symbols are used correctly for each pair.

🎯 Exam Tip: Always double-check the direction of the inequality symbol. "A < B" means A is less than B, and "A > B" means A is greater than B.

 

Operations on the number line:

Thus, \( 8 + 4 = 12 \)

Subtracting \( 8 - 4 \) on number line

Thus, \( 8 - 4 = 4 \)

Multiplying \( 5 \times 2 \) on number line-

\( 5 \times 2 \) i.e., 5 times 2

Thus, \( 5 \times 2 = 10 \)

 

Question 2. Practice, by taking different numbers for addition on number line.
(i) \( 7 + 6 \)
(ii) \( 11 + 4 \)
Answer:
(i) Taking \( 7 + 6 \) on number line-

Thus, \( 7 + 6 = 13 \)

(ii) Taking \( 11 + 4 \) on number line-

Thus, \( 11 + 4 = 15 \).
In simple words: To add numbers on a number line, you start at the first number and move to the right by the second number's value. The point where you land is the sum.

🎯 Exam Tip: Always start at the first number and count jumps equal to the second number. Ensure jumps are to the right for addition and left for subtraction.

 

Question 3. Practice, by taking different numbers for subtraction on number line.
Answer:
(i) Taking \( 6 - 2 \) on number line-

Thus, \( 6 - 2 = 4 \)

(ii) Taking \( 9 - 6 \) on number line-

Thus, \( 9 - 6 = 3 \).
In simple words: To subtract on a number line, you start at the first number and move to the left by the second number's value. The point you land on is the difference.

🎯 Exam Tip: Remember to always move left when subtracting on a number line, and count carefully to avoid errors.

 

Question 1. Under closure property, take some pair of whole numbers. Is their sum also a whole number? Did you find any pair whose sum is not a whole number?
Answer: Yes, when we add any two whole numbers, their sum is always another whole number. This shows that whole numbers are closed under addition. For example, if we take the whole numbers 2 and 9, their sum is \( 2 + 9 = 11 \), which is also a whole number. Similarly, \( 8 + 15 = 23 \), \( 14 + 3 = 17 \), \( 16 + 4 = 20 \), and \( 11 + 7 = 18 \) are all whole numbers. We will not find any pair of whole numbers whose sum is not a whole number.
In simple words: If you add any two whole numbers, you will always get a whole number as the answer. You won't find any two whole numbers that, when added, give a result that is not a whole number.

🎯 Exam Tip: The set of whole numbers includes zero and all positive integers (0, 1, 2, 3...). Addition always keeps you within this set.

 

Question 2. Are whole numbers closed under subtraction?
Answer: No, whole numbers are not closed under subtraction. This means that if you subtract one whole number from another, the result is not always a whole number. For instance, if we subtract 2 from 4, we get \( 4 - 2 = 2 \), which is a whole number. However, if we try to subtract 12 from 7, we get \( 7 - 12 = -5 \), which is a negative number and not a whole number. This single example proves that subtraction is not closed for whole numbers.
In simple words: You cannot always subtract one whole number from another and get a whole number. Sometimes you get a negative number, which is not a whole number.

🎯 Exam Tip: To prove an operation is *not* closed, you only need one counterexample (one instance where it doesn't work).

 

Question 1. Test the commutative property for addition with different pairs of whole numbers. Does the sum change if you change the order of the numbers?
Answer: No, the sum of two whole numbers does not change if we change the order of the numbers. This means that addition is commutative for whole numbers. Let's look at five pairs of numbers:
(i) \( 17 + 9 = 26 \) or \( 9 + 17 = 26 \).
\( \implies 26 = 26 \)
(ii) \( 12 + 1 = 13 \) or \( 1 + 12 = 13 \).
\( \implies 13 = 13 \)
(iii) \( 4 + 25 = 29 \) or \( 25 + 4 = 29 \).
\( \implies 29 = 29 \)
(iv) \( 7 + 3 = 10 \) or \( 3 + 7 = 10 \).
\( \implies 10 = 10 \)
(v) \( 6 + 19 = 25 \) or \( 19 + 6 = 25 \).
\( \implies 25 = 25 \)
In all these examples, changing the order of the numbers did not change the sum. This property makes addition predictable.
In simple words: When you add two whole numbers, the answer stays the same even if you swap the order of the numbers.

🎯 Exam Tip: The commutative property applies to addition and multiplication, but not to subtraction or division for whole numbers.

 

Question 1. Complete the table.

Answer: Completing the table:
In simple words: This table shows which math operations work the same way even if you change the order of the numbers (commutative). Addition and multiplication are commutative, meaning the result doesn't change. But subtraction and division are not commutative, so changing the order will change the answer.

🎯 Exam Tip: Remember the commutative property for whole numbers: \( a + b = b + a \) and \( a \times b = b \times a \). This helps identify operations where order matters and where it doesn't.

 

Question 1. Complete the following table.

Answer: Completing the table:
In simple words: When you add zero to any number, the number itself remains unchanged. Zero is called the additive identity because it does not change the value when added.

🎯 Exam Tip: Remember the property of zero: "Any number plus zero equals that number" and "Zero plus any number equals that number."

 

Question 2. Fill the table.

Answer: Completing the table:
In simple words: When you multiply any number by one, the number remains unchanged. One is called the multiplicative identity because it does not change the value when multiplied.

🎯 Exam Tip: Remember the property of one: "Any number times one equals that number" and "One times any number equals that number."