Integers Class 6 Worksheet — Free PDF Download with Answers

Integers extend the whole numbers to include negative numbers: $\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}$. They answer a simple question that whole numbers cannot: what happens when you subtract a larger number from a smaller one? The answer is a negative integer.

Negative numbers are everywhere in daily life. Temperatures drop below zero in winter ($-5^\circ$C). Bank accounts can be overdrawn (a balance of $-200$ means you owe money). Elevations go below sea level (the Dead Sea is at $-430$ m). Integers give us the language to describe all of these situations precisely.

In Class 6, students learn to represent integers on a number line, compare and order them, and perform addition and subtraction. This is the first time most students encounter negative numbers, so building a strong visual and conceptual foundation is critical for success in algebra and coordinate geometry in later classes.

* Integers — $\{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\}$. Includes positive integers, negative integers, and zero.
* Number line — Negative integers are to the left of $0$; positive integers to the right. A number further right is always greater.
* Absolute value — The distance of an integer from $0$, always non-negative: $|{-7}| = 7$, $|5| = 5$.
* Ordering — On the number line, left means smaller: $-5 < -2 < 0 < 3 < 7$.
* Addition rules:
- Same signs: add absolute values, keep the sign. $(-4) + (-3) = -7$.
- Different signs: subtract the smaller absolute value from the larger, take the sign of the larger. $(-8) + 5 = -3$.
* Subtraction rule — Subtracting an integer is the same as adding its opposite: $a - b = a + (-b)$. So $5 - (-3) = 5 + 3 = 8$.
* Additive inverse — For every integer $a$, there exists $-a$ such that $a + (-a) = 0$.
* Properties — Integers are closed under addition and subtraction. Addition is commutative and associative. $0$ is the additive identity.

1. Print the PDF — Download from the links below.

2. Start with Level 1 (Easy) — 20 questions on representing integers on a number line, comparing, and simple addition.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key.

5. Revise mistakes — For every sign error, draw a number line and trace the operation step by step.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Place the following integers on a number line: $-3, 0, 4, -1, 2$.
Solution: From left to right: $-3, -1, 0, 2, 4$.

2. Compute $(-6) + 4$.
Solution: Different signs: $6 - 4 = 2$. The larger absolute value ($6$) is negative, so the answer is $-2$.

3. Which is greater: $-8$ or $-3$?
Solution: $-3 > -8$ because $-3$ is further to the right on the number line.

Level 2 — Medium

1. Compute $(-12) - (-7)$.
Solution: $(-12) - (-7) = -12 + 7 = -5$.

2. The temperature at midnight was $-4^\circ$C. By noon it rose by $11^\circ$C. What is the noon temperature?
Solution: $-4 + 11 = 7^\circ$C.

3. Arrange in ascending order: $5, -9, 0, -3, 7, -7$.
Solution: $-9 < -7 < -3 < 0 < 5 < 7$.

Level 3 — Hard

1. Find the integer $x$ such that $(-15) + x = -4$.
Solution: $x = -4 - (-15) = -4 + 15 = 11$.

2. The sum of two integers is $-8$. One of them is $13$. Find the other.
Solution: Other integer $= -8 - 13 = -21$.

3. Simplify: $(-3) + 7 + (-11) + 4 + (-2) + 9$.
Solution: Positive sum $= 7 + 4 + 9 = 20$. Negative sum $= (-3) + (-11) + (-2) = -16$. Total $= 20 + (-16) = 4$.

CBSE (NCERT — Ganita Prakash / Math Magic)
The "Integers" chapter introduces negative numbers through real-world contexts (temperature, altitude, banking). CBSE emphasises the number line, addition, and subtraction of integers. Properties like commutativity and associativity are explored through examples.

ICSE (Selina / ML Aggarwal)
ICSE also covers integers in a dedicated chapter with a slightly more formal treatment. ICSE exams include more word problems involving temperature changes, altitude differences, and financial transactions. The absolute value concept may be introduced more explicitly.

IB MYP (Mathematics Framework)
The MYP covers integers within the "Integers & Order of Operations" unit. Students explore negative numbers through investigation and apply them in real-world contexts. The IB also expects students to work with order of operations (BODMAS/PEMDAS) involving negative numbers.

Key Differences:
* CBSE: Context-driven introduction; number line emphasis.
* ICSE: More formal; heavier on word problems.
* IB: Integrates with order of operations; inquiry-based.

Download your free Integers worksheets:

* Integers CBSE Worksheet — 60 questions aligned to NCERT
* Integers ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online:

* Practice Online — CBSE
* Practice Online — ICSE
* Practice Online — IB

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on an integer problem? Get a step-by-step solution.
* Spark Coach — AI tutor that guides with hints, not answers.
* Free Worksheets for All Classes — Worksheets from Class 1 to 10 across all boards.
* Play Mode for Class 1-4 — Fun number games for younger learners.

Continue your Class 6 practice:

* Whole Numbers Class 6 Worksheet
* Numbers & Place Value Class 6 Worksheet
* Fractions & Decimals Class 6 Worksheet
* Algebra & Simple Equations Class 6 Worksheet
* Number Play Class 6 Worksheet