Multi-step word problems.
Subtopic Navigator
- Introduction to Multi-Step Word Problems
- Problem Solving Strategies
- Addition and Subtraction Multi-Step Problems
- Multiplication and Division Multi-Step Problems
- Mixed Operations Problems
- Methods & Techniques
- Common Mistakes & Misconceptions
- Real-World Applications
- Practice Exercises
- Conclusion & Summary
Lesson Objectives
- Read and understand multi-step word problems carefully
- Identify the steps needed to solve a problem
- Choose the correct operations (addition, subtraction, multiplication, division)
- Solve problems in the correct order
- Check answers for reasonableness using estimation
- Apply problem-solving strategies to real-world situations
Introduction to Multi-Step Word Problems
Multi-step word problems require more than one mathematical operation to find the answer. They help us solve real-life situations that involve several steps, such as shopping, budgeting, cooking, or planning a trip. Solving these problems builds critical thinking and prepares you for more advanced mathematics.
What is a Multi-Step Word Problem?
A problem that requires two or more operations (addition, subtraction, multiplication, division) to find the final answer.
A problem that requires two or more operations (addition, subtraction, multiplication, division) to find the final answer.
Key Definitions:
• Multi-step problem: A problem that requires more than one mathematical operation to solve.
• Operation: Addition, subtraction, multiplication, or division.
• Hidden question: An intermediate answer needed before finding the final answer.
• Reasonable answer: An answer that makes sense based on estimation and context.
• Multi-step problem: A problem that requires more than one mathematical operation to solve.
• Operation: Addition, subtraction, multiplication, or division.
• Hidden question: An intermediate answer needed before finding the final answer.
• Reasonable answer: An answer that makes sense based on estimation and context.
Problem Solving Strategies
Solving multi-step word problems requires a systematic approach. The following strategies will help you break down complex problems into manageable steps.
Step-by-Step Problem Solving Method:
1. Read the problem carefully: Understand what is being asked.
2. Identify what is known: List all the given information.
3. Identify what is unknown: What do you need to find?
4. Determine the hidden questions: What intermediate answers do you need?
5. Plan the steps: Decide which operations to use and in what order.
6. Solve step by step: Perform each calculation carefully.
7. Check your answer: Is it reasonable? Does it make sense in the context?
8. Write the final answer: Include units and a complete sentence.
1. Read the problem carefully: Understand what is being asked.
2. Identify what is known: List all the given information.
3. Identify what is unknown: What do you need to find?
4. Determine the hidden questions: What intermediate answers do you need?
5. Plan the steps: Decide which operations to use and in what order.
6. Solve step by step: Perform each calculation carefully.
7. Check your answer: Is it reasonable? Does it make sense in the context?
8. Write the final answer: Include units and a complete sentence.
Problem Solving Flowchart
| Step | Action | Question to Ask |
|---|---|---|
| 1 | Read | What is the problem asking? |
| 2 | Identify | What information is given? |
| 3 | Plan | What steps are needed? |
| 4 | Solve | Perform calculations in order |
| 5 | Check | Does my answer make sense? |
Example: Using the Problem Solving Method
Problem: Sarah bought a shirt for ₦2,500 and a pair of shoes for ₦4,500. She gave the cashier ₦10,000. How much change did she receive?
Solution using the method:
Step 1: Read carefully → Need to find change.
Step 2: Known: shirt = ₦2,500, shoes = ₦4,500, paid = ₦10,000.
Step 3: Plan: First find total cost, then subtract from amount paid.
Step 4: Total = 2,500 + 4,500 = 7,000; Change = 10,000 - 7,000 = 3,000.
Step 5: Check: 7,000 + 3,000 = 10,000 ✓
Answer: Sarah received ₦3,000 change.
Problem: Sarah bought a shirt for ₦2,500 and a pair of shoes for ₦4,500. She gave the cashier ₦10,000. How much change did she receive?
Solution using the method:
Step 1: Read carefully → Need to find change.
Step 2: Known: shirt = ₦2,500, shoes = ₦4,500, paid = ₦10,000.
Step 3: Plan: First find total cost, then subtract from amount paid.
Step 4: Total = 2,500 + 4,500 = 7,000; Change = 10,000 - 7,000 = 3,000.
Step 5: Check: 7,000 + 3,000 = 10,000 ✓
Answer: Sarah received ₦3,000 change.
Watch Out!
Don't rush! Read the problem at least twice before starting. Look for clue words that indicate which operation to use.
Don't rush! Read the problem at least twice before starting. Look for clue words that indicate which operation to use.
Practice for Problem Solving Strategies
- List the steps you would take to solve: "John had 120 oranges. He sold 45 on Monday and 38 on Tuesday. How many are left?"
- What is the hidden question in: "A baker bakes 24 loaves per hour. He works for 6 hours. He sells 85 loaves. How many are left?"
- Why is it important to check your answer after solving a multi-step problem?
Addition and Subtraction Multi-Step Problems
Many multi-step problems involve only addition and subtraction. These problems often ask for totals, differences, or remaining amounts after several changes.
Example 1: Finding Total After Multiple Purchases
Problem: A school bought 345 notebooks, 278 pencils, and 156 erasers. How many items did they buy in total?
Solution:
Step 1: Add notebooks and pencils: 345 + 278 = 623
Step 2: Add erasers: 623 + 156 = 779
Answer: The school bought 779 items.
Problem: A school bought 345 notebooks, 278 pencils, and 156 erasers. How many items did they buy in total?
Solution:
Step 1: Add notebooks and pencils: 345 + 278 = 623
Step 2: Add erasers: 623 + 156 = 779
Answer: The school bought 779 items.
Example 2: Finding Remaining Amount After Spending
Problem: Mrs. Ade had ₦15,000. She spent ₦4,500 on food, ₦3,200 on transport, and ₦2,800 on clothes. How much money does she have left?
Solution:
Step 1: Find total spent: 4,500 + 3,200 = 7,700; 7,700 + 2,800 = 10,500
Step 2: Subtract from starting amount: 15,000 - 10,500 = 4,500
Answer: Mrs. Ade has ₦4,500 left.
Problem: Mrs. Ade had ₦15,000. She spent ₦4,500 on food, ₦3,200 on transport, and ₦2,800 on clothes. How much money does she have left?
Solution:
Step 1: Find total spent: 4,500 + 3,200 = 7,700; 7,700 + 2,800 = 10,500
Step 2: Subtract from starting amount: 15,000 - 10,500 = 4,500
Answer: Mrs. Ade has ₦4,500 left.
Example 3: Comparing Populations
Problem: Town A has 45,678 people. Town B has 32,456 fewer people than Town A. Town C has 12,345 more people than Town B. What is the population of Town C?
Solution:
Step 1: Find Town B population: 45,678 - 32,456 = 13,222
Step 2: Find Town C population: 13,222 + 12,345 = 25,567
Answer: Town C has 25,567 people.
Problem: Town A has 45,678 people. Town B has 32,456 fewer people than Town A. Town C has 12,345 more people than Town B. What is the population of Town C?
Solution:
Step 1: Find Town B population: 45,678 - 32,456 = 13,222
Step 2: Find Town C population: 13,222 + 12,345 = 25,567
Answer: Town C has 25,567 people.
Watch Out!
When a problem says "fewer than," you subtract. When it says "more than," you add. Pay attention to the order!
When a problem says "fewer than," you subtract. When it says "more than," you add. Pay attention to the order!
Practice for Addition and Subtraction Multi-Step Problems
- A shop sold 234 bags of rice on Monday, 187 on Tuesday, and 256 on Wednesday. How many bags were sold in total?
- A man had ₦50,000. He paid ₦12,500 for rent, ₦8,750 for food, and ₦5,250 for electricity. How much is left?
- City X has 234,567 people. City Y has 45,678 fewer people. City Z has 23,456 more than City Y. Find City Z's population.
- A library had 12,345 books. They received 2,500 new books and then donated 1,200 books. How many books are now in the library?
- A car travelled 234 km, then another 156 km, then 89 km. How far did it travel in total?
Multiplication and Division Multi-Step Problems
Some multi-step problems involve multiplication and division. These often include finding totals from equal groups, sharing equally, or calculating rates.
Example 1: Finding Total from Equal Groups
Problem: A factory produces 234 bottles per hour. How many bottles are produced in 8 hours?
Solution:
234 × 8 = 1,872 bottles
Answer: 1,872 bottles
Problem: A factory produces 234 bottles per hour. How many bottles are produced in 8 hours?
Solution:
234 × 8 = 1,872 bottles
Answer: 1,872 bottles
Example 2: Multi-Step with Multiplication and Subtraction
Problem: A school ordered 24 boxes of notebooks. Each box contains 50 notebooks. If 345 notebooks were damaged, how many good notebooks are there?
Solution:
Step 1: Find total notebooks: 24 × 50 = 1,200
Step 2: Subtract damaged: 1,200 - 345 = 855
Answer: 855 good notebooks.
Problem: A school ordered 24 boxes of notebooks. Each box contains 50 notebooks. If 345 notebooks were damaged, how many good notebooks are there?
Solution:
Step 1: Find total notebooks: 24 × 50 = 1,200
Step 2: Subtract damaged: 1,200 - 345 = 855
Answer: 855 good notebooks.
Example 3: Division and Addition
Problem: 1,260 oranges are to be packed equally into 30 crates. How many oranges are in each crate?
Solution:
1,260 ÷ 30 = 42 oranges per crate
Answer: 42 oranges
Problem: 1,260 oranges are to be packed equally into 30 crates. How many oranges are in each crate?
Solution:
1,260 ÷ 30 = 42 oranges per crate
Answer: 42 oranges
Example 4: Multi-Step with Division and Multiplication
Problem: A car travels 480 km on 40 litres of fuel. How far can it travel on 25 litres?
Solution:
Step 1: Find distance per litre: 480 ÷ 40 = 12 km per litre
Step 2: Find distance for 25 litres: 12 × 25 = 300 km
Answer: 300 km
Problem: A car travels 480 km on 40 litres of fuel. How far can it travel on 25 litres?
Solution:
Step 1: Find distance per litre: 480 ÷ 40 = 12 km per litre
Step 2: Find distance for 25 litres: 12 × 25 = 300 km
Answer: 300 km
Watch Out!
In problems involving rates (like km per litre, cost per item), always find the unit rate first (how much per one unit).
In problems involving rates (like km per litre, cost per item), always find the unit rate first (how much per one unit).
Practice for Multiplication and Division Multi-Step Problems
- A bakery bakes 156 loaves of bread per hour. How many loaves in 12 hours?
- A school has 28 classes with 35 students in each class. If 120 students are absent, how many are present?
- 3,600 eggs are packed equally into 120 cartons. How many eggs in each carton?
- A car travels 540 km on 45 litres of fuel. How far on 30 litres?
- A farmer harvested 2,400 kg of rice. He packs it into 80 kg bags. How many bags does he fill?
Mixed Operations Problems
The most challenging multi-step problems combine all four operations: addition, subtraction, multiplication, and division. These problems require careful planning and attention to order.
Example 1: Shopping with Budget
Problem: Mr. John bought 5 shirts at ₦3,500 each and 3 pairs of trousers at ₦5,000 each. He paid with ₦50,000. How much change did he receive?
Solution:
Step 1: Cost of shirts: 5 × 3,500 = 17,500
Step 2: Cost of trousers: 3 × 5,000 = 15,000
Step 3: Total cost: 17,500 + 15,000 = 32,500
Step 4: Change: 50,000 - 32,500 = 17,500
Answer: ₦17,500 change
Problem: Mr. John bought 5 shirts at ₦3,500 each and 3 pairs of trousers at ₦5,000 each. He paid with ₦50,000. How much change did he receive?
Solution:
Step 1: Cost of shirts: 5 × 3,500 = 17,500
Step 2: Cost of trousers: 3 × 5,000 = 15,000
Step 3: Total cost: 17,500 + 15,000 = 32,500
Step 4: Change: 50,000 - 32,500 = 17,500
Answer: ₦17,500 change
Example 2: Profit Calculation
Problem: A trader bought 120 bags of rice at ₦15,000 each. He sold them at ₦18,000 each. What was his total profit?
Solution:
Step 1: Total cost: 120 × 15,000 = 1,800,000
Step 2: Total selling price: 120 × 18,000 = 2,160,000
Step 3: Profit: 2,160,000 - 1,800,000 = 360,000
Answer: ₦360,000 profit
Problem: A trader bought 120 bags of rice at ₦15,000 each. He sold them at ₦18,000 each. What was his total profit?
Solution:
Step 1: Total cost: 120 × 15,000 = 1,800,000
Step 2: Total selling price: 120 × 18,000 = 2,160,000
Step 3: Profit: 2,160,000 - 1,800,000 = 360,000
Answer: ₦360,000 profit
Example 3: Average Calculation
Problem: The scores of 5 students in a test are 85, 92, 78, 88, and 95. What is the average score?
Solution:
Step 1: Sum of scores: 85 + 92 = 177; 177 + 78 = 255; 255 + 88 = 343; 343 + 95 = 438
Step 2: Average: 438 ÷ 5 = 87.6
Answer: The average score is 87.6
Problem: The scores of 5 students in a test are 85, 92, 78, 88, and 95. What is the average score?
Solution:
Step 1: Sum of scores: 85 + 92 = 177; 177 + 78 = 255; 255 + 88 = 343; 343 + 95 = 438
Step 2: Average: 438 ÷ 5 = 87.6
Answer: The average score is 87.6
Example 4: Area and Cost
Problem: A rectangular garden is 25 m long and 12 m wide. Grass costs ₦500 per square metre. What is the total cost to cover the garden with grass?
Solution:
Step 1: Area = length × width = 25 × 12 = 300 square metres
Step 2: Total cost = 300 × 500 = 150,000
Answer: ₦150,000
Problem: A rectangular garden is 25 m long and 12 m wide. Grass costs ₦500 per square metre. What is the total cost to cover the garden with grass?
Solution:
Step 1: Area = length × width = 25 × 12 = 300 square metres
Step 2: Total cost = 300 × 500 = 150,000
Answer: ₦150,000
Example 5: Multi-Step with Remainder
Problem: A school has 450 students. They want to arrange them in rows of 24. How many full rows will there be? How many students will be left?
Solution:
Step 1: 450 ÷ 24 = 18 remainder 18 (since 18 × 24 = 432, 450 - 432 = 18)
Answer: 18 full rows, 18 students left.
Problem: A school has 450 students. They want to arrange them in rows of 24. How many full rows will there be? How many students will be left?
Solution:
Step 1: 450 ÷ 24 = 18 remainder 18 (since 18 × 24 = 432, 450 - 432 = 18)
Answer: 18 full rows, 18 students left.
Watch Out!
When solving mixed operation problems, follow the order of operations (multiplication and division before addition and subtraction) unless the problem's steps require a different order.
When solving mixed operation problems, follow the order of operations (multiplication and division before addition and subtraction) unless the problem's steps require a different order.
Practice for Mixed Operations Problems
- A shop sells pencils at ₦200 each and erasers at ₦150 each. If a customer buys 8 pencils and 6 erasers, how much does he pay?
- A farmer has 24 cows. Each cow produces 15 litres of milk per day. He sells the milk at ₦800 per litre. How much money does he earn in 7 days?
- The test scores are 78, 85, 92, 67, 88, and 94. Find the average.
- A rectangular field is 45 m long and 30 m wide. Fencing costs ₦1,200 per metre. What is the total cost to fence the field?
- A school has 500 students. They are arranged in rows of 32. How many full rows? How many students left?
Methods & Techniques
Mastering multi-step word problems requires practice and effective strategies. Use these techniques to improve.
Verification / Checking Strategy:
1. Use estimation: Round numbers and estimate the final answer before calculating exactly.
2. Work backwards: Start from your answer and reverse the operations to see if you get back to the given numbers.
3. Check each step: Verify each intermediate calculation before moving to the next step.
4. Does it make sense? Consider whether your answer is reasonable in the context of the problem.
1. Use estimation: Round numbers and estimate the final answer before calculating exactly.
2. Work backwards: Start from your answer and reverse the operations to see if you get back to the given numbers.
3. Check each step: Verify each intermediate calculation before moving to the next step.
4. Does it make sense? Consider whether your answer is reasonable in the context of the problem.
Example: Checking with Estimation
Problem: 5 shirts at ₦3,500 each + 3 trousers at ₦5,000 each. Estimate total.
Estimate:
Shirts: 5 × 3,500 ≈ 5 × 4,000 = 20,000
Trousers: 3 × 5,000 = 15,000
Estimate total: 20,000 + 15,000 = 35,000
Exact total: 17,500 + 15,000 = 32,500 (close to 35,000) ✓
Problem: 5 shirts at ₦3,500 each + 3 trousers at ₦5,000 each. Estimate total.
Estimate:
Shirts: 5 × 3,500 ≈ 5 × 4,000 = 20,000
Trousers: 3 × 5,000 = 15,000
Estimate total: 20,000 + 15,000 = 35,000
Exact total: 17,500 + 15,000 = 32,500 (close to 35,000) ✓
Common Pitfalls & How to Avoid Them:
• Pitfall 1: Missing a step → Solution: List all steps before calculating.
• Pitfall 2: Using the wrong operation → Solution: Identify clue words (total = add, difference = subtract, each = multiply, share = divide).
• Pitfall 3: Forgetting units → Solution: Always write units in your answer.
• Pitfall 4: Rushing → Solution: Read the problem twice and plan before solving.
• Pitfall 5: Not checking answer → Solution: Always estimate or work backwards to verify.
• Pitfall 1: Missing a step → Solution: List all steps before calculating.
• Pitfall 2: Using the wrong operation → Solution: Identify clue words (total = add, difference = subtract, each = multiply, share = divide).
• Pitfall 3: Forgetting units → Solution: Always write units in your answer.
• Pitfall 4: Rushing → Solution: Read the problem twice and plan before solving.
• Pitfall 5: Not checking answer → Solution: Always estimate or work backwards to verify.
Clue Words for Operations
| Addition | Subtraction | Multiplication | Division |
|---|---|---|---|
| Total, sum, altogether, in all, combined | Difference, less, fewer, remaining, left, how many more | Product, times, each, per, of, twice, triple | Quotient, share, split, divide, average, each |
Technique Practice
- Estimate the answer for: 48 × 19 + 234.
- Work backwards: If the answer is 50 and you added 20 and multiplied by 2, what was the original number?
- Identify the correct operation for: "How many more" and "altogether".
- A student solved 5 × 12 + 8 = 100. Is this correct? If not, what is the correct answer?
Real-World Applications
Multi-step word problems appear in many real-life situations. Understanding how to solve them helps in budgeting, shopping, cooking, planning events, and many other daily activities.
Application 1: Monthly Budget
Scenario: A family's monthly income is ₦250,000. They spend ₦80,000 on rent, ₦50,000 on food, ₦20,000 on transport, and ₦15,000 on utilities. They want to save the rest. How much can they save?
Problem: Find total expenses, then subtract from income.
Solution:
Total expenses = 80,000 + 50,000 + 20,000 + 15,000 = 165,000
Savings = 250,000 - 165,000 = 85,000
Answer: They can save ₦85,000.
Scenario: A family's monthly income is ₦250,000. They spend ₦80,000 on rent, ₦50,000 on food, ₦20,000 on transport, and ₦15,000 on utilities. They want to save the rest. How much can they save?
Problem: Find total expenses, then subtract from income.
Solution:
Total expenses = 80,000 + 50,000 + 20,000 + 15,000 = 165,000
Savings = 250,000 - 165,000 = 85,000
Answer: They can save ₦85,000.
Application 2: Planning a Party
Scenario: A party planner needs to buy 120 plates. Plates come in packs of 24. How many packs should she buy?
Problem: Divide total needed by pack size.
Solution:
120 ÷ 24 = 5 packs exactly
Answer: 5 packs
Scenario: A party planner needs to buy 120 plates. Plates come in packs of 24. How many packs should she buy?
Problem: Divide total needed by pack size.
Solution:
120 ÷ 24 = 5 packs exactly
Answer: 5 packs
Application 3: Cooking and Recipes
Scenario: A recipe for 8 people requires 4 cups of flour. How many cups are needed for 20 people?
Problem: Find cups per person, then multiply.
Solution:
Cups per person = 4 ÷ 8 = 0.5 cups
For 20 people = 0.5 × 20 = 10 cups
Answer: 10 cups
Scenario: A recipe for 8 people requires 4 cups of flour. How many cups are needed for 20 people?
Problem: Find cups per person, then multiply.
Solution:
Cups per person = 4 ÷ 8 = 0.5 cups
For 20 people = 0.5 × 20 = 10 cups
Answer: 10 cups
Application 4: Travel Planning
Scenario: A bus travels 240 km in 3 hours. At the same speed, how far will it travel in 5 hours?
Problem: Find speed, then multiply by time.
Solution:
Speed = 240 ÷ 3 = 80 km/h
Distance in 5 hours = 80 × 5 = 400 km
Answer: 400 km
Scenario: A bus travels 240 km in 3 hours. At the same speed, how far will it travel in 5 hours?
Problem: Find speed, then multiply by time.
Solution:
Speed = 240 ÷ 3 = 80 km/h
Distance in 5 hours = 80 × 5 = 400 km
Answer: 400 km
Application 5: Shopping with Discount
Scenario: A ₦25,000 jacket is on sale at 20% off. How much does it cost after discount?
Problem: Find discount amount, then subtract.
Solution:
Discount = 20% of 25,000 = 0.20 × 25,000 = 5,000
Sale price = 25,000 - 5,000 = 20,000
Answer: ₦20,000
Scenario: A ₦25,000 jacket is on sale at 20% off. How much does it cost after discount?
Problem: Find discount amount, then subtract.
Solution:
Discount = 20% of 25,000 = 0.20 × 25,000 = 5,000
Sale price = 25,000 - 5,000 = 20,000
Answer: ₦20,000
Cross-Curricular Connections
- Science: Calculating averages, rates, and measurements
- Economics: Budgeting, profit and loss, discounts
- Cooking: Scaling recipes, measuring ingredients
- Travel: Distance, time, speed calculations
- Sports: Averages, totals, differences in scores
Cumulative Practice Exercises
Try these problems on your own. Show all working steps. Use estimation to check your answers.
- A shop sold 245 bags of rice on Monday, 312 on Tuesday, and 278 on Wednesday. How many bags were sold in three days?
- A woman had ₦75,000. She bought a dress for ₦12,500, shoes for ₦8,750, and a bag for ₦15,000. How much money is left?
- A factory produces 345 bottles per hour. How many bottles in 12 hours?
- A school has 24 classes with 32 students in each class. If 48 students are absent, how many are present?
- A car travels 420 km on 35 litres of fuel. How far on 25 litres?
- A trader bought 80 bags of cement at ₦4,500 each. He sold them at ₦5,200 each. What was his total profit?
- The scores of 6 students are 75, 82, 90, 68, 85, and 92. Find the average.
- A rectangular garden is 35 m long and 20 m wide. Fencing costs ₦800 per metre. Find the total cost to fence the garden.
- A school has 520 students. They are arranged in rows of 28. How many full rows? How many students left?
- A ₦45,000 television is on sale at 15% off. What is the sale price?
- A recipe for 6 people needs 3 cups of flour. How many cups for 15 people?
- A bus travels 300 km in 4 hours. At the same speed, how far in 7 hours?
- A shop sells pencils at ₦150 each and rulers at ₦250 each. A customer buys 10 pencils and 5 rulers. How much does he pay?
- Error analysis: A student solved 12 × 8 + 6 = 102. Is this correct? If not, correct it.
- A farmer has 36 cows. Each cow produces 12 litres of milk per day. He sells milk at ₦600 per litre. How much money does he earn in 5 days?
Answers to Cumulative Exercises
- Problem: 245 + 312 + 278.
Answer: 835 bags - Problem: 75,000 - (12,500 + 8,750 + 15,000).
Answer: 75,000 - 36,250 = ₦38,750 - Problem: 345 × 12.
Answer: 4,140 bottles - Problem: (24 × 32) - 48.
Answer: 768 - 48 = 720 students - Problem: (420 ÷ 35) × 25.
Answer: 12 × 25 = 300 km - Problem: 80 × (5,200 - 4,500).
Answer: 80 × 700 = ₦56,000 profit - Problem: (75 + 82 + 90 + 68 + 85 + 92) ÷ 6.
Answer: 492 ÷ 6 = 82 - Problem: Perimeter = 2 × (35 + 20) = 110 m; Cost = 110 × 800 = ₦88,000
- Problem: 520 ÷ 28 = 18 remainder 16.
Answer: 18 full rows, 16 students left - Problem: Discount = 0.15 × 45,000 = 6,750; Sale price = 45,000 - 6,750 = ₦38,250
- Problem: (3 ÷ 6) × 15 = 0.5 × 15 = 7.5 cups
- Problem: Speed = 300 ÷ 4 = 75 km/h; Distance = 75 × 7 = 525 km
- Problem: (10 × 150) + (5 × 250) = 1,500 + 1,250 = ₦2,750
- Problem: 12 × 8 + 6 = 96 + 6 = 102, not 100. The student was actually correct! 12 × 8 = 96, + 6 = 102 ✓
- Problem: 36 × 12 × 5 × 600 = 36 × 12 = 432 litres per day; 432 × 5 = 2,160 litres in 5 days; 2,160 × 600 = ₦1,296,000
Conclusion & Summary
Multi-step word problems help us solve real-life situations that require several mathematical operations. By following a systematic approach — reading carefully, planning steps, solving one at a time, and checking your answer — you can solve even the most complex problems.
Key Takeaways:
1. Read carefully: Understand what the problem is asking.
2. Plan steps: Identify hidden questions and decide the order of operations.
3. Solve step by step: Perform one calculation at a time and write intermediate answers.
4. Check your work: Use estimation or work backwards to verify.
5. Practice regularly: The more you practice, the better you become at identifying the steps.
6. Real-world use: Budgeting, shopping, cooking, travel, and many other daily activities.
Keep practising with different types of problems. Multi-step problem solving is a valuable life skill!
Video Resource
Watch this video for more examples of solving multi-step word problems.
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