Mixed Word Problems (Grade 5)
Mixed word problems are questions that combine two or more operations (addition, subtraction, multiplication, division) in a single problem. Unlike single-step problems, these require you to read carefully, plan the steps, and apply the correct operations in the right order.
In Class 5, mixed word problems may involve whole numbers, decimals, fractions, and money. They test your ability to break a complex problem into smaller steps and solve each part logically.
The key to solving mixed word problems is: read, identify the operations, plan the steps, calculate, and check.
What is Mixed Word Problems - Class 5 Maths (Operations)?
A mixed word problem is a problem that requires more than one mathematical operation to solve. It may involve a combination of:
- Addition and subtraction
- Multiplication and division
- Multiplication and addition (or subtraction)
- Operations with whole numbers, fractions, or decimals
Strategy:
- Read the problem twice.
- Identify what is given and what is asked.
- Decide which operations to use.
- Solve step by step.
- Check if the answer makes sense.
Solved Examples
Example 1: Example 1: Addition and Subtraction
Problem: Ria had ₹500. She spent ₹175 on books and ₹120 on stationery. Her mother gave her ₹200 more. How much does Ria have now?
Solution:
Step 1: Total spent = 175 + 120 = ₹295
Step 2: After spending: 500 − 295 = ₹205
Step 3: Mother gave ₹200: 205 + 200 = ₹405
Answer: Ria has ₹405.
Example 2: Example 2: Multiplication and Addition
Problem: Arjun buys 4 notebooks at ₹35 each and 3 pens at ₹12 each. What is the total cost?
Solution:
Step 1: Cost of notebooks = 4 × 35 = ₹140
Step 2: Cost of pens = 3 × 12 = ₹36
Step 3: Total = 140 + 36 = ₹176
Answer: The total cost is ₹176.
Example 3: Example 3: Multiplication and Subtraction
Problem: A school ordered 12 boxes of chalk. Each box has 50 pieces. Teachers used 385 pieces. How many are left?
Solution:
Step 1: Total chalk = 12 × 50 = 600
Step 2: Left = 600 − 385 = 215
Answer: 215 pieces of chalk are left.
Example 4: Example 4: Division and Addition
Problem: 96 students are divided equally into 4 groups. Each group gets 5 extra students from another class. How many students are now in each group?
Solution:
Step 1: Students per group = 96 ÷ 4 = 24
Step 2: After extras: 24 + 5 = 29
Answer: Each group has 29 students.
Example 5: Example 5: Three Operations
Problem: Priya earns ₹45 per hour. She works 6 hours and spends ₹80 on lunch. She then divides the remaining money equally between herself and her sister. How much does each get?
Solution:
Step 1: Earnings = 45 × 6 = ₹270
Step 2: After lunch: 270 − 80 = ₹190
Step 3: Each gets: 190 ÷ 2 = ₹95
Answer: Each gets ₹95.
Example 6: Example 6: Fractions in Word Problems
Problem: Dev has 60 marbles. He gives ¼ to Kavi and ⅓ of the remaining to Meera. How many does Dev have left?
Solution:
Step 1: Given to Kavi = ¼ of 60 = 15
Step 2: Remaining = 60 − 15 = 45
Step 3: Given to Meera = ⅓ of 45 = 15
Step 4: Dev has: 45 − 15 = 30
Answer: Dev has 30 marbles left.
Example 7: Example 7: Decimal Word Problem
Problem: Neha buys 2.5 kg of apples at ₹120 per kg and 1.5 kg of bananas at ₹40 per kg. What is the total cost?
Solution:
Step 1: Apples = 2.5 × 120 = ₹300
Step 2: Bananas = 1.5 × 40 = ₹60
Step 3: Total = 300 + 60 = ₹360
Answer: The total cost is ₹360.
Example 8: Example 8: Distance Problem
Problem: Rahul cycles 4.5 km to school and 4.5 km back, 5 days a week. How far does he cycle in a week?
Solution:
Step 1: Daily distance = 4.5 + 4.5 = 9 km
Step 2: Weekly distance = 9 × 5 = 45 km
Answer: Rahul cycles 45 km in a week.
Example 9: Example 9: Sharing and Remaining
Problem: Aditi has 250 toffees. She gives 15 toffees each to 8 friends and keeps the rest. How many does she keep?
Solution:
Step 1: Given away = 15 × 8 = 120
Step 2: Kept = 250 − 120 = 130
Answer: Aditi keeps 130 toffees.
Example 10: Example 10: Multi-Step with Comparison
Problem: Shop A sells a cricket bat for ₹450 and a ball for ₹75. Shop B sells the same bat for ₹425 and the ball for ₹90. Which shop gives a cheaper total?
Solution:
Step 1: Shop A total = 450 + 75 = ₹525
Step 2: Shop B total = 425 + 90 = ₹515
Step 3: Difference = 525 − 515 = ₹10
Answer: Shop B is cheaper by ₹10.
Key Points to Remember
- Mixed word problems need two or more operations to solve.
- Always read the problem twice before starting.
- Identify what is given and what is asked.
- Break the problem into smaller steps.
- Use the correct order of operations (BODMAS/DMAS).
- Problems can involve whole numbers, decimals, fractions, and money.
- After solving, check if the answer is reasonable.
- Write the answer with the correct unit (₹, km, kg, etc.).
Practice Problems
- Kavi has ₹800. He buys 3 books at ₹125 each and 2 pens at ₹30 each. How much money is left?
- A box contains 144 chocolates. ¼ are distributed to Class A and ⅓ of the remaining to Class B. How many are left?
- Meera earns ₹250 on Monday and ₹310 on Tuesday. She spends ₹175. How much does she save?
- A farmer harvests 325 kg of wheat and 480 kg of rice. He sells 550 kg in total. How much grain remains?
- Dev buys 3.5 m of cloth at ₹80 per metre and pays with a ₹500 note. What change does he get?
- 12 packets of biscuits cost ₹360. How much do 5 packets cost?
- Ria scores 85, 92, 78, and 95 in four tests. What is her average score?
- A train travels 240 km in 4 hours. How far will it travel in 7 hours at the same speed?
Frequently Asked Questions
Q1. What are mixed word problems?
Mixed word problems are problems that require two or more mathematical operations (like addition and multiplication, or division and subtraction) to find the answer.
Q2. How do I decide which operations to use?
Look for clue words: “bought” and “total” suggest multiplication and addition. “Gave away” and “remaining” suggest subtraction. “Shared equally” suggests division.
Q3. What is the best strategy for multi-step problems?
Break the problem into smaller steps. Solve one step at a time. Write down intermediate answers. Then combine them for the final answer.
Q4. What if the problem involves fractions and whole numbers?
Solve the fraction part first (like finding ¼ of a number), then continue with the remaining operations. Keep track of your intermediate results.
Q5. How do I check my answer?
Estimate the answer first using rounded numbers. If your exact answer is close to the estimate, it is likely correct. You can also work backwards from the answer.
Q6. What is BODMAS and when do I use it?
BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) tells the order of operations. Use it when a single expression has multiple operations, like 3 + 4 × 5.
Q7. Can mixed word problems have decimals?
Yes. Many real-life problems involve decimal amounts (money, weight, distance). Apply the same strategies: identify operations, solve step by step.
Q8. Why are mixed word problems harder than single-step ones?
They require planning multiple steps, choosing the right operations, and keeping track of intermediate results. Practice improves speed and accuracy.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Multi-step word problems using all four operations are part of the Operations chapter in NCERT/CBSE Class 5 Maths.
Related Topics
- Word Problems on Four Operations
- 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)
