Whole Number Sums for Class 6 — Free CBSE Worksheet PDF with Answers

You have been working with whole numbers since primary school. But Class 6 CBSE is where you start seeing them differently. Now you learn why $a + b = b + a$ always works, what happens when you multiply by zero, and how the number line stretches to the right forever. These properties are not random rules — they are the building blocks of algebra. When you study equations in Class 7, you will use the commutative and distributive properties constantly.

Whole numbers are the set $0, 1, 2, 3, 4, \ldots$. Natural numbers are $1, 2, 3, \ldots$ (no zero). The single difference between the two sets is the inclusion of zero. Class 6 students must remember this distinction — it shows up in nearly every chapter exercise.

This worksheet has 60 questions across three levels. Level 1 covers identifying properties and basic number-line questions. Level 2 applies properties to simplify expressions, fill in the blanks, and find patterns. Level 3 has multi-step reasoning, word problems, and pattern discovery.

The four key properties of addition: closure (sum of whole numbers is a whole number), commutative ($a + b = b + a$), associative ($(a + b) + c = a + (b + c)$), and additive identity ($a + 0 = a$). For multiplication: closure, commutative ($a \times b = b \times a$), associative ($(a \times b) \times c = a \times (b \times c)$), multiplicative identity ($a \times 1 = a$), and multiplication by zero ($a \times 0 = 0$).

Subtraction and division do not satisfy commutativity or associativity for whole numbers. So $7 - 3 \neq 3 - 7$ and $6 \div 2 \neq 2 \div 6$. Also, division by zero is undefined — $5 \div 0$ is not zero, it is undefined. This trips up many students in MCQs.

The distributive property of multiplication over addition states that $a \times (b + c) = a \times b + a \times c$. It also works over subtraction: $a \times (b - c) = a \times b - a \times c$. This is more than just a formal rule — it is a calculation shortcut.

To find $35 \times 98$ quickly: write $98 = 100 - 2$, so $35 \times 98 = 35 \times 100 - 35 \times 2 = 3500 - 70 = 3430$. To find $25 \times 104$: write $104 = 100 + 4$, so $25 \times 104 = 25 \times 100 + 25 \times 4 = 2500 + 100 = 2600$. Many CBSE Class 6 questions test this shortcut directly.

The number line shows whole numbers as evenly spaced dots starting from $0$ and going right. Every whole number has a successor (the next one) and every whole number except $0$ has a predecessor (the previous one). The successor of $999$ is $1000$. The predecessor of $1000$ is $999$. There is no predecessor of $0$ in whole numbers (since $-1$ is not a whole number).

Triangular numbers are $1, 3, 6, 10, 15, 21, \ldots$ — they form triangles of dots. Square numbers are $1, 4, 9, 16, 25, 36, \ldots$ — they form squares. The classic Class 6 pattern: the sum of the first $n$ odd numbers is $n^2$. So $1 = 1$, $1 + 3 = 4$, $1 + 3 + 5 = 9$, $1 + 3 + 5 + 7 = 16$, and so on.