Whole Numbers Class 6: Properties, Patterns & Number Line

Class 6 Maths Worksheet — Free PDF with Answers

This is your one-stop class 6 maths worksheet collection — every topic, every chapter, completely free with step-by-step answers. Whether you searched for a maths class 6 worksheet or a worksheet math class 6 resource, you have landed in the right place. SparkEd's Class 6 maths practice covers the full CBSE syllabus with 60 questions per topic, and each worksheet comes as a printable PDF.

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For revision before exams, try the maths worksheet for class 6th with answers alongside our maths mcq for class 6 with answers sets. Teachers can use the class 6 maths mcq question paper bank for quick classroom tests. Browse all class 6 maths worksheets cbse topics on the All Class 6 worksheets page, or start with the popular Number Play worksheet. Ready to practise? Head to SparkEd home and pick your chapter.

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What Are Whole Numbers?

Looking for a class 6 math worksheet or maths worksheet for class 6 with answers? This comprehensive resource covers everything you need. Before we talk about whole numbers, let us quickly recall natural numbers. The counting numbers $1, 2, 3, 4, 5, \ldots$ are called natural numbers. We use them every day to count objects.

Now, what if you have nothing to count? That is where zero comes in. When we include $0$ along with all the natural numbers, we get the set of whole numbers:

So the key difference is simple:
- Natural numbers: $1, 2, 3, 4, 5, \ldots$ (start from 1)
- Whole numbers: $0, 1, 2, 3, 4, 5, \ldots$ (start from 0)

Every natural number is a whole number, but $0$ is a whole number that is NOT a natural number. The smallest whole number is $0$, while the smallest natural number is $1$. There is no largest whole number because we can always add $1$ to get the next one.

Beyond this worksheet, SparkEd offers interactive online practice for Whole Numbers with step-by-step solutions and progress tracking — perfect for daily revision.

Predecessor and Successor

Two important concepts with whole numbers are predecessor and successor.

Successor: The number that comes just after a given number. To find the successor, add $1$.

Predecessor: The number that comes just before a given number. To find the predecessor, subtract $1$.

Examples:
- Successor of $15 = 15 + 1 = 16$
- Predecessor of $15 = 15 - 1 = 14$
- Successor of $0 = 1$
- Predecessor of $1 = 0$

Important: The whole number $0$ has no predecessor in the whole number system because $0 - 1 = -1$, which is not a whole number. Every other whole number has both a predecessor and a successor.

Whole Numbers on the Number Line

A number line is a straight line where each point corresponds to a number. To draw a number line for whole numbers:

1. Draw a horizontal line with an arrow on the right (showing numbers continue forever).
2. Mark a point and label it $0$.
3. Mark equal spaces to the right and label them $1, 2, 3, 4, \ldots$

The number line is a powerful tool because it helps us visualise addition, subtraction, and comparison.

Addition on the number line: To add $3 + 4$, start at $3$ and move $4$ steps to the right. You land on $7$.

Subtraction on the number line: To subtract $7 - 3$, start at $7$ and move $3$ steps to the left. You land on $4$.

Comparing numbers: On the number line, a number to the right is always greater. So $5 > 3$ because $5$ is to the right of $3$.

Multiplication on the number line: To find $3 \times 4$, start at $0$ and make $3$ jumps of $4$ units each. You land on $12$.

The number line also makes it clear that between any two whole numbers, there is a fixed number of whole numbers (or none if they are consecutive).

Properties of Whole Numbers

Whole numbers follow several important properties. Understanding these properties makes calculations faster and helps you check your work.

Closure Property

When you add or multiply two whole numbers, the result is always a whole number.

Examples:
- $3 + 5 = 8$ (whole number) -- closed under addition
- $4 \times 6 = 24$ (whole number) -- closed under multiplication

But subtraction and division are NOT closed:
- $3 - 5 = -2$ (not a whole number)
- $5 \div 2 = 2.5$ (not a whole number)

So whole numbers are closed under addition and multiplication, but not under subtraction and division.

Commutative Property

The order does not matter for addition and multiplication.

Examples:
- $3 + 7 = 7 + 3 = 10$
- $4 \times 5 = 5 \times 4 = 20$

Subtraction and division are NOT commutative:
- $7 - 3 = 4$ but $3 - 7 = -4$ (different results)
- $12 \div 4 = 3$ but $4 \div 12 = \frac{1}{3}$ (different results)

Associative Property

When adding or multiplying three or more numbers, the grouping does not matter.

Example:
- $(2 + 3) + 4 = 5 + 4 = 9$ and $2 + (3 + 4) = 2 + 7 = 9$. Same answer.
- $(2 \times 3) \times 4 = 6 \times 4 = 24$ and $2 \times (3 \times 4) = 2 \times 12 = 24$. Same answer.

This property is useful when you want to rearrange numbers to make mental math easier. For example, $17 + 28 + 3$ is easier if you group it as $17 + 3 + 28 = 20 + 28 = 48$.

Distributive Property

Multiplication distributes over addition and subtraction.

Example: Calculate $7 \times 102$ mentally.

This is one of the most useful properties for quick mental calculations.

Identity Elements

Additive Identity: Adding $0$ to any whole number gives the same number.

$0$ is called the additive identity because it does not change the number.

Multiplicative Identity: Multiplying any whole number by $1$ gives the same number.

$1$ is called the multiplicative identity.

Multiplication by Zero:

Any number multiplied by zero gives zero. This is different from the identity property.

Division by Zero: Division by zero is not defined. You cannot divide any number by $0$. The expression $\frac{a}{0}$ has no meaning.

Patterns in Whole Numbers

Whole numbers form many interesting patterns. Recognizing patterns is an important skill in mathematics.

Pattern 1: Adding consecutive odd numbers starting from 1
- $1 = 1 = 1^2$
- $1 + 3 = 4 = 2^2$
- $1 + 3 + 5 = 9 = 3^2$
- $1 + 3 + 5 + 7 = 16 = 4^2$

The sum of the first $n$ odd numbers always equals $n^2$.

Pattern 2: Triangular numbers
- $1, 3, 6, 10, 15, 21, \ldots$
- These are formed by $1, 1+2, 1+2+3, 1+2+3+4, \ldots$
- The $n$th triangular number $= \frac{n(n+1)}{2}$

Pattern 3: Multiplication patterns
- $1 \times 1 = 1$
- $11 \times 11 = 121$
- $111 \times 111 = 12321$

Notice the palindrome pattern in the products.

Pattern 4: Products of consecutive numbers
- $1 \times 2 = 2$
- $2 \times 3 = 6$
- $3 \times 4 = 12$
- Each product equals the smaller number squared plus that number: $n \times (n+1) = n^2 + n$

Looking for patterns trains your brain to think mathematically. Try to spot patterns whenever you work with numbers.

Solved Examples

Let us work through some typical Class 6 problems on whole numbers.

Example 1: Predecessor and Successor

Question: Find the predecessor and successor of 10000.

Solution:
- Successor of $10000 = 10000 + 1 = 10001$
- Predecessor of $10000 = 10000 - 1 = 9999$

Example 2: Using the Distributive Property

Question: Find $15 \times 98$ using the distributive property.

Solution:

Example 3: Number Line

Question: Which whole number is 6 units to the right of 8 on the number line?

Solution: Moving right means adding. So the number is $8 + 6 = 14$.

Example 4: Patterns

Question: Find the sum $1 + 3 + 5 + 7 + 9 + 11$ without adding each number.

Solution: These are the first $6$ odd numbers. The sum of the first $n$ odd numbers $= n^2$.

Verify: $1 + 3 + 5 + 7 + 9 + 11 = 36$. Correct.

Common Mistakes to Avoid

Practice on SparkEd

Understanding whole numbers is the foundation for everything you will learn in higher classes, from integers to rational numbers to algebra. The best way to build confidence is through practice.

SparkEd offers 60 practice questions on Whole Numbers for Class 6, with step-by-step solutions and instant feedback. Jump into practice and solidify your understanding.

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