Word Problems on Four Operations
Word problems on four operations require students to read a real-life situation, identify which operation(s) to use — addition, subtraction, multiplication, or division — and then solve step by step.
In Class 5, word problems often involve multiple steps and a mix of operations. The challenge is not just calculating, but understanding what the question is asking and choosing the right operation.
This topic builds on all four arithmetic operations and connects maths to everyday situations like shopping, travel, sharing, and scoring. A Class 5 student should be able to solve problems that combine two or three operations in a single question.
The RUPAC method helps solve word problems systematically:
- R — Read the problem carefully
- U — Understand what is given and what is asked
- P — Plan which operation(s) to use
- A — Answer by calculating step by step
- C — Check if the answer is reasonable
What is Word Problems on Four Operations - Class 5 Maths (Operations)?
Word problems are mathematical questions presented in the form of a story or real-life scenario. To solve them:
- Read the problem carefully — twice if needed.
- Identify the given information and what you need to find.
- Choose the correct operation(s).
- Calculate step by step.
- Check if the answer makes sense.
Keyword guide:
| Operation | Keywords |
|---|---|
| Addition | total, altogether, combined, sum, in all, both, together, increased by |
| Subtraction | difference, how many more, how many less, remaining, left, decreased by, gave away |
| Multiplication | times, each, every, per, total of equal groups, product |
| Division | equally, share, distribute, per group, split, divided into, how many groups |
Multi-step problems use two or more operations. Read the entire problem before starting, and solve one step at a time.
Solved Examples
Example 1: Example 1: Addition — Combining Amounts
Problem: Ria collected 12,450 stamps in the first year and 8,375 stamps in the second year. How many stamps does she have in total?
Solution:
Step 1: Operation needed: Addition ("in total")
Step 2: 12,450 + 8,375 = 20,825
Answer: Ria has 20,825 stamps in total.
Example 2: Example 2: Subtraction — Finding the Difference
Problem: A school had 4,560 books. They donated 1,285 books to a library. How many books are left?
Solution:
Step 1: Operation needed: Subtraction ("left")
Step 2: 4,560 - 1,285 = 3,275
Answer: 3,275 books are left.
Example 3: Example 3: Multiplication — Equal Groups
Problem: A mango seller packs 36 mangoes in each crate. He has 245 crates. How many mangoes does he have?
Solution:
Step 1: Operation needed: Multiplication ("each", equal groups)
Step 2: 36 x 245 = 8,820
Answer: He has 8,820 mangoes.
Example 4: Example 4: Division — Equal Sharing
Problem: Arjun has ₹7,500. He wants to buy cricket bats costing ₹250 each. How many bats can he buy?
Solution:
Step 1: Operation needed: Division ("how many" groups of ₹250)
Step 2: 7,500 / 250 = 30
Answer: Arjun can buy 30 cricket bats.
Example 5: Example 5: Two-Step — Multiplication and Addition
Problem: Priya earns ₹1,200 per day on weekdays and ₹1,800 per day on weekends. How much does she earn in a week? (5 weekdays + 2 weekend days)
Solution:
Step 1: Weekday earnings = 5 x 1,200 = ₹6,000
Step 2: Weekend earnings = 2 x 1,800 = ₹3,600
Step 3: Total = 6,000 + 3,600 = ₹9,600
Answer: Priya earns ₹9,600 in a week.
Example 6: Example 6: Two-Step — Multiplication and Subtraction
Problem: A shopkeeper had 5,000 toffees. He sold 48 packets with 75 toffees each. How many toffees are left?
Solution:
Step 1: Toffees sold = 48 x 75 = 3,600
Step 2: Toffees left = 5,000 - 3,600 = 1,400
Answer: 1,400 toffees are left.
Example 7: Example 7: Three-Step — All Operations
Problem: Aman has ₹10,000. He buys 12 notebooks at ₹65 each and 8 pens at ₹25 each. He then divides the remaining money equally among his 4 siblings. How much does each sibling get?
Solution:
Step 1: Cost of notebooks = 12 x 65 = ₹780
Step 2: Cost of pens = 8 x 25 = ₹200
Step 3: Total spent = 780 + 200 = ₹980
Step 4: Remaining = 10,000 - 980 = ₹9,020
Step 5: Each sibling gets = 9,020 / 4 = ₹2,255
Answer: Each sibling gets ₹2,255.
Example 8: Example 8: Comparison Problem
Problem: School A has 1,245 students and School B has 3 times as many students as School A. How many students are there in both schools combined?
Solution:
Step 1: School B students = 3 x 1,245 = 3,735
Step 2: Total = 1,245 + 3,735 = 4,980
Answer: Both schools have 4,980 students combined.
Example 9: Example 9: Distance and Time
Problem: An auto-rickshaw travels 45 km in one trip. It makes 6 trips per day. After 5 days, how many kilometres has it covered?
Solution:
Step 1: Distance per day = 45 x 6 = 270 km
Step 2: Distance in 5 days = 270 x 5 = 1,350 km
Answer: The auto-rickshaw has covered 1,350 km.
Example 10: Example 10: Surplus and Shortage
Problem: A school needs 2,400 chapatis for a community lunch. The kitchen can make 150 chapatis per batch. After making 14 batches, how many more chapatis are needed?
Solution:
Step 1: Chapatis made = 150 x 14 = 2,100
Step 2: More needed = 2,400 - 2,100 = 300
Answer: 300 more chapatis are needed.
Real-World Applications
Where word problems on four operations are used:
- Shopping: Calculating total cost when buying different items, finding change, and comparing unit prices. Example: 3 kg rice at ₹65/kg + 2 kg sugar at ₹45/kg = ₹195 + ₹90 = ₹285.
- Travel: Finding distance, time, and fuel requirements. If a car uses 8 litres per 100 km, how much fuel for 350 km? (8 x 3.5 = 28 litres)
- Cooking: Scaling recipes up or down. A recipe for 4 people uses 200 g flour — for 10 people, you need 200 x 10 / 4 = 500 g.
- Sports: Calculating averages (total runs / matches), totals (runs per over x overs), and differences (winning margin).
- School events: Budgeting for a trip, distributing prizes, counting chairs for an assembly.
- Banking: Deposits, withdrawals, and simple interest calculations.
Common patterns in multi-step problems:
| Pattern | Operations Used | Example |
|---|---|---|
| Buy multiple items, find total | Multiplication + Addition | 4 books at ₹85 + 3 pens at ₹20 |
| Buy items, find change | Multiplication + Subtraction | ₹500 - total cost |
| Make items, find shortage | Multiplication + Subtraction | Target - items made |
| Earn and spend, find savings per month | Subtraction + Multiplication | (Income - Expenses) x months |
| Distribute equally, find per-person share | Addition + Division | Total collected / number of people |
Key Points to Remember
- Read the problem carefully before choosing an operation. Read it twice if needed.
- Look for keywords: "total" (add), "left" (subtract), "each" (multiply), "equally" (divide).
- Multi-step problems require solving one step at a time. Write intermediate answers clearly.
- Always label your answer with units (₹, km, kg, items).
- Check your answer by asking: Does it make sense? Is it too large or too small?
- Draw a picture or diagram if the problem is confusing.
- Identify what is given and what is asked before solving.
- Use estimation to verify your final answer is in the right range.
Practice Problems
- A train carries 1,850 passengers per trip. How many passengers does it carry in 15 trips?
- Dev had ₹25,000. He spent ₹8,750 on a phone and ₹3,200 on a cover. How much money is left?
- A factory makes 2,340 toys per day. It packs them in boxes of 18. How many boxes are filled daily?
- Neha reads 45 pages per day. How many pages will she read in 4 weeks (28 days)?
- A school ordered 36 boxes of pencils with 144 pencils each. 850 pencils were found defective. How many good pencils are there?
- Aditi earns ₹15,600 per month. She spends ₹9,450 and saves the rest. How much does she save in 6 months?
- A cricket team scored 245, 312, and 198 runs in three matches. What is their average score per match?
- A garden has 24 rows with 35 plants each. 156 plants dried up. How many healthy plants are left?
Frequently Asked Questions
Q1. How do you decide which operation to use in a word problem?
Look for keywords. "Total" or "altogether" means addition. "Left" or "remaining" means subtraction. "Each" or "per" with equal groups means multiplication. "Share equally" or "distribute" means division. In multi-step problems, you may need more than one operation.
Q2. What is a multi-step word problem?
A multi-step word problem requires two or more operations to find the answer. For example, finding the total cost of different items (multiplication), then subtracting from the budget (subtraction). Solve one step at a time.
Q3. How do you check if a word problem answer is correct?
Work backwards using the inverse operation. If you added to find a total, subtract to check. If you multiplied, divide. Also ask: Does the answer make sense in the context? A person's change cannot be more than what they paid.
Q4. What if a word problem uses all four operations?
Break the problem into smaller parts. Identify what each sentence tells you and what operation it requires. Solve step by step, writing each intermediate result clearly. Then combine the results according to BODMAS.
Q5. Why do word problems use Indian names and contexts?
Word problems use familiar names, places, and situations so students can relate to them. Using Indian currency (₹), local food (mangoes, chapatis), and everyday scenarios (auto-rickshaw, cricket) makes the problems easier to understand and more engaging.
Q6. How do you handle remainders in word problems?
It depends on the context. If packing items into boxes, a remainder means one extra partially-filled box is needed (round up). If distributing money equally, the remainder is what is left over. Always state the remainder clearly in your answer.
Q7. What is the difference between 'how many more' and 'how many in all'?
'How many more' asks for the difference between two quantities — use subtraction. 'How many in all' asks for the total — use addition. Reading the question carefully helps you choose the right operation.
Q8. Can estimation help with word problems?
Yes. Before solving, round the numbers and estimate the answer. If your exact answer is close to the estimate, it is likely correct. If it is very different, recheck your calculation.
Q9. What are comparison word problems?
These problems compare two quantities using phrases like 'times as many', 'twice as much', or 'more than'. For example, 'School B has 3 times as many students as School A.' Multiply or divide depending on what is asked.
Q10. Should I always write the operation before solving?
Yes. Writing the mathematical expression before calculating helps avoid mistakes. For example, write '48 x 75 = ?' before computing. It also helps your teacher see your thinking process.
Related Topics
- Order of Operations (BODMAS)
- Addition of Large Numbers
- Subtraction of Large Numbers
- Multiplication of Large Numbers
- Division of Large Numbers
- Mental Math (Grade 5)
- Multiplication of 4-Digit Numbers
- Division of 4-Digit by 2-Digit Numbers
- Simplification Using BODMAS
- Properties of Operations (Grade 5)
- Unitary Method (Grade 5)
- Mixed Word Problems (Grade 5)
