GSEB Class 6 Maths Solutions Chapter 2 Whole Numbers InText Questions

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Question 1. Write the predecessor and successor of 19; 1997; 12000; 49; 100000.
Answer:

Exam Tip: To find the predecessor, subtract 1 from the number. To find the successor, add 1 to the number. This is a basic but important concept for whole numbers.

 

Question 2. Is there any natural number that has no predecessor?
Answer: Yes, the smallest natural number, which is 1, has no predecessor within the set of natural numbers.
In simple words: Yes, the number 1 does not have a natural number before it.

Exam Tip: Remember the definition of natural numbers (1, 2, 3...) to answer questions about their properties, especially the first and last numbers.

 

Question 3. Is there any natural number which has no successor? Is there a last natural number?
Answer:
(i) No, there is no natural number which has no successor.
(ii) No, there is no last natural number.
In simple words: No, for every natural number, you can always find a next one. There isn't a final or biggest natural number.

Exam Tip: Natural numbers are infinite; they continue without end, meaning every natural number has a successor and there is no "last" one.

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Question 1. Are all natural numbers also whole numbers?
Answer: Yes, all natural numbers are whole numbers.
In simple words: All the counting numbers (like 1, 2, 3) are also part of the group of whole numbers.

Exam Tip: Understand the difference between natural numbers (1, 2, 3...) and whole numbers (0, 1, 2, 3...). Whole numbers include zero, while natural numbers do not.

 

Question 2. Are all whole numbers also natural numbers?
Answer: No, all whole numbers are not natural numbers. Because 0 is a whole number but it is not a natural number.
In simple words: Not all whole numbers are natural numbers. This is because zero is a whole number, but it is not a natural number.

Exam Tip: The key distinction is the number zero. Zero is a whole number but not a natural number, which makes this statement false.

 

Question 3. Which is the greatest whole number?
Answer: Since, every whole number has a successor. There is no greatest whole number.
In simple words: There is no greatest whole number. You can always add one to any whole number to get a new, bigger one.

Exam Tip: Like natural numbers, whole numbers are infinite. This means there's no single "largest" whole number you can identify.

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Question 1. Find 4 + 5; 2 + 6; 3 + 5 and 1 + 6 using the number line.
Answer:
(i) 4 + 5

Let us start from 4. Since, we have to add 5 to this number, we make 5 jumps to the right. Each jump being equal to 1 unit. After five jumps we reach at 9.
\( 4 + 5 = 9 \)
(ii) 2 + 6

Let us start from 2. Since, we have to add 6 to this number, we make 6 equal jumps, each jump being equal to 1 unit, to the right and reach to 8.
\( 2 + 6 = 8 \)
(iii) 3 + 5

We start from 3. We make 5 equal jumps. Each jump being equal to 1 unit to the right and reach to 8.
\( 3 + 5 = 8 \)
(iv) 1 + 6

As we have to add 6 to 1, therefore, we start from 1 and make 6 equal jumps to the right. Each jump being equal to 1 unit. We reach to 7.
\( 1 + 6 = 7 \)
In simple words: To add numbers on a number line, start at the first number and make jumps to the right according to the second number. Each jump counts as one unit. The point where you land is the answer.

Exam Tip: When using a number line for addition, always move to the right. The number of jumps represents the second operand, and the starting point is the first operand.

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Question 1. Find 8 – 3; 6 – 2; 9 – 6 using the number line.
Answer:
(i) 8 - 3

To subtract 3 from 8, start from 8 and make 3 equal jumps towards left. Each jump being equal to 1 unit. So, we reach at 5,
\( 8 - 3 = 5 \)
(ii) 6 - 2

To subtract 2 from 6, we start from 6. Make 2 equal jumps towards left. Each jump being equal to 1 unit. So, we reach at 4,
\( 6 - 2 = 4 \)
(iii) 9 - 6

To subtract 6 from 9, we start from 9 and make 6 equal jumps towards left. Each jump being equal to 1 unit. So, we reach at 3,
\( 9 - 6 = 3 \)
In simple words: To subtract numbers using a number line, begin at the first number and make jumps to the left according to the second number. Each jump represents one unit, and your landing spot is the final answer.

Exam Tip: For subtraction on a number line, always move to the left. The number of jumps corresponds to the subtrahend, and the starting point is the minuend.

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Question 1. Find 2 x 6, 3 x 3; 4 x 2 using the number line.
Answer:
(i) 2 x 6

Starting from 0, move 2 units at a time to the right. Make 6 such moves. So, we reach at 12.
\( 2 \times 6 = 12 \)
(ii) 3 x 3

Starting from 0, move 3 units at a time to the right. Make 3 such moves. So, we reach at 9.
\( 3 \times 3 = 9 \)
(iii) 4 x 2

Starting from 0, move 4 units at a time to the right. Make 2 such moves. So, we reach at 8.
\( 4 \times 2 = 8 \)
In simple words: To multiply on a number line, start at zero and make equal jumps to the right. The size of each jump is the first number, and the count of jumps is the second number. The point where you land is the product.

Exam Tip: For multiplication on a number line, think of it as repeated addition. Make 'x' jumps of 'y' units each to find the product of 'x' times 'y'.

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Question 1. Find: 7 + 18 + 13; 16 + 12 + 4
Answer:
(i) \( 7 + 18 + 13 = (7 + 13) + 18 = 20 + 18 = 38 \) We rearrange the numbers to make adding easier.
(ii) \( 16 + 12 + 4 = (16 + 4) + 12 = 20 + 12 = 32 \) Here, we group numbers that sum to a round figure for quicker calculation.
In simple words: When adding several numbers, you can change the order or group them in different ways to make the addition simpler.

Exam Tip: Use the associative property of addition to group numbers that add up to multiples of 10 (or other round numbers) to simplify calculations.

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Question 1. Find: 25 x 8358 x 4; 625 x 3759 x 8
Answer:
(i) \( 25 \times 8358 \times 4 = (25 \times 4) \times 8358 \) (Using associativity of whole numbers)
\( = (100) \times 8358 = 835800 \)
(ii) \( 625 \times 3759 \times 8 = (625 \times 8) \times 3759 \) (Using associativity of whole numbers)
\( = 5000 \times 3759 \)
\( = 5 \times 1000 \times 3759 \)
\( = (3759 \times 5) \times 1000 \)
\( = 18795 \times 1000 \)
\( = 18795000 \)
So, \( 625 \times 3759 \times 8 = 18795000 \)
In simple words: When multiplying three or more numbers, you can group them in any order to find the product. It helps to multiply numbers that easily form round figures like 100 or 1000 first.

Exam Tip: Apply the associative property of multiplication to group numbers (like 25 and 4, or 625 and 8) that yield powers of 10, significantly simplifying the multiplication process.

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Question 1. Find 15 x 68; 17 x 23; 69 x 78 + 22 x 69 using distributive property.
Answer:
(i) \( 15 \times 68 = (10 + 5) \times 68 \)
\( = (10 \times 68) + (5 \times 68) \) (By distributivity of multiplication over addition)
\( = 680 + 340 = 1020 \)
(ii) \( 17 \times 23 = 17 \times (20 + 3) \)
\( = (17 \times 20) + (17 \times 3) \) (By distributivity of multiplication over addition)
\( = 340 + 51 = 391 \)
(iii) \( 69 \times 78 + 22 \times 69 = 69[78 + 22] \)
\( = 69[100] \)
\( = 6900 \)
So, \( 69 \times 78 + 22 \times 69 = 6900 \)
In simple words: The distributive property helps us multiply a number by a sum or difference. You can break down one of the numbers, multiply the other number by each part, and then add or subtract the results.

Exam Tip: The distributive property \(a \times (b + c) = (a \times b) + (a \times c)\) is crucial for simplifying expressions and performing mental calculations more easily. Always look for common factors or ways to break down numbers into convenient sums/differences.

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Question 1. Which numbers can be shown. only as a line?
Answer: The numbers 2, 5, 7, 11, 13, 14, 17, 19, ... can be shown only as a line. These are numbers that cannot form perfect squares or rectangles with more than one row/column.
In simple words: Numbers that can only be arranged in a straight line, like 2, 5, 7, etc., are usually prime numbers or numbers that don't make neat square or rectangular dot patterns.

Exam Tip: Numbers that can only be represented as a single line of dots are typically prime numbers or numbers that only have 1 and themselves as factors if arranged in a rectangular grid. For composite numbers, if one factor is 1, it's still a line.

 

Question 2. Which can be shown as squares?
Answer: The numbers 4, 9, 16, 25 ... .can be shown as squares. These are known as perfect squares.
In simple words: Numbers like 4, 9, 16, and 25 can be arranged to form a square shape, with an equal number of dots on each side.

Exam Tip: Perfect square numbers are those that can form a square grid of dots (e.g., 2x2=4, 3x3=9). They are important in geometry and number theory.

 

Question 3. Which can be shown as rectangles?
Answer: The numbers like 4, 6, 8, 9, 10, 12, ... can be shown as rectangles. These numbers have factors other than just 1 and themselves.
In simple words: Numbers such as 4, 6, 8, 9, 10, and 12 can be arranged into rectangle shapes. All composite numbers can be shown as rectangles.

Exam Tip: Any composite number (a number with more than two factors) can be represented as a rectangle of dots, including squares, as squares are special types of rectangles.

 

Question 4. Write down the first seven numbers that can be arranged as triangles, e.g. 3, 6, ...
Answer: We have

Thus, the first seven triangular numbers are: 3, 6, 10, 15, 21, 28 and 36.
In simple words: Triangular numbers are special numbers that can form a triangular shape when arranged as dots. To find them, you keep adding the next counting number: 1, 1+2=3, 1+2+3=6, and so on.

Exam Tip: Triangular numbers are found by summing consecutive natural numbers starting from 1. The nth triangular number is given by the formula \( \frac{n(n+1)}{2} \).

 

Question 5. Some numbers can be shown by two rectangles, for example,
Answer: There can be many such examples. Some of them are as follows:

(v) 30

In simple words: Many numbers can be shown as rectangles using different combinations of rows and columns. This means they have multiple factors that can form the sides of a rectangle.

Exam Tip: Understanding rectangular numbers helps visualize factors. Any number that can be expressed as a product of two integers (other than 1 and itself, for non-prime examples) can form a rectangle.