Integer Word Problems

• Translate real-life situations into integer expressions using positive and negative numbers.
• Model changes such as deposits/withdrawals, temperature rise/fall, elevation gain/loss, and score changes.
• Choose the correct operation (addition or subtraction of integers) from the context.
• Interpret the final sign of an answer in everyday language.

1. Assigning signs to quantities

   • Gain, profit, rise, deposit, north, above sea level → often represented by positive integers.
   • Loss, fall, withdraw, south, below sea level, debt → often represented by negative integers.
   • Read the problem carefully — the key word tells you the sign.

2. Modelling a sequence of changes — Add each change to the starting value:

   • Starting balance + deposit + withdrawal = final balance.
   • Starting temperature + rise + fall = final temperature.

3. Finding the net change — Net change = final value − initial value.
   A negative net change means a decrease; a positive net change means an increase.

4. Comparing quantities — "How much higher/lower?" means subtract the smaller value from the larger, paying attention to direction.

5. Problem-solving steps (CBSE method)

   1. Read and underline given numbers and what is asked.
   2. Assign +/− signs based on context.
   3. Write an integer expression.
   4. Calculate step by step.
   5. Write the answer with units and check if the sign makes sense.

The temperature at 6 a.m. was −5 °C. By noon it rose by 8 °C, and by 6 p.m. it fell by 3 °C. Find the temperature at 6 p.m.

Step 1 — starting temperature: −5 °C
Step 2 — rise of 8 °C means add +8: −5 + 8 = 3 °C (at noon)
Step 3 — fall of 3 °C means add −3: 3 + (−3) = 0 °C
Answer: 0 °C at 6 p.m.
Check: net change = +8 − 3 = +5; −5 + 5 = 0 ✓

Mohan deposited ₹500 and then withdrew ₹750 from his bank account. If he started with ₹200, what is his balance now?

Step 1 — starting balance: +200
Step 2 — deposit +500: 200 + 500 = 700
Step 3 — withdrawal −750: 700 + (−750) = −50
Answer: ₹−50 (he owes ₹50, i.e. an overdraft of ₹50)

• A submarine at −40 m dives 15 m deeper. What is its new depth? (−55 m)
• A team scored +12, −5, and +8 in three rounds starting from 0. What is the total? (15 points)
• An elevator starts at the ground floor (0), goes up 6 floors, then down 9 floors. Where is it? (Floor −3, i.e. 3 floors below ground if basements are numbered negatively)

Open the Practice tab for graded integer word problems.