Unitary Method Introduction
The unitary method is a way of solving problems by first finding the value of one unit. Once you know the value of one, you can find the value of any number of units by multiplying.
In Class 4, you will use the unitary method to solve problems about prices, quantities, distances, and time. This method is simple, powerful, and used in everyday life.
What is Unitary Method - Class 4 Maths (Operations)?
The unitary method has two steps:
Step 1: Find the value of 1 unit (divide the total by the number of units).
Step 2: Find the value of the required number of units (multiply the unit value by the required number).
Value of 1 unit = Total value ÷ Number of units
Value of many units = Value of 1 unit × Required number
Unitary Method Introduction Formula
Step 1: Find value of 1 → Divide
Step 2: Find value of many → Multiply
Key idea: Always go through "1" — this is why it is called the unitary method (unit = 1).
Solved Examples
Example 1: Example 1: Cost of items
Problem: 5 notebooks cost ₹75. Find the cost of 8 notebooks.
Solution:
Step 1: Cost of 1 notebook = ₹75 ÷ 5 = ₹15
Step 2: Cost of 8 notebooks = ₹15 × 8 = ₹120
Answer: 8 notebooks cost ₹120.
Example 2: Example 2: Weight of mangoes
Problem: 12 mangoes weigh 3 kg. How much do 20 mangoes weigh?
Solution:
Step 1: Weight of 1 mango = 3 kg ÷ 12 = 0.25 kg (or 250 g)
Step 2: Weight of 20 mangoes = 0.25 × 20 = 5 kg
Answer: 20 mangoes weigh 5 kg.
Example 3: Example 3: Distance travelled
Problem: An auto-rickshaw travels 24 km in 3 hours. How far will it travel in 7 hours at the same speed?
Solution:
Step 1: Distance in 1 hour = 24 ÷ 3 = 8 km
Step 2: Distance in 7 hours = 8 × 7 = 56 km
Answer: The auto-rickshaw will travel 56 km in 7 hours.
Example 4: Example 4: Price of cloth
Problem: 4 metres of cloth cost ₹360. Find the cost of 7 metres.
Solution:
Step 1: Cost of 1 metre = ₹360 ÷ 4 = ₹90
Step 2: Cost of 7 metres = ₹90 × 7 = ₹630
Answer: 7 metres of cloth cost ₹630.
Example 5: Example 5: Chapatis for a party
Problem: 6 people eat 18 chapatis. How many chapatis are needed for 15 people?
Solution:
Step 1: Chapatis per 1 person = 18 ÷ 6 = 3
Step 2: Chapatis for 15 people = 3 × 15 = 45
Answer: 45 chapatis are needed for 15 people.
Example 6: Example 6: Earning and working
Problem: Priya earns ₹1,400 in 7 days. How much does she earn in 12 days?
Solution:
Step 1: Earning per day = ₹1,400 ÷ 7 = ₹200
Step 2: Earning in 12 days = ₹200 × 12 = ₹2,400
Answer: Priya earns ₹2,400 in 12 days.
Example 7: Example 7: Finding the number of items
Problem: 1 pencil costs ₹6. How many pencils can Aman buy with ₹54?
Solution:
Step 1: Number of pencils = ₹54 ÷ ₹6 = 9
Answer: Aman can buy 9 pencils.
Example 8: Example 8: Fuel consumption
Problem: A car uses 8 litres of petrol to travel 96 km. How much petrol is needed for 150 km?
Solution:
Step 1: Petrol for 1 km = 8 ÷ 96 = 1/12 litre
Step 2: Petrol for 150 km = (1/12) × 150 = 150/12 = 12.5 litres
Answer: 12.5 litres of petrol is needed.
Example 9: Example 9: Workers and painting
Problem: 3 painters paint a wall in 12 hours. How long would 1 painter take?
Solution:
Step 1: Total work = 3 × 12 = 36 painter-hours.
Step 2: 1 painter = 36 ÷ 1 = 36 hours.
Answer: 1 painter would take 36 hours. (Note: More workers = less time. This is an inverse relationship.)
Example 10: Example 10: Cricket bat production
Problem: A factory makes 150 cricket bats in 6 days. How many bats in 10 days?
Solution:
Step 1: Bats per day = 150 ÷ 6 = 25
Step 2: Bats in 10 days = 25 × 10 = 250
Answer: The factory makes 250 bats in 10 days.
Key Points to Remember
- The unitary method finds the value of 1 unit first, then uses it to find the value of any number of units.
- Step 1: Divide to find the value of 1.
- Step 2: Multiply to find the value of many.
- This method works for cost, weight, distance, time, quantity — any proportional relationship.
- Always check: does the answer make sense? More items should cost more. Fewer items should cost less.
- The unitary method assumes a constant rate (e.g., same price per item, same speed).
- It is the foundation for ratios, proportions, and percentages in higher classes.
Practice Problems
- 3 kg of rice costs ₹180. Find the cost of 7 kg.
- A car covers 240 km in 4 hours. How far does it go in 9 hours?
- 8 workers dig a trench in 5 days. How many days would 1 worker take?
- 15 chocolates cost ₹90. How many chocolates can you buy for ₹150?
- If 6 books weigh 1.8 kg, what is the weight of 10 books?
- Aditi types 200 words in 5 minutes. How many words can she type in 12 minutes?
- 4 packets of biscuits cost ₹120. Find the cost of 11 packets.
Frequently Asked Questions
Q1. What is the unitary method?
The unitary method is a technique where you first find the value of one unit by dividing, then multiply to find the value of the required number of units.
Q2. Why is it called the 'unitary' method?
The word 'unitary' comes from 'unit', meaning one. The method always goes through finding the value of one unit as an intermediate step.
Q3. What are the two steps of the unitary method?
Step 1: Divide the total value by the number of items to find the value of one item. Step 2: Multiply the value of one item by the number you need.
Q4. Can the unitary method be used for time problems?
Yes. If a task takes a certain time for a given number of workers, you can find how long one worker takes (divide) and then calculate for any number of workers.
Q5. What if the value of 1 unit is not a whole number?
That is perfectly fine. Work with decimals or fractions. For example, if 3 items cost ₹10, then 1 item costs ₹10/3 = ₹3.33 approximately.
Q6. When does the unitary method not work?
It does not work when the relationship is not proportional. For example, if adding more workers to a very small task does not speed it up, the unitary method would give a wrong answer.
Q7. How is the unitary method used in daily life?
Shopping (price per item), cooking (ingredients for different servings), travel (distance per hour), and budgeting (cost per day) all use the unitary method.
Q8. What comes after the unitary method in higher classes?
The unitary method leads to the study of ratios, proportions, percentages, and rate problems in Classes 5 and 6. It is the foundation for all proportional reasoning.
