Class 7 Integers Worksheet – Operations with Positive and Negative Numbers

Master integers for Class 7 with addition, subtraction, multiplication, and division of positive and negative numbers. Includes solved examples and real-world problems on temperature, profit/loss, and more.

What are Integers?

Integers are whole numbers that include positive numbers, negative numbers, and zero. They extend infinitely in both directions: ..., −3, −2, −1, 0, 1, 2, 3, ... Negative numbers appear to the left of zero on a number line, and positive numbers appear to the right. Integers are used whenever we need to represent values that can go in two opposite directions — temperature above and below zero, profit and loss, altitude above and below sea level.

Rules for Integer Operations

Addition: When two numbers have the same sign, add them and keep that sign. When they have different signs, subtract the smaller from the larger and take the sign of the larger number.

Subtraction: Rewrite subtraction as addition of the opposite number, then follow the addition rules. For example, 5 − 3 becomes 5 + (−3).

Multiplication and Division: If both numbers have the same sign, the result is positive. If the signs are different, the result is negative. This rule applies to both multiplication and division.

Solved Example

A submarine starts at 150 m below sea level. It descends 85 m further, then ascends 120 m. Find its final position.

Step-by-Step Solution

The starting position is −150 m, since below sea level is negative. After descending 85 m further: −150 + (−85) = −235 m. After ascending 120 m: −235 + 120 = −115 m.

Answer: The submarine is at 115 m below sea level, or −115 m.

Practice Problems

• A temperature starts at −3°C, rises 8°C by noon, then drops 5°C by evening. Find the temperature at each stage. → Multi-step Addition and Subtraction
• A diver is at −45 m and a bird flies at +120 m. Find the vertical distance between them. → Finding Distance Using Difference
• In a quiz, correct answers earn +5 marks and wrong answers lose 2 marks. A student gets 12 right and 5 wrong. Find the total score. → Real-world Scoring Problem
• A lift starts at ground floor. It goes up 12, down 5, up 8, then down 15 floors. Where does it end up? → Tracking Position Through Multiple Operations
• A business makes ₹15,000 profit in January, loses ₹8,000 in February, and profits ₹12,000 in March. Find the net result. → Profit and Loss with Integers
• A bank account starts at ₹5,000 and goes through multiple deposits and withdrawals. Find the final balance, then add withdrawal charges. → Multi-transaction Banking Problem

Scoring Guide

• 20–24 marks: Excellent! You are ready for properties of integers, integer equations, and coordinate geometry.
• 15–19 marks: Very Good! Practice sign rules for multiplication and division daily. Focus on multi-step word problems.
• 10–14 marks: Good Effort! Review addition and subtraction rules thoroughly. Use a number line to visualise operations.
• 0–9 marks: Keep Trying! Start with addition and subtraction only. Use real-life examples like temperature and money to build understanding.

Tips and Common Mistakes

The sign rules for multiplication and division trip up most students. Same signs always give a positive result. Different signs always give a negative result. Memorise this and apply it every time.

Subtracting a negative number is the same as adding a positive. So 5 − (−3) becomes 5 + 3 = 8. Students often get this wrong by subtracting instead.

When adding two negative numbers, do not subtract them. The result becomes more negative. For example, (−5) + (−3) = −8, not −2.

Always write out the signs clearly in your working. Skipping this step is where most calculation errors creep in.

For word problems, assign signs before calculating. Decide which direction is positive and which is negative, then translate the problem into integer operations.

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