CBSE Class 6 Mathematics Whole Numbers Worksheet Set 08

Section A

Question 1. Counting numbers are called
(i) Whole Numbers
(ii) Natural Numbers
(iii) Integers
(iv) None of the options
Answer: (ii) Natural Numbers
Natural numbers are the set of positive integers starting from 1, 2, 3, 4, and so on, which are used for counting objects.
In simple words: Counting numbers are called natural numbers because we use them to count things in nature.

Exam Tip: Remember that natural numbers start from 1, whereas whole numbers start from 0.

Question 2. The product of first five whole numbers is :
(i) 0
(ii) 120
(iii) 24
(iv) 10
Answer: (i) 0
The first five whole numbers are 0, 1, 2, 3, and 4.
Product = \(0 \times 1 \times 2 \times 3 \times 4 = 0\)
In simple words: Since zero is included among the first five whole numbers, multiplying any set of numbers by zero always results in zero.

Exam Tip: Always check if zero is part of the sequence when calculating a product; any multiplication involving zero gives zero instantly.

Question 3. Which number is a whole number but not a natural number :
(i) 1
(ii) 2
(iii) 0
(iv) 3
Answer: (iii) 0
Whole numbers start from 0, 1, 2, 3, ..., while natural numbers start from 1, 2, 3, ... Therefore, 0 is a whole number but not a natural number.
In simple words: Zero belongs to whole numbers, but counting starts from 1, so 0 is not a natural number.

Exam Tip: Keep the definitions clear: Whole Numbers = {0, 1, 2, 3, ...} and Natural Numbers = {1, 2, 3, ...}.

Question 4. Which natural number has no predecessor :
(i) 1
(ii) 0
(iii) 2
(iv) 3
Answer: (i) 1
In the system of natural numbers, 1 is the first number. There is no natural number before 1.
In simple words: Since natural numbers begin at 1, the number 1 has no predecessor in natural numbers.

Exam Tip: Be careful with number systems: 0 has no predecessor in whole numbers, but 1 has no predecessor in natural numbers.

Question 5. Successor of 1099 is :
(i) 1000
(ii) 2000
(iii) 1100
(iv) 1098
Answer: (iii) 1100
The successor of a number is obtained by adding 1 to it.
\(1099 + 1 = 1100\)
In simple words: The successor is simply the next number you get after adding 1.

Question 6. Comparison of length is possible in case of:
(i) Two lines
(ii) Two rays
(iii) Two segments
(iv) a ray and a segment
Answer: (iii) Two segments
A line segment has a fixed, finite length with two endpoints. Lines and rays extend infinitely in one or both directions, so their exact lengths cannot be measured or compared.
In simple words: Only line segments have definite lengths that can be measured and compared.

Exam Tip: Remember that line segments have fixed lengths, whereas lines and rays are infinite.

Question 7. The vertex of an angle lies :
(i) in its interior
(ii) in its exterior
(iii) on the angle
(iv) None of the options
Answer: (iii) on the angle
An angle is formed by two rays sharing a common endpoint called the vertex. Thus, the vertex is the corner point located directly on the angle itself.
In simple words: The vertex is the joining point of the two rays forming the angle, so it lies right on the angle.

Exam Tip: The vertex is the exact meeting point where the two arms of the angle intersect.

Question 8. The total parts in a triangle are :
(i) 3
(ii) 4
(iii) 5
(iv) 6
Answer: (iv) 6
A triangle has 3 sides and 3 angles, making a total of 6 parts (or elements).
In simple words: A triangle has three sides and three angles, which combine to make 6 parts in total.

Exam Tip: The six fundamental parts of any triangle are its three sides and three interior angles.

Question 9. The number in straight lines passing through one point are :
(i) 1
(ii) 2
(iii) 3
(iv) infinity
Answer: (iv) infinity
An infinite number of straight lines can be drawn passing through a single given point.
In simple words: You can pass countless lines through one single dot.

Exam Tip: Contrast this with two distinct points, through which only one unique straight line can pass.

Question 10. A line segment joining any two points on a circle is known as :
(i) Radius
(ii) Chord
(iii) Diameter
(iv) Segment
Answer: (ii) Chord
A chord is a line segment whose endpoints both lie on the circumference of the circle.
In simple words: Any line connecting two points on the edge of a circle is called a chord.

Exam Tip: The longest chord of a circle is the diameter, which passes through the center.

Section B

Question 1. The radius of a circle is 5cm. What is its diameter?
Answer: Radius (\(r\)) = 5 cm
Diameter (\(d\)) = \(2 \times r\)
\(d = 2 \times 5 = 10 \text{ cm}\)
In simple words: The diameter is always twice the length of the radius.

Exam Tip: Formula to remember: Diameter = \(2 \times \text{Radius}\).

Question 2. Draw a rough sketch of a quadrilateral ABCD. Draw one of its diagonals, which point of the diagonal lie in the interior of the quadrilateral?
Answer:
Steps of construction:
1. Draw a quadrilateral ABCD with vertices A, B, C, and D.
2. Draw a diagonal from vertex A to vertex C (AC) or from vertex B to vertex D (BD).
3. All points of the diagonal segment (except the endpoints A and C) lie completely in the interior of the quadrilateral.
In simple words: The line segment connecting opposite corners (diagonal) runs entirely inside the shape.

Exam Tip: A diagonal connects two non-consecutive vertices of a polygon.

Question 3. Find the value of \(1507 - (625 \div 25)\).
Answer: Using BODMAS, first perform division inside the parentheses:
\(625 \div 25 = 25\)
Now subtract this value from 1507:
\(1507 - 25 = 1482\)
In simple words: First divide 625 by 25, then subtract the result from 1507.

Exam Tip: Always follow the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

Question 4. Write the smallest 4 digit number having three different digits.
Answer: To form the smallest 4-digit number with three different digits, we use the smallest possible digits from left to right (0, 1, 2, ...):
Thousands place must be 1 (cannot be 0).
Hundreds place should be 0.
Tens place should be 2.
Units place can repeat the smallest digit or use the next available digit, but since we need exactly three different digits, we can repeat 2 or 0. To make it the smallest, we repeat 0 or 2. Let us check: 1002 uses digits 1, 0, 2 (three different digits).
Thus, the number is 1002.
In simple words: Arrange the smallest possible digits to form the number while ensuring three unique digits are used.

Exam Tip: Never start a 4-digit number with 0; the thousands place must be at least 1.

Section C

Question 5. Draw a circle and mark two points : (i) in its interior (ii) in its exterior (iii) on the circle
Answer:
Steps of construction:
1. Draw a circle with center O.
2. Mark point P inside the circle (interior).
3. Mark point Q outside the circle (exterior).
4. Mark point R on the boundary of the circle (on the circle).
In simple words: Interior means inside, exterior means outside, and on the circle means right on the boundary line.

Exam Tip: Clearly label each point with reference to the circle's boundary.

Question 6. Draw a rough sketch of the following figures and label them : (i) Collinear point P, Q and R (ii) Concurrent lines AB, CD and EF (iii) XY intersecting PQ at M.
Answer:
(i) Collinear points P, Q, and R lie on a single straight line.
(ii) Concurrent lines AB, CD, and EF pass through a single common point of intersection.
(iii) Line XY and line PQ intersect each other at point M.
In simple words: Collinear means on the same line, concurrent means meeting at one common point, and intersecting means crossing each other.

Exam Tip: Use a ruler to draw straight lines clearly and label all intersection points accurately.

Question 7. Find the number which when divided by 56 gives a quotient 108 and reminder 39.
Answer: Using the division algorithm:
\(\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}\)
Divisor = 56
Quotient = 108
Remainder = 39
\(\text{Dividend} = (56 \times 108) + 39\)
\(56 \times 108 = 6048\)
\(\text{Dividend} = 6048 + 39 = 6087\)
In simple words: Multiply the divisor by the quotient and add the remainder to find the original number.

Exam Tip: Always verify your answer by dividing the resulting number back by the divisor.

Question 8. Add \(437 + 680 + 363 + 220\) by suitable arrangement.
Answer: Rearrange the terms using commutative and associative properties to make the addition easier by getting multiples of 10:
\(= (437 + 363) + (680 + 220)\)
\(= 800 + 900\)
\(= 1700\)
In simple words: Group numbers that add up to round numbers (like multiples of 100) first to calculate faster.

Exam Tip: Look at the units digits (7 + 3 = 10 and 0 + 0 = 0) to pair numbers smartly.

Section D

Question 9. Find the difference between the smallest 5 digit number and the largest three digit number.
Answer:
Smallest 5-digit number = 10000
Largest 3-digit number = 999
Difference = \(10000 - 999\)
\(10000 - 999 = 9001\)
In simple words: Subtract the largest 3-digit number (999) from the smallest 5-digit number (10000).

Exam Tip: Smallest n-digit number is 1 followed by \((n-1)\) zeros; largest n-digit number is \(n\) nines.

Question 10. Find the following products using different properties. (i) \(297 \times 17 + 297 \times 3\) (ii) \(8431 \times 110\)
Answer:
(i) Using distributive property (\(a \times b + a \times c = a \times (b + c)\)):
\(297 \times 17 + 297 \times 3 = 297 \times (17 + 3)\)
\(= 297 \times 20\)
\(= 5940\)

(ii) Using distributive property by splitting 110 into \((100 + 10)\):
\(8431 \times 110 = 8431 \times (100 + 10)\)
\(= (8431 \times 100) + (8431 \times 10)\)
\(= 843100 + 84310\)
\(= 927410\)
In simple words: Use properties like distribution to simplify multiplication without long calculations.

Exam Tip: The distributive property over addition is one of the most powerful tools for mental math.

Question 11. Draw any circle and show : (a) its centre (b) its radius (c) a diameter (d) a sector (e) a segment (f) an arc
Answer:
Steps of explanation and representation:
- Centre: The fixed internal point from which all points on the circle are equidistant.
- Radius: A line segment from the centre to any point on the circle.
- Diameter: A line segment passing through the centre with endpoints on the circle.
- Sector: The region enclosed by two radii and an arc.
- Segment: The region enclosed by a chord and an arc.
- Arc: Any connected part of the circle's circumference.
In simple words: All these parts describe different lines, regions, and boundaries associated with a circle.

Exam Tip: Practice drawing circles with a compass and labeling each term clearly with arrows.

Question 12. Assume the following question with respect to the adjoining figure : (a) Name three triangles in the figure. (b) Write the names of the seven angles. (c) identify three collinear points
Answer:
(a) Three triangles in the figure: \(\triangle ABD\), \(\triangle ADC\), and \(\triangle ABC\).
(b) Seven angles in the figure: \(\angle B\), \(\angle C\), \(\angle BAD\), \(\angle DAC\), \(\angle BAC\), \(\angle ADB\), and \(\angle ADC\).
(c) Three collinear points: Points B, D, and C lie on the same straight line segment BC.
In simple words: Examine the smaller shapes and intersecting lines within the main triangle to identify all individual triangles, angles, and points on a single line.

Exam Tip: When naming angles and triangles, always list the letters systematically so the vertex is in the middle for angles.