Unitary Method

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit. It is a method that we use for most of the calculations in math. You will find this method useful while solving questions on ratio and proportion, algebra, geometry, etc.

Through the unitary method, we can find the missing value. For example, if 1 packet of juice costs $5, then what would the cost of 5 such packets be? Then we can easily find that the cost of 5 packets, i.e. $25. Let's understand this concept in detail in this lesson.

Let's recap the unitary method definition. "It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit."

Here is a situation to understand this method. Emma went to an ice cream parlor and bought 5 ice-creams. She paid $125 to the shopkeeper. The next day, she again goes to the same parlor and orders 3 icecreams. So, how much will she be paying for 3 ice-creams? This may seem hard to calculate! However, we can solve this problem using the unitary method.

Steps to Use Unitary Method

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

• Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.
• Step 2: To find the cost of 3 ice-creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

In the unitary method, the value of many things is given and we need to either find the value of more or fewer things. In order to do that, we must first find the value of one thing by division and then find the value of more or fewer things by multiplication.

This diagram of the unitary method depicts that if we have to find the cost of 1 item from the given cost of many items, we apply division operation. While, if we have to find the cost of many items from the cost of 1 item, we apply multiplication operation.

In the unitary method, we always count the value of a unit or one quantity first, and then we calculate the values of more or fewer quantities. That is why this method is termed the unitary method. There are two types of unitary methods because they result in two types of variations and those are given below:

• Direct Variation
• Indirect Variation

Direct Variation in Unitary Method

This type describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases, and if one quantity decreases, the other quantity also decreases. For example, If the speed of a car is increased, it covers more distance in a fixed amount of time. So, speed and distance are two quantities that are related to each other in direct variation.

Indirect Variation in Unitary Method

This type describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases, and if one quantity decreases the other quantity increases. For example, increasing the speed of the car will result in covering a fixed distance in lesser time. Speed and time are two quantities that are related to each other in indirect variation.

Unitary method in maths is also used to find the ratio between two quantities. Consider the following situation. A contractor employed two men, Ryan and David, to work in his factory and paid them daily wages. Ryan is paid $150 and David is paid $110 for each day's work. Ryan saves $800 per month and David saves $500 per month. Can you find the ratio of their monthly expenditure?

• Let’s find their monthly income by using the unitary method. Ryan’s wages for one day= $150. Ryan’s wages for one month= $(150 × 30) = $4500. Similarly, David’s wages for one month= $(110 × 30) = $3300.
• Now find their monthly expenditure. Ryan’s monthly expenditure = $4500 - $800 = $3700. David’s monthly expenditure = $3300 - $500 = $2800.
• The ratio of their monthly expenditure is given by, Ryan’s monthly expenditure/David’s monthly expenditure=3700/2800=37/28.

Proportion is defined as the relationship between two ratios. So, with the help of the unitary method, we can also find the missing value in the given proportion of two quantities. For example, if the cost and number of balloons sold by two different sellers are defined in a proportion as 3:4::15:x. Here we can find the missing value of x by using the concept of the unitary method. If the cost of 4 balloons is $3, then the number of balloons bought in $15 is 3/4 = 15/x, which is the same as, 3x=60. So, the number of balloons is 20.

Let's move on to solve some more real-life problems based on the unitary method.

Unitary method is very helpful in solving various problems that we come across in our daily life. Some of those real-life applications of the unitary method are given below:

• To find the speed of an object for a given distance, if the speed and distance are given in different quantities.
• To find the number of people required to complete a given amount of work.
• To find the area of a square of a given length if the ratio of its area and side is given.
• To find the cost of a specific number of objects, if the cost and number of objects are given in different quantities.
• To find the percentage of a quantity.

Important Notes:

1. The value of many quantities is found by multiplying the value of one quantity by the number of quantities.
2. The value of one quantity is found by dividing the value of many quantities by the number of quantities.

Topics Related to Unitary Method

Check these interesting articles related to the concept of the unitary method in math.

• Ratio
• Rate Definition
• Unit Conversion
• Proportion
• Commercial Math
• Percentage
• Discount
• Ratio Calculator

How do you Solve Unitary Method Questions?

To solve questions based on the unitary method, we have to first find the number of objects at the unit level, then we find it for higher values. For example, if the cost of 5 chocolates is $10, then to find the cost of 6 chocolates, it is better to find the cost of 1 chocolate first. Then we multiply it by 6 to get the cost of 6 chocolates.

What is the Unitary Method for Percentage?

To find the 100^th amount or the value of an object, the unitary method is used. Consider the following example. In a hospital, 10% of the monthly consumption of milk of patients is 1540L. What is the 100% monthly consumption of milk in the hospital? In this case, the unitary method can be used to find the 1% monthly consumption and then multiply 100 by the amount of 1% of monthly consumption of milk.

What is the Formula for Unitary Method?

The formula for the unitary method is to find the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

What is the Unitary Ratio?

When either side of the ratio is equal to 1 it is called unitary ratio. The unitary method in maths uses this for comparison. For example, there are 10 girls and 20 boys in a class. The ratio of girls to boys is 1:2. This is a unitary ratio.

What are the Types of Unitary Method?

There are two types of unitary methods based on the variations and those are given below:

• Direct Variation
• Indirect Variation

What is Unitary Method in Ratio and Proportion?

In ratio and proportion, the unitary method is used to find the quantity of one object when the quantity of another object and the ratio between two are given.