Word Problems on Integers
Integers (positive and negative whole numbers and zero) appear in many real-life situations: temperature, altitude, bank transactions, and floor levels. Word problems on integers test your ability to add, subtract, multiply, and divide integers in context.
The key is to assign positive and negative signs correctly based on the context.
What is Word Problems on Integers - Grade 7 Maths (Integers)?
Sign conventions in word problems:
- Positive (+): Gain, deposit, above sea level, rise in temperature, floor above ground.
- Negative (−): Loss, withdrawal, below sea level, drop in temperature, basement floor.
Word Problems on Integers Formula
Steps to solve:
- Read the problem and assign positive/negative signs to values.
- Identify the operation (add, subtract, multiply, divide).
- Calculate using integer rules.
- Interpret the answer in context.
Types and Properties
Common contexts:
- Temperature: Rise (+), fall (−).
- Money: Earn/deposit (+), spend/withdraw (−).
- Altitude: Above sea level (+), below sea level (−).
- Building floors: Above ground (+), basement (−).
Solved Examples
Example 1: Temperature Problem
Problem: The temperature at noon is 5°C. By midnight it drops by 8°C. What is the midnight temperature?
Solution:
- Temperature = 5 + (−8) = 5 − 8 = −3°C
Answer: −3°C.
Example 2: Bank Balance
Problem: Ravi has ₹2,000 in his account. He withdraws ₹3,500. What is his balance?
Solution:
- Balance = 2000 − 3500 = −1,500 (overdrawn by ₹1,500)
Answer: −₹1,500 (overdraft).
Example 3: Altitude Problem
Problem: A submarine is at −200 m (below sea level). It rises 75 m. What is its new position?
Solution:
- New position = −200 + 75 = −125 m
Answer: 125 m below sea level.
Example 4: Profit and Loss
Problem: A shopkeeper makes profits of ₹500, ₹300, and losses of ₹200 and ₹400 over 4 days. Find the net result.
Solution:
- Net = 500 + 300 + (−200) + (−400) = 800 − 600 = ₹200 profit
Answer: Net profit of ₹200.
Real-World Applications
Real-world uses:
- Weather reports: Temperature readings use positive and negative integers.
- Finance: Credit and debit in bank accounts.
- Geography: Heights above and depths below sea level.
- Sports: Scores above or below par in golf.
Key Points to Remember
- Assign positive and negative signs based on context.
- Rise/gain/deposit = positive. Drop/loss/withdrawal = negative.
- Add positives and negatives using integer rules.
- A negative answer means the opposite direction (loss, below zero, etc.).
Practice Problems
- The temperature is −7°C. It rises by 12°C. What is the new temperature?
- A lift goes from floor 3 to basement 2. How many floors did it move?
- Priya earns ₹4,000 and spends ₹5,500. What is her financial position?
- A bird at 50 m altitude dives 80 m into the sea. What is its position?
Frequently Asked Questions
Q1. How do you decide the sign in integer word problems?
Use context: gains, rises, deposits are positive. Losses, drops, withdrawals are negative.
Q2. What does a negative answer mean?
It means the result is in the opposite direction: below zero temperature, below sea level, overdraft in bank, etc.
Q3. Can you multiply in word problems on integers?
Yes. For example, if temperature drops 3°C every hour for 5 hours: total change = (−3) × 5 = −15°C.
