Decimal Word Problems (Grade 5)
Decimal word problems test your ability to apply decimal operations — addition, subtraction, multiplication, and division — to real-life situations.
In Class 5, word problems involve money (rupees and paise), length (metres and centimetres), weight (kilograms and grams), and capacity (litres and millilitres). These problems require you to read carefully, identify the correct operation, and calculate accurately with decimal numbers.
The key to solving decimal word problems is understanding what the question is asking and choosing the right operation: add (when combining), subtract (when finding a difference or remainder), multiply (when repeating a quantity), or divide (when sharing equally).
Word problems mirror real situations. When Priya buys 3 notebooks at ₹45.50 each, she multiplies. When Dev checks how much change he gets from ₹100 after spending ₹67.25, he subtracts. This topic brings together all your decimal skills into practical problem-solving.
What is Decimal Word Problems - Class 5 Maths (Decimals)?
A decimal word problem is a real-life situation described in words where the numbers involved are decimals. To solve one, follow this strategy:
- Read the problem carefully — twice if needed.
- Identify the key information: the numbers given and what is being asked.
- Decide the operation: addition, subtraction, multiplication, or division.
- Solve by performing the calculation carefully, keeping decimal points aligned.
- Write the answer with the correct unit (₹, kg, m, litres, etc.).
- Check if the answer is reasonable.
How to identify the operation:
| Keywords in Problem | Operation |
|---|---|
| total, altogether, combined, in all, sum, plus | Addition |
| how much more, left, remaining, difference, change, less | Subtraction |
| each, per item, times, total cost of many, groups of | Multiplication |
| equally, each gets, per person, average, divide, share | Division |
Types and Properties
Type 1: Addition word problems
These involve combining two or more decimal quantities.
Example: Ria bought 2.5 kg of rice and 1.75 kg of dal. Total weight = 2.5 + 1.75 = 4.25 kg.
Type 2: Subtraction word problems
These involve finding what is left or the difference between two quantities.
Example: Aman had ₹50. He spent ₹32.75. Money left = 50 − 32.75 = ₹17.25.
Type 3: Multiplication word problems
These involve repeated quantities or finding a total for multiple items.
Example: One pen costs ₹15.50. Cost of 4 pens = 15.50 × 4 = ₹62.00.
Type 4: Division word problems
These involve sharing equally or finding a rate.
Example: 7.2 litres shared among 6 bottles = 7.2 ÷ 6 = 1.2 litres each.
Type 5: Multi-step problems
These require two or more operations. Read carefully to plan your steps.
Example: Kavi buys 3 books at ₹85.50 each and pays ₹300. Change = 300 − (85.50 × 3) = 300 − 256.50 = ₹43.50.
Solved Examples
Example 1: Addition — Combining Weights
Problem: Ria bought 2.75 kg of apples and 1.5 kg of bananas from the market. What is the total weight of the fruits she bought?
Solution:
Step 1: Identify the operation. "Total weight" → addition.
Step 2: Write the decimals one below the other, aligning the decimal points. Add a trailing zero to make the decimal places equal:
2.75
+ 1.50
------
4.25
Step 3: Add column by column: 5+0=5, 7+5=12 (write 2, carry 1), 2+1+1=4.
Answer: The total weight is 4.25 kg.
Example 2: Subtraction — Finding Change
Problem: Dev had ₹100. He bought a notebook for ₹45.75. How much money does he have left?
Solution:
Step 1: Identify the operation. "How much left" → subtraction.
Step 2: Write as: ₹100.00 − ₹45.75
100.00
− 45.75
--------
54.25
Step 3: Subtract from right: 0−5 (borrow) → 10−5=5. 9−7=2. 9−5=4. 0−4 (borrow) → 10−4=6. But wait — let us redo carefully: 100.00 − 45.75. Working right to left: 0−5, borrow, 10−5=5. 9−7=2 (tens-hundredths). 9−5=4 (we had borrowed). 9−4=5 (after borrow again). Final: 54.25.
Answer: Dev has ₹54.25 left.
Example 3: Multiplication — Cost of Multiple Items
Problem: One pen costs ₹12.50. Kavi buys 6 pens for his friends. What is the total cost?
Solution:
Step 1: Identify the operation. "Total cost of 6 pens" at a price each → multiplication.
Step 2: Calculate 12.50 × 6.
Step 3: First multiply as whole numbers: 1250 × 6 = 7500.
Step 4: Count decimal places in original: 12.50 has 2 decimal places. Place the decimal 2 places from the right in 7500 → 75.00.
Answer: The total cost is ₹75.00.
Example 4: Division — Equal Sharing
Problem: Neha has 8.4 litres of mango juice. She pours it equally into 4 bottles. How much juice is in each bottle?
Solution:
Step 1: Identify the operation. "Equally into 4 bottles" → division.
Step 2: Calculate 8.4 ÷ 4.
Step 3: 8 ÷ 4 = 2. Place decimal. 4 ÷ 4 = 1.
Step 4: Quotient = 2.1.
Verification: 2.1 × 4 = 8.4 ✓
Answer: Each bottle has 2.1 litres of juice.
Example 5: Subtraction — Comparing Heights
Problem: Arjun is 1.52 m tall. Aditi is 1.38 m tall. How much taller is Arjun than Aditi?
Solution:
Step 1: Identify the operation. "How much taller" = difference → subtraction.
Step 2: Calculate 1.52 − 1.38.
1.52
−1.38
-----
0.14
Step 3: 2−8: borrow, 12−8=4. 4−3=1. 1−1=0.
Answer: Arjun is 0.14 m (or 14 cm) taller than Aditi.
Example 6: Multiplication — Distance Travelled
Problem: An auto-rickshaw travels 3.8 km in one trip from the school to Ria's house. How far does it travel if it makes 5 such trips in a day?
Solution:
Step 1: Identify the operation. Same distance repeated 5 times → multiplication.
Step 2: Calculate 3.8 × 5.
Step 3: 38 × 5 = 190. Place decimal (1 decimal place): 19.0.
Answer: The auto-rickshaw travels 19 km in 5 trips.
Example 7: Multi-step — Shopping Bill
Problem: Priya bought 3 packets of chapatis at ₹22.50 each and a pack of butter for ₹48.75. What is her total bill?
Solution:
Step 1: First, find the cost of 3 chapati packets (multiplication):
22.50 × 3 = ₹67.50
Step 2: Then, add the cost of butter (addition):
₹67.50 + ₹48.75 = ₹116.25
Answer: The total bill is ₹116.25.
Example 8: Multi-step — Remaining Rope
Problem: Meera has a rope 10 m long. She cuts two pieces — one of 3.25 m and another of 2.8 m. What length of rope is left?
Solution:
Step 1: Find total length cut (addition): 3.25 + 2.80 = 6.05 m.
Step 2: Find remaining length (subtraction): 10.00 − 6.05 = 3.95 m.
Answer: 3.95 m of rope is left.
Example 9: Division — Finding the Average
Problem: Rahul scored 8.5, 9.0, 7.5, and 9.0 marks in four class tests. What is his average score?
Solution:
Step 1: Find the total (addition): 8.5 + 9.0 + 7.5 + 9.0 = 34.0
Step 2: Divide by the number of tests: 34.0 ÷ 4 = 8.5
Verification: 8.5 × 4 = 34.0 ✓
Answer: Rahul's average score is 8.5.
Example 10: Multi-step — Cricket Bat and Ball
Problem: Aman had ₹500. He bought a cricket bat for ₹285.50 and a ball for ₹75.25. How much money is left?
Solution:
Step 1: Find total spent (addition): ₹285.50 + ₹75.25 = ₹360.75
Step 2: Find money left (subtraction): ₹500.00 − ₹360.75 = ₹139.25
Reasonableness check: Aman spent roughly ₹286 + ₹75 = ₹361, and ₹500 − ₹361 = ₹139. Our answer ₹139.25 is close. ✓
Answer: Aman has ₹139.25 left.
Real-World Applications
Where do we encounter decimal word problems in daily life?
- Shopping: Calculating total bills, discounts, and change when prices include paise.
- Cooking: Measuring ingredients — 0.5 kg of flour, 1.25 litres of milk.
- Travel: Calculating distances (the school is 2.3 km away), fuel costs (petrol at ₹105.60 per litre), and travel time.
- Sports: Recording scores (9.5 in gymnastics), calculating averages, and comparing timings (ran 100 m in 12.35 seconds).
- Health: Measuring weight (child weighs 32.5 kg), height (1.42 m tall), and medicine doses (2.5 ml syrup).
- Banking: Interest calculations, account balances, and transaction amounts all use decimals.
Key Points to Remember
- Read the problem twice — underline the numbers and the question being asked.
- Identify keywords to determine the operation: total/altogether → add; difference/left/remaining → subtract; each/per item → multiply; equally/average/share → divide.
- Always align decimal points when adding or subtracting. Add trailing zeros to equalise decimal places.
- When multiplying, count the total decimal places in both numbers and place the decimal accordingly in the answer.
- Write your answer with the correct unit (₹, kg, m, litres, km, etc.).
- For multi-step problems, solve one step at a time and use the result in the next step.
- Check if your answer is reasonable — estimate roughly and see if the calculated answer is close.
- Common mistakes: misaligning decimal points, forgetting to include units, and using the wrong operation.
Practice Problems
- Aditi bought 1.25 kg of mangoes and 2.75 kg of oranges. What is the total weight of fruits she bought?
- A water bottle holds 1.5 litres. If Meera fills 8 such bottles, how many litres of water does she need?
- Kavi had ₹200. He spent ₹78.60 on stationery and ₹43.50 on snacks. How much money is left?
- A ribbon is 12.6 m long. If it is cut into 7 equal pieces, what is the length of each piece?
- Priya's tiffin box weighs 0.35 kg when empty and 1.15 kg when full. What is the weight of the food inside?
- One litre of milk costs ₹52.50. What is the cost of 4 litres?
- Dev ran 2.3 km on Monday, 3.15 km on Tuesday, and 1.85 km on Wednesday. What is the total distance he ran in three days?
- Neha scored 46.5 marks in Maths and 38.75 marks in Science. How many more marks did she score in Maths than in Science?
Frequently Asked Questions
Q1. How do you solve decimal word problems?
Read the problem carefully, identify the numbers and what is being asked, choose the correct operation (add, subtract, multiply, or divide), solve step by step with proper decimal alignment, and write the answer with the correct unit.
Q2. What keywords indicate addition in word problems?
Words like total, altogether, combined, in all, sum, how much together, and plus indicate you need to add the decimal numbers.
Q3. What keywords indicate subtraction?
Words like how much more, how much less, left, remaining, difference, change, and take away indicate subtraction.
Q4. How do you handle different numbers of decimal places in word problems?
Add trailing zeros to make the decimal places equal before adding or subtracting. For example, when adding 2.5 and 3.25, write 2.5 as 2.50 so both have two decimal places. This ensures proper alignment.
Q5. What are multi-step decimal word problems?
These are problems that require two or more operations to solve. For example, finding the cost of 5 items at ₹23.50 each and then subtracting from ₹200 involves multiplication followed by subtraction. Solve one step at a time.
Q6. How do you check if your answer to a decimal word problem is correct?
Use the reverse operation. If you added, subtract the answer from the total. If you divided, multiply the quotient by the divisor. You can also estimate the answer roughly and see if your exact answer is in the right range.
Q7. Why should you always write the unit in the answer?
Units tell what the number represents — ₹ means money, kg means weight, m means length. Without the unit, the answer is incomplete. ₹54.25 tells you it is money, while 54.25 m tells you it is a length.
Q8. How are decimal word problems different from whole number word problems?
The approach is exactly the same — you still add, subtract, multiply, or divide based on what the problem asks. The only additional care needed is handling the decimal point correctly during calculations: aligning it for addition/subtraction and counting decimal places for multiplication.
Related Topics
- Addition of Decimals
- Multiplication of Decimals
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Subtraction of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
