Learning Objectives
- Identify clue words that tell which operation (add, subtract, multiply, divide) to use.
- Solve word problems using addition, subtraction, multiplication, and division.
- Solve multi-step word problems that use two operations.
- Use the estimate-and-check approach to verify answers.
Let Us Begin!
Maths is not just about numbers on a page -- it is everywhere around us! When your mother counts money at the vegetable market, when your father divides sweets equally among family members, or when you figure out how many days are left until your birthday -- you are solving word problems.
The trick to solving word problems is to read carefully, find the clue words, decide which operation to use, and then solve step by step. Let us learn how!
[Image: A flowchart showing problem-solving steps: "Read the problem" → "Identify what is given" → "Identify what to find" → "Choose operation (+, −, ×, ÷)" → "Solve" → "Check your answer". Title: "Steps to Solve a Word Problem".]
Clue Words -- Finding the Right Operation
Certain words in a problem give you a hint about which operation to use:
| Operation | Clue Words | What It Means |
|---|
| Addition (+) | total, altogether, in all, sum, combined, both, more than, increased by | Putting amounts together to find a bigger number |
| Subtraction (-) | left, remaining, difference, fewer, less than, how many more, decreased by, gave away | Taking away or finding how much more one amount is than another |
| Multiplication (x) | each, every, groups of, times, per, rows of, twice, thrice | Adding the same number many times; equal groups |
| Division (÷) | share equally, divide, distribute, split, per person, each gets, how many groups | Splitting into equal parts or finding how many equal groups |
Think: If a problem says "Ravi had 50 marbles and gave away 18," which clue word tells you to subtract? The words "gave away" tell you something was taken away.
Worked Examples -- One Operation
Example 1: Addition
Problem: A school in Jaipur has 486 boys and 397 girls. How many students are there altogether?
Clue word: "altogether" means add.
Solution: 486 + 397 = 883. There are 883 students altogether.
Example 2: Subtraction
Problem: A fruit seller in Mumbai had 750 mangoes. He sold 468 mangoes. How many mangoes are left?
Clue word: "left" means subtract.
Solution: 750 - 468 = 282. There are 282 mangoes left.
Example 3: Multiplication
Problem: A bus has 45 seats. If there are 8 such buses, how many seats are there in all the buses?
Clue word: "each" bus has 45 seats, and we need the total for 8 buses -- multiply.
Solution: 45 x 8 = 360. There are 360 seats in all.
Example 4: Division
Problem: Grandmother brought 96 laddoos for Diwali. She wants to share them equally among 8 neighbours. How many laddoos will each neighbour get?
Clue word: "share equally" means divide.
Solution: 96 ÷ 8 = 12. Each neighbour will get 12 laddoos.
Multi-Step Problems (Two Operations)
Some problems need more than one step. Read carefully and solve one step at a time.
Example 5: Addition + Subtraction
Problem: Aarav had Rs 500. His father gave him Rs 250 more. He then bought a book for Rs 175. How much money does Aarav have now?
Step 1: Total money = 500 + 250 = Rs 750.
Step 2: Money left = 750 - 175 = Rs 575. Aarav has Rs 575.
Example 6: Multiplication + Addition
Problem: A shopkeeper in Kolkata sold 6 packets of biscuits at Rs 35 each and 4 bottles of juice at Rs 20 each. What was the total sale?
Step 1: Biscuits = 6 x 35 = Rs 210.
Step 2: Juice = 4 x 20 = Rs 80.
Step 3: Total = 210 + 80 = Rs 290.
Estimate-and-Check Approach
Before solving a problem, make a quick estimate (a rough guess) by rounding the numbers. After solving, check if your answer is close to the estimate. If it is very different, you may have made a mistake.
Example: Estimate and Check
Problem: A farmer harvested 387 kg of wheat and 214 kg of rice. What is the total harvest?
Estimate: Round 387 to 400 and 214 to 200. Estimate = 400 + 200 = about 600 kg.
Exact answer: 387 + 214 = 601 kg. The estimate (600) is very close to 601, so the answer is correct.
Key Words
| Word | Meaning |
|---|
| Clue word | A word in the problem that hints at which operation to use |
| Altogether / Total | Clue words for addition -- combine amounts |
| Remaining / Left | Clue words for subtraction -- find what is left after taking away |
| Each / Groups of | Clue words for multiplication -- equal groups |
| Share equally | Clue words for division -- split into equal parts |
| Estimate | A rough answer found by rounding numbers; used to check if the exact answer makes sense |
⭐ Key Points to Remember
- Read the problem carefully. Underline the clue words and the question.
- Clue words: total/altogether = add; left/remaining = subtract; each/groups = multiply; share equally = divide.
- For multi-step problems, solve one step at a time.
- Use estimate-and-check: round numbers, estimate the answer, then solve and compare.
- Always write the unit (Rs, kg, km, etc.) with your answer.
Practice Questions
A. Identify the Operation (Write +, -, x, or ÷)
1. "How many pencils are left?"
2. "What is the total cost?"
3. "If each box has 12 apples..."
4. "Divide equally among 5 friends."
B. Solve the Word Problems (Show your working)
1. A train from Delhi to Chennai covers 1,243 km on the first day and 1,089 km on the second day. What is the total distance covered?
2. Meena had Rs 1,000. She spent Rs 365 on books and Rs 240 on a bag. How much money is remaining?
3. A school ordered 24 boxes of chalk. Each box has 50 pieces. How many pieces of chalk were ordered in all?
4. A farmer has 432 oranges. He packs them equally into 9 baskets. How many oranges are in each basket?
5. There are 28 students in each class. If there are 6 classes in the school, how many students are there altogether?
6. Ravi collected 215 stamps in January and 189 stamps in February. He gave 120 stamps to his friend. How many stamps does he have now?
7. A shopkeeper bought 8 cartons of mangoes. Each carton has 36 mangoes. He sold 195 mangoes by evening. How many mangoes are left?
8. Mother bought 5 kg of rice at Rs 60 per kg and 3 kg of sugar at Rs 45 per kg. What was the total amount she paid?
9. A library has 1,560 books. If 780 books are in English and the rest are in Hindi, how many Hindi books are there?
10. A factory makes 125 toys every day. How many toys will it make in 7 days?
11. Grandma made 240 gulab jamuns for a wedding. She arranged them equally on 8 plates. How many gulab jamuns are on each plate?
12. A bus can carry 52 passengers. If 3 buses are full and a fourth bus has only 38 passengers, how many passengers are there in total?
C. Multiple Choice Questions
1. The clue word "remaining" tells us to:
(a) add(b) subtract(c) multiply(d) divide
2. If 5 friends share 45 toffees equally, each friend gets:
(a) 40(b) 50(c) 9(d) 225
3. Estimate of 298 + 412 (by rounding to nearest hundred) is:
(a) 600(b) 700(c) 710(d) 800
🎨 Think and Do -- Fun Activity
Create Your Own Word Problems: Use the information below to write one word problem for each operation. Then swap with a classmate and solve each other's problems!
| Operation | Your Word Problem |
|---|
| Addition | |
| Subtraction | |
| Multiplication | |
| Division | |
Classmate's name who solved your problems: ____________________________