103 LearnersLast updated on June 12th, 2025
Unitary Method
The unitary method is used to determine the value of multiple units by finding the value of a single unit. In real-life problems, we use the unitary method to determine the cost or time per unit. Let’s learn how it works.
What is the Unitary Method in Math?
In mathematics, the unitary method holds significant importance. It is a method where the value of a given number of units can be deduced by only finding the value of a single unit.
This method works because of proportionality; when one quantity changes, it triggers a change in other quantities as well. The quantity increases or decreases depending on the relationship. Using this method, we can also determine the unknown values in the ratio and proportion, i.e., by applying the value of a single unit.
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How to Apply the Unitary Method?
Use the following steps to apply the unitary method:
- Determine what the unit depicts in the given problem. For example: one meter of cloth or one liter of milk.
- To find out the value of one unit, we should divide the total value by the given quantity.
- Multiply the value of a single unit with the given number of units to get the final value.
For example: the cost of 10 meters of cloth = $150, calculate the cost of 5 meters of cloth.
Cost of 1m = 150/10 = $15
Therefore, the cost of 5 meters = 15 × 5 = $75.
Types of Unitary Method
The unitary method comes in two different variants. The two types are mentioned below:
Direct Variation: In direct variation, if one quantity increases or decreases, the other quantity also increases or decreases in the same proportion. For e.g., the more you buy, the more you will have to spend. So the number of things that you buy and the total expenditure are in direct variation.
Indirect Variation: A mathematical relationship where two quantities are indirectly connected to each other means they are in indirect variation. In the indirect variation, when one quantity increases, the other decreases, and vice versa. For e.g., increase in the number of workers for a particular task will decrease the time taken to complete it.
Tips and Tricks for Unitary Method
Finding it difficult to solve problems using the unitary method? These below mentioned tips and tricks should help you solve them easily:
- As a first step, you need to identify the context of the problem, i.e., what needs to be determined.
- Check if the problem involves direct or indirect variation.
- Write the quantities in a simple ratio form to make it easier to solve.
- Ensure that you follow all the steps and that the final result includes the proper unit.
- Always practice by applying it in real-life problems. For e.g., if 10 pens cost $100, what is the cost of 5 pens? To find the cost of one pen, we will divide 100 by 10. So 100/10 = 10; Therefore, 5 pens will cost 10 × 5 = $50.
Real-World Applications of Unitary Method
The unitary method is a mathematical concept that has numerous applications in various fields. We will now learn how they can be applied:
- Students can apply the unitary method to calculate the discount amount or the total cost of a product.
- They can estimate the time to reach a destination by using the distance per unit.
- Using this method, students can determine the monthly salary of a worker based on their daily wage.
- It helps them calculate the approximate fuel needed in advance to avoid any inconvenience.
- By determining the quantity required for a person, families can plan meal recipes accordingly for all members.
Common Mistakes and How to Avoid Them in Unitary Method
The unitary method is a fundamental concept for solving many real-life issues. However, some students might find it tricky, but it can be learned easily if you spot the errors you make. Here’s a list of common mistakes and ways to avoid them:
Mistake 1
Not Determining the Value of Single Unit First
Students might try to solve the problem without finding the value of a single unit.
Example: 10 bottles cost $200. Find the cost of 5 bottles.
They might solve it directly without finding the value of a single unit.
Ensure that you calculate the value of a single unit. Then use it to find the value of a given number of units.
Mistake 2
Ignoring Unit Conversions
They frequently forget to convert the units before the calculations.
Example: A man saves $2000 per week. To calculate how much he could do each day:
Incorrect: $2000 by 30
Always ensure that you use the correct units throughout the calculation.
Corrected: Weeks should be converted to days:
1 week = 7 days
Therefore, the man saves per day = 2000/7 = $285.7.
Mistake 3
Not understanding the problem
Sometimes they fail to understand the context of the problem, which results in incorrect calculation. It is important to know the objective. For better understanding, you can break the issue into simple terms.
Mistake 4
Rounding too Early
They tend to round off values too early in the calculation, which will result in incorrect results.
They may directly round off the incorrect fraction, 25/250 which gives an inaccurate answer. Follow the step-by-step process and round off at the final step.
Example: 25 chocolates cost $250. Find the cost of 10 chocolates.
Corrected: Find the cost of a single unit = 250/ 25 =10
Cost of 10 chocolates = 10 × 10 = 100.
Mistake 5
Confusion between Direct and Indirect Variations
They sometimes get confused with the terms direct and indirect variation, which can lead to errors in problem-solving. Remember, if two quantities increase or decrease together in the same proportion, they are in direct variation. Whereas, if one quantity decreases while the other increases, they are said to be in indirect variation.
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Solved Examples of Unitary Method
Problem 1
If 3 scrapbooks cost $150. Calculate the cost of 7 scrapbooks.
The cost of 7 scrapbooks is 350.
Explanation
Determining the cost of 1 scrapbook: 150/3 = 50
Now, we find the cost of 7 scrapbooks: 50 × 7 = 350
Therefore, the cost of 7 scrapbooks is 350.
Problem 2
If 12 students can complete a task in 24 days, calculate the number of days it will take for 6 students to complete the same task.
The number of days it will take for 6 students to complete the same task is 48 days.
Explanation
We now calculate the work completed by 1 student in 24 days:
Total work completed = 12 × 24 = 288
So, the number of days it will take for 6 students:
288/6 = 48
Therefore, the number of days it will take for 6 students to complete the same task is 48 days.
Problem 3
A bus covers 300 km in 5 hours. How far will it travel in 10 hours at the same speed?
The distance traveled by the bus in 10 hours is 600 km.
Explanation
Calculate the distance traveled in 1 hour: 300/5 = 60km
We now calculate the distance in 10 hours: 60 × 10 = 600 km
Therefore, the distance traveled by the bus in 10 hours is 600 km
Problem 4
If 4 children can make a clay pot in 16 days. How many days will it take for 8 children to make the same clay pot?
The number of days required for 8 children is 8 days.
Explanation
To calculate the total work of 4 children in 16 days:
4 × 16 = 64 days
Now we determine the number of days required for 8 children:
64/8 = 8 days
Therefore, the number of days for 8 children is 8 days.
Problem 5
3 kg of lemons cost $60, what is the cost of 9 kg of apples?
The cost of 9 apples is $180.
Explanation
The cost of 1 kg of lemon: 60/3 = $20
The cost of 9kg of lemons: 20 × 9 = $180
Therefore, the cost of 9 apples is $180.
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FAQs on the Unitary Method
1.What do you mean by the unitary method?
2.Give one example for the application of the unitary method.
3.What are the two types of unitary method.
4.The two types of unitary method are direct variation and indirect variation.
5.Are the unitary method and ratio-proportion method the same?
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Dr. Sarita Ghanshyam Tiwari
About the Author
Dr. Sarita Tiwari is a passionate educator specializing in Commercial Math, Vedic Math, and Abacus, with a mission to make numbers magical for young learners. With 8+ years of teaching experience and a Ph.D. in Business Economics, she blends academic rigo
Fun Fact
: She believes math is like music—once you understand the rhythm, everything just flows!
