Maths
Word Problems
Learning Objectives
- Understand what a word problem is and how it differs from a plain sum.
- Identify the correct operation (addition, subtraction, multiplication, or division) from the problem.
- Recognise key words that signal which operation to use.
- Solve addition and subtraction word problems involving 3-digit and 4-digit numbers.
- Solve multiplication and division word problems using tables up to 10.
- Solve multi-step word problems that need more than one operation.
- Check answers by re-reading the problem and verifying the solution makes sense.
What is a Word Problem?
A word problem is a maths question written as a story. Instead of just seeing numbers and signs like "25 + 18 = ?", you read a short story and figure out what to do with the numbers.
Word problems help us use maths in real life — when we go shopping, share sweets with friends, count cricket runs, or plan for a school trip!
Every word problem has three parts: information (what you know), a question (what you need to find), and a solution (the maths you do to get the answer).
How to Solve a Word Problem
Follow these 4 simple steps every time you see a word problem:
Step 1: READ — Read the problem carefully. Read it twice if needed. Understand the story.
Step 2: IDENTIFY — Find the numbers. Look for key words. Decide which operation to use (add, subtract, multiply, or divide).
Step 3: SOLVE — Write the number sentence (equation). Do the calculation carefully.
Step 4: CHECK — Does your answer make sense? Re-read the question. Is the answer too big or too small? Write the answer in a complete sentence.
Step 2: IDENTIFY — Find the numbers. Look for key words. Decide which operation to use (add, subtract, multiply, or divide).
Step 3: SOLVE — Write the number sentence (equation). Do the calculation carefully.
Step 4: CHECK — Does your answer make sense? Re-read the question. Is the answer too big or too small? Write the answer in a complete sentence.
Remember: The most important step is READING carefully. Many mistakes happen because students don't read the full problem!
Key Words That Tell You Which Operation to Use
Certain words in a problem give you a clue about which operation to use. Here is a helpful chart:
| Operation | Key Words | What It Means |
|---|---|---|
| Addition (+) | total, sum, altogether, in all, combined, both, more than, increased by | Putting things together to find how many in all |
| Subtraction (−) | left, remaining, difference, less than, fewer, took away, gave away, how many more | Taking away or finding how much is left |
| Multiplication (×) | each, times, groups of, rows of, every, twice, thrice, double, triple | Adding the same number many times |
| Division (÷) | share, divide, equally, per, split, distribute, each gets, how many groups | Splitting into equal parts or groups |
⚠️ Be careful! Sometimes "more" can mean addition OR subtraction. "How many more does Ravi have than Sita?" means SUBTRACT to find the difference!
Addition Word Problems
Use addition when you need to find the total or put things together.
Problem 1: Aarav bought a notebook for ₹45 and a pencil box for ₹78 from the school stationery shop. How much did he spend in all?
Key word: "in all" → Addition
Solution: ₹45 + ₹78 = ₹123
Answer: Aarav spent ₹123 in all.
Key word: "in all" → Addition
Solution: ₹45 + ₹78 = ₹123
Answer: Aarav spent ₹123 in all.
Problem 2: In a cricket match, India scored 246 runs in the first innings and 189 runs in the second innings. What was India's total score?
Key word: "total" → Addition
Solution: 246 + 189 = 435
Answer: India's total score was 435 runs.
Key word: "total" → Addition
Solution: 246 + 189 = 435
Answer: India's total score was 435 runs.
Problem 3: During Diwali, Meena made 156 diyas and her sister made 127 diyas. How many diyas did they make altogether?
Key word: "altogether" → Addition
Solution: 156 + 127 = 283
Answer: They made 283 diyas altogether.
Key word: "altogether" → Addition
Solution: 156 + 127 = 283
Answer: They made 283 diyas altogether.
Problem 4: A train from Delhi to Jaipur carries 385 passengers. At Gurgaon station, 148 more passengers board the train. How many passengers are on the train now?
Key word: "more... board" → Addition
Solution: 385 + 148 = 533
Answer: There are 533 passengers on the train now.
Key word: "more... board" → Addition
Solution: 385 + 148 = 533
Answer: There are 533 passengers on the train now.
Subtraction Word Problems
Use subtraction when you need to find what is left, the difference, or how much more/less.
Problem 1: Priya had ₹500. She bought a book for ₹175 at the bazaar. How much money is left with her?
Key word: "left" → Subtraction
Solution: ₹500 − ₹175 = ₹325
Answer: Priya has ₹325 left.
Key word: "left" → Subtraction
Solution: ₹500 − ₹175 = ₹325
Answer: Priya has ₹325 left.
Problem 2: There are 432 students in Sunrise Public School. If 198 are girls, how many are boys?
Key word: "how many are boys" (finding remaining) → Subtraction
Solution: 432 − 198 = 234
Answer: There are 234 boys in the school.
Key word: "how many are boys" (finding remaining) → Subtraction
Solution: 432 − 198 = 234
Answer: There are 234 boys in the school.
Problem 3: Rohit scored 87 runs in a cricket match. Virat scored 63 runs. How many more runs did Rohit score than Virat?
Key word: "how many more" → Subtraction (finding difference)
Solution: 87 − 63 = 24
Answer: Rohit scored 24 more runs than Virat.
Key word: "how many more" → Subtraction (finding difference)
Solution: 87 − 63 = 24
Answer: Rohit scored 24 more runs than Virat.
Problem 4: A shopkeeper had 650 packets of chips. He sold 278 packets during the Holi festival. How many packets are remaining?
Key word: "remaining" → Subtraction
Solution: 650 − 278 = 372
Answer: 372 packets are remaining.
Key word: "remaining" → Subtraction
Solution: 650 − 278 = 372
Answer: 372 packets are remaining.
Multiplication Word Problems
Use multiplication when you have equal groups and need to find the total, or when something happens many times.
Problem 1: There are 7 rows of chairs in the school assembly hall. Each row has 8 chairs. How many chairs are there in all?
Key word: "each row has" → Multiplication
Solution: 7 × 8 = 56
Answer: There are 56 chairs in all.
Key word: "each row has" → Multiplication
Solution: 7 × 8 = 56
Answer: There are 56 chairs in all.
Problem 2: Anita buys 5 packets of bindis for Diwali. Each packet has 12 bindis. How many bindis does she have in total?
Key word: "each packet has" → Multiplication
Solution: 5 × 12 = 60
Answer: Anita has 60 bindis in total.
Key word: "each packet has" → Multiplication
Solution: 5 × 12 = 60
Answer: Anita has 60 bindis in total.
Problem 3: A bus makes 4 trips every day between two cities. How many trips does it make in 6 days?
Key word: "every day... in 6 days" → Multiplication
Solution: 4 × 6 = 24
Answer: The bus makes 24 trips in 6 days.
Key word: "every day... in 6 days" → Multiplication
Solution: 4 × 6 = 24
Answer: The bus makes 24 trips in 6 days.
Problem 4: Ravi's mother makes 9 rotis for dinner every night. How many rotis does she make in a week (7 days)?
Key word: "every night... in a week" → Multiplication
Solution: 9 × 7 = 63
Answer: She makes 63 rotis in a week.
Key word: "every night... in a week" → Multiplication
Solution: 9 × 7 = 63
Answer: She makes 63 rotis in a week.
Division Word Problems
Use division when you need to share equally, split into groups, or find how many in each group.
Problem 1: Grandma has 36 laddoos. She wants to share them equally among her 4 grandchildren. How many laddoos will each child get?
Key word: "share equally" → Division
Solution: 36 ÷ 4 = 9
Answer: Each child will get 9 laddoos.
Key word: "share equally" → Division
Solution: 36 ÷ 4 = 9
Answer: Each child will get 9 laddoos.
Problem 2: A teacher has 45 notebooks to distribute equally among 9 students. How many notebooks will each student get?
Key word: "distribute equally" → Division
Solution: 45 ÷ 9 = 5
Answer: Each student will get 5 notebooks.
Key word: "distribute equally" → Division
Solution: 45 ÷ 9 = 5
Answer: Each student will get 5 notebooks.
Problem 3: There are 56 mangoes in a basket. If we pack them into bags of 8 mangoes each, how many bags do we need?
Key word: "bags of 8 each" (how many groups) → Division
Solution: 56 ÷ 8 = 7
Answer: We need 7 bags.
Key word: "bags of 8 each" (how many groups) → Division
Solution: 56 ÷ 8 = 7
Answer: We need 7 bags.
Problem 4: A train journey from Mumbai to Pune takes 3 hours. If the total distance is 150 km, how many kilometres does the train travel per hour?
Key word: "per hour" → Division
Solution: 150 ÷ 3 = 50
Answer: The train travels 50 km per hour.
Key word: "per hour" → Division
Solution: 150 ÷ 3 = 50
Answer: The train travels 50 km per hour.
Multi-Step Word Problems
Some problems need more than one step to solve. You may need to add first, then subtract — or multiply first, then add. Read carefully!
Problem 1: Sita went to the bazaar with ₹200. She bought a doll for ₹85 and a colouring book for ₹45. How much money does she have left?
Step 1: Find total spent: ₹85 + ₹45 = ₹130 (Addition)
Step 2: Find money left: ₹200 − ₹130 = ₹70 (Subtraction)
Answer: Sita has ₹70 left.
Step 1: Find total spent: ₹85 + ₹45 = ₹130 (Addition)
Step 2: Find money left: ₹200 − ₹130 = ₹70 (Subtraction)
Answer: Sita has ₹70 left.
Problem 2: A school ordered 6 boxes of pencils. Each box has 10 pencils. The teacher gave away 18 pencils to students. How many pencils are left?
Step 1: Find total pencils: 6 × 10 = 60 (Multiplication)
Step 2: Find pencils left: 60 − 18 = 42 (Subtraction)
Answer: 42 pencils are left.
Step 1: Find total pencils: 6 × 10 = 60 (Multiplication)
Step 2: Find pencils left: 60 − 18 = 42 (Subtraction)
Answer: 42 pencils are left.
Key Words Table
| Word / Phrase | Operation | Example |
|---|---|---|
| Total / Sum / Altogether / In all / Combined | Addition (+) | "How many in all?" → Add |
| Left / Remaining / Difference / Fewer / Took away | Subtraction (−) | "How many are left?" → Subtract |
| Each / Times / Groups of / Rows of / Every | Multiplication (×) | "5 groups of 4" → Multiply |
| Share / Equally / Per / Split / Distribute | Division (÷) | "Share 20 among 4" → Divide |
| How many more / How much more | Subtraction (−) | "How many more than?" → Subtract |
| Twice / Double / Thrice / Triple | Multiplication (×) | "Twice as many" → Multiply by 2 |
⭐ Key Points to Remember
- A word problem is a maths question written as a story.
- Always follow the 4 steps: Read → Identify → Solve → Check.
- Look for key words to decide which operation to use.
- Addition: finding total, putting together, combining.
- Subtraction: finding what's left, difference, how many more.
- Multiplication: equal groups, repeated addition, "each" or "every".
- Division: sharing equally, splitting into groups, "per" or "each gets".
- Some problems need two steps — solve one part first, then use that answer for the next part.
- Always write your answer in a complete sentence with the correct unit (₹, km, kg, etc.).
- Check: Does your answer make sense? Is it too big or too small?
Finished learning? Now test what you know!