Unitary Method (Grade 5)
The unitary method is a technique for solving problems by first finding the value of one unit (one item, one kg, one metre, etc.) and then using it to find the value of any number of units.
The word “unitary” comes from “unit” (meaning one). The idea is simple: if you know the cost of 5 pens, you can find the cost of 1 pen (divide by 5), and then the cost of 8 pens (multiply by 8).
The unitary method is one of the most powerful and widely used techniques in Class 5 Maths. It works for problems involving cost, weight, distance, time, and many other quantities.
What is Unitary Method - Class 5 Maths (Operations)?
The unitary method is a two-step problem-solving technique:
- Step 1: Find the value of one unit (divide the given total by the given quantity).
- Step 2: Find the value of the required number of units (multiply the value of one unit by the required quantity).
This method works when quantities are in direct proportion: as one quantity increases, the other increases at the same rate.
Unitary Method (Grade 5) Formula
Value of 1 unit = Total value ÷ Number of units
Value of required units = Value of 1 unit × Required number
Types and Properties
Common applications of the unitary method:
- Cost problems: If 6 books cost ₹180, what do 10 books cost?
- Weight problems: If 3 kg costs ₹150, what does 7 kg cost?
- Distance-time problems: If a car covers 240 km in 4 hours, how far in 6 hours?
- Work problems: If 5 workers finish a job in 10 days, how long do 8 workers take?
- Quantity conversion: If 12 eggs cost ₹72, what is the cost of 1 egg?
Solved Examples
Example 1: Example 1: Cost of Pencils
Problem: 8 pencils cost ₹40. What is the cost of 12 pencils?
Solution:
Step 1: Cost of 1 pencil = 40 ÷ 8 = ₹5
Step 2: Cost of 12 pencils = 5 × 12 = ₹60
Answer: 12 pencils cost ₹60.
Example 2: Example 2: Weight of Apples
Problem: 5 kg of apples cost ₹600. What is the cost of 3 kg?
Solution:
Step 1: Cost of 1 kg = 600 ÷ 5 = ₹120
Step 2: Cost of 3 kg = 120 × 3 = ₹360
Answer: 3 kg of apples cost ₹360.
Example 3: Example 3: Distance Problem
Problem: A car covers 180 km in 3 hours. How far will it travel in 5 hours at the same speed?
Solution:
Step 1: Distance in 1 hour = 180 ÷ 3 = 60 km
Step 2: Distance in 5 hours = 60 × 5 = 300 km
Answer: The car will travel 300 km.
Example 4: Example 4: Earning Problem
Problem: Aman earns ₹2,400 in 6 days. How much does he earn in 10 days?
Solution:
Step 1: Earnings per day = 2,400 ÷ 6 = ₹400
Step 2: Earnings in 10 days = 400 × 10 = ₹4,000
Answer: Aman earns ₹4,000 in 10 days.
Example 5: Example 5: Fuel Consumption
Problem: A bus uses 20 litres of diesel to travel 160 km. How much diesel is needed for 240 km?
Solution:
Step 1: Diesel for 1 km = 20 ÷ 160 = 0.125 litres
Step 2: Diesel for 240 km = 0.125 × 240 = 30 litres
Answer: 30 litres of diesel is needed.
Example 6: Example 6: Cloth Problem
Problem: 4 metres of cloth cost ₹320. Priya wants 7 metres. How much will she pay?
Solution:
Step 1: Cost of 1 m = 320 ÷ 4 = ₹80
Step 2: Cost of 7 m = 80 × 7 = ₹560
Answer: Priya will pay ₹560.
Example 7: Example 7: Notebooks and Pages
Problem: 3 notebooks have 540 pages in total. How many pages are in 8 such notebooks?
Solution:
Step 1: Pages in 1 notebook = 540 ÷ 3 = 180
Step 2: Pages in 8 notebooks = 180 × 8 = 1,440
Answer: 8 notebooks have 1,440 pages.
Example 8: Example 8: Time Problem
Problem: A machine fills 150 bottles in 30 minutes. How many bottles does it fill in 1 hour (60 minutes)?
Solution:
Step 1: Bottles per minute = 150 ÷ 30 = 5
Step 2: Bottles in 60 minutes = 5 × 60 = 300
Answer: The machine fills 300 bottles in 1 hour.
Example 9: Example 9: Finding Quantity from Cost
Problem: If 1 kg of rice costs ₹55, how many kg can Neha buy with ₹385?
Solution:
Step 1: Value of 1 unit is already known: ₹55 per kg.
Step 2: Number of kg = 385 ÷ 55 = 7 kg
Answer: Neha can buy 7 kg of rice.
Example 10: Example 10: Saving Problem
Problem: Dev saves ₹750 in 5 weeks. How much will he save in 12 weeks at the same rate?
Solution:
Step 1: Savings per week = 750 ÷ 5 = ₹150
Step 2: Savings in 12 weeks = 150 × 12 = ₹1,800
Answer: Dev will save ₹1,800 in 12 weeks.
Real-World Applications
Where do we use the unitary method?
- Shopping: Finding the cost of any quantity from the unit price.
- Cooking: Scaling recipes up or down (if recipe serves 4, adjust for 6).
- Travel: Calculating fuel needed for a trip based on mileage.
- Work planning: Estimating time or workers needed for a task.
- Unit pricing: Comparing prices per kg at different shops to find the best deal.
Key Points to Remember
- The unitary method has two steps: find the value of 1, then find the value of many.
- Step 1: Value of 1 unit = total ÷ given number.
- Step 2: Value of required units = value of 1 × required number.
- This method works when quantities are in direct proportion.
- Always find the “per unit” value first (per kg, per item, per hour).
- The unitary method can solve cost, distance, time, weight, and work problems.
- To find the quantity you can buy: quantity = total money ÷ price per unit.
Practice Problems
- 6 pens cost ₹90. What is the cost of 15 pens?
- A car uses 12 litres of petrol for 144 km. How much petrol is needed for 240 km?
- 9 workers paint a wall in 3 days. How long will 3 workers take?
- If 4 kg of mangoes cost ₹480, what is the cost of 7 kg?
- A train covers 420 km in 6 hours. How far will it travel in 10 hours?
- Aditi types 240 words in 8 minutes. How many words can she type in 15 minutes?
- If 1 dozen bananas cost ₹48, what is the cost of 30 bananas?
- Rahul earns ₹3,500 in 7 days. How much will he earn in 30 days?
Frequently Asked Questions
Q1. What is the unitary method?
The unitary method is a two-step technique: first find the value of one unit (divide), then find the value of the required number of units (multiply).
Q2. Why is it called the unitary method?
The word “unitary” comes from “unit” (one). The method revolves around finding the value of one unit first.
Q3. What are the two steps?
Step 1: Divide the total value by the given number to find the value of 1 unit. Step 2: Multiply the value of 1 unit by the required number.
Q4. What is direct proportion?
Direct proportion means as one quantity increases, the other also increases at the same rate. Example: more items cost more money. The unitary method works for direct proportion.
Q5. Can the unitary method be used for work problems?
Yes. If 5 workers do a job in 10 days, one worker does it in 50 days. 8 workers do it in 50 ÷ 8 = 6.25 days. (Note: work problems involve inverse proportion.)
Q6. How do I find how many items I can buy?
Divide the total money by the cost per item. Example: if pencils cost ₹5 each and you have ₹45, you can buy 45 ÷ 5 = 9 pencils.
Q7. What if the value of one unit is a decimal?
That is fine. Continue with the decimal value. For example, if 3 items cost ₹10, then 1 item costs 10 ÷ 3 = ₹3.33 approximately.
Q8. How is the unitary method different from cross-multiplication?
Both solve proportion problems. The unitary method finds the value of 1 unit first. Cross-multiplication sets up a proportion equation. Both give the same answer.
Q9. Is the unitary method in the NCERT Class 5 syllabus?
Yes. The unitary method for solving word problems is part of the Operations chapter in NCERT/CBSE Class 5 Maths.
Related Topics
- Word Problems on Four Operations
- Division of Large Numbers
- Addition of Large Numbers
- Subtraction of Large Numbers
- Multiplication of Large Numbers
- Order of Operations (BODMAS)
- 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)
- Mixed Word Problems (Grade 5)
