CBSE Class 7 Maths — Integers

Chapter Overview & Weightage

Integers is the first chapter in Class 7 Maths and one of the foundational chapters of the entire mathematics curriculum. Getting the rules of integer operations solid here saves enormous confusion in algebra later.

Key Concepts You Must Know

What are integers? The set of whole numbers extended to include negative numbers: $\{..., -3, -2, -1, 0, 1, 2, 3, ...\}$

Number line: Positive integers go right, negative integers go left. Zero is neither positive nor negative.

Comparing integers: Further right on the number line = greater. $-2 > -5$ (because $-2$ is to the right of $-5$).

Absolute value $|x|$: The distance from zero, always non-negative. $|-7| = 7$, $|4| = 4$, $|0| = 0$.

Operations on Integers

Addition

• Same signs: add absolute values, keep the sign. $(-5) + (-3) = -8$
• Different signs: subtract smaller absolute value from larger, take the sign of the larger. $(-7) + 4 = -3$ (since $|-7| > |4|$, answer is negative)

Subtraction

Convert to addition: $a - b = a + (-b)$.

Multiplication and Division

Same rule applies to division. Same signs → positive. Different signs → negative.

Properties of Integers

Closure: Integers are closed under $+$, $-$, $\times$, but NOT under $\div$ (since $5 \div 2$ is not an integer).

Commutativity: $a + b = b + a$ and $a \times b = b \times a$ for integers. Subtraction and division are NOT commutative.

Associativity: $(a + b) + c = a + (b + c)$. Same for multiplication. Not for subtraction.

Distributivity: $a \times (b + c) = a \times b + a \times c$

Identity: 0 for addition ($a + 0 = a$), 1 for multiplication ($a \times 1 = a$)

Additive inverse: $a + (-a) = 0$. The additive inverse of $-7$ is $+7$.

Solved Previous Year Questions

PYQ 1 (1 mark)

Evaluate: $(-25) \times (-4) \times (-3)$

$(-25) \times (-4) = 100$ (negative × negative = positive)

$100 \times (-3) = -300$ (positive × negative = negative)

Answer: $-300$

PYQ 2 (2 marks)

The temperature in Shimla was $-7°C$ on Monday. It fell by $3°C$ on Tuesday and rose by $5°C$ on Wednesday. What was the temperature on Wednesday?

Tuesday: $-7 - 3 = -10°C$

Wednesday: $-10 + 5 = -5°C$

Answer: $-5°C$

PYQ 3 (2 marks)

Using distributive property, evaluate: $(-15) \times 47 + (-15) \times 53$

$(-15) \times 47 + (-15) \times 53 = (-15) \times (47 + 53) = (-15) \times 100 = -1500$

Without distributivity: $-705 + (-795) = -1500$. Same answer — but distributivity saves time.

Difficulty Distribution

Expert Strategy

Master the sign rules cold. These rules are used in every subsequent year of mathematics. Drill until they’re automatic.

For word problems: Temperature change, profit/loss, depth/height, and bank balance are classic integer word problem contexts. The key: identify what is positive and what is negative at the start.

Use the number line for small numbers. For questions like “which is greater: $-3$ or $-8$”, mentally visualize the number line.

Common Traps