# Unitary Method

Let's explore the world of unitary method with real life examples in this mini lesson. We will learn about definition of unitary method, its types and stepwise solutions to the problems on it. So, let's get going!

Hey kids! Do you get confused at times when you need to make payment on buying some items?

Want to learn a method that makes your shopping experience better by doing the correct transaction and not get cheated on the prices at any time?

Here we have unitary method to help you out! It's very useful method when we go to a shop to buy books and other stationaries.

Unitary method 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.

## Lesson Plan

 1 What is Unitary Method? 2 Solved Examples Based on Unitary Method 3 Interactive Questions 4 FREE Downloadable Resources on Unitary Method

## Free PDFs for Offline Revision

Get your copy of Unitary Method E-book along with Worksheets and Tips and Tricks PDFs for Free!

## What is Unitary Method?

Let's recap the definition.

"Unitary method 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.

Ria went to an ice-cream parlour and bought $$5$$ ice-creams.

She paid $$\text{Rs.}\;125$$ to the shopkeeper.

Next day she again goes to same parlour 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 :

First, let us make a note of the information we have.

There are $$5$$ ice-creams.

$$5$$ ice-creams cost $$\text{Rs.}\;125$$.

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:

\begin{align}&=\frac{\text{Total cost of ice-creams}}{\text{Total number of ice-creams}}\\&=\frac{125}{5}\\&=25\end{align}

Therefore, the cost of $$1$$ ice-cream is $$\text{Rs.}\;25$$.

STEP 2:

To find the cost of $$3$$ ice-creams, multiply the cost of $$1$$ ice-cream with the number of ice-creams.

Cost of 3 ice-creams:

\begin{align} &\!= \!\text{Cost of 1 ice-cream} \! \times \! \text{Number of ice-creams} \\ & \!=\! 25 \! \times \! 3 \\ & \!=\! 75 \\ \end{align}

Finally, we have the cost of $$3$$ ice-creams i.e. $$\text{Rs.}\;75$$.

In unitary method, the value of many things is given and we need to either find the value of more or less 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 less things by multiplication.

## Unitary Method: Calculator

Let's have some FUN while you LEARN! Here is a simulation which calculates the cost of a ball when we input the cost of many balls.

Use the following simulation to find the cost of more or fewer balls. Try changing the number of balls and their costs and observe the change in cost of 1 ball.

So, what are you waiting for, let's PLAY!

We hope this served you as a good unitary method calculator.

## What Are the Different Types of Unitary Methods?

There are two types of unitary methods because they result in two types of variations.

### Direct Variation

This type describes the direct relationship between two quantities.

In simple words, if one quantity increases, the other quantity also increases and vice-versa.

For example:

If the speed of a car is increased, it covers more distance in a fixed amount of time.

### Inverse Variation

This type describes the indirect relationship between two quantities.

In simple words, if one quantity increases, the other quantity decreases and vice-versa.

For example:

Increasing the speed of the car will result in covering a fixed distance in lesser time.

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

## Learn These Along with Unitary Method!

We hope you are enjoying the journey of unitary method. Would you like to be a champ?

Here are a few more lessons related to unitary method. These topics will not only help you master the concept for unitary method, but also other topics related to it.

 Click on any of the short lessons you want to explore! Ratio Proportion Commercial Math Percentage Discount

### Unitary Method: Ratio and Proportion

Unitary method in maths is also used to find the ratio between two quantities.

Consider the following situation.

A contractor employed two men, Ram and Shyam, to work in his factory and paid them daily wages.

Ram is paid $$\text{Rs.}\;150$$ and Shyam is paid $$\text{Rs.}\;110$$ for each day's work.

Ram saves $$\text{Rs.}\;800$$ per month and Shyam saves $$\text{Rs.}\;500$$ per month.

Can you find the ratio of their monthly expenditure?

Let’s find their monthly income by using the unitary method.

Ram’s wages for one day $$= \text{Rs.} \;150$$

Ram’s wages for one month

\begin{align}&= \text{Rs. } (150 \times 30)\\&= \text{Rs. }4500\end{align}

Similarly, Shyam’s wages for one month

\begin{align}&= \text{Rs. }(110 \times 30)\\&= \text{Rs. }3300\end{align}

Now find their monthly expenditure.

Ram’s monthly expenditure

\begin{align}&= \text{Rs. }4500 - \text{Rs. }800 \\&= \text{Rs. }3700 \end{align}

Shyam’s monthly expenditure

\begin{align}&= \text{Rs. }3300 - \text{Rs. }500 \\& = \text{Rs. }2800 \end{align}

The ratio of their monthly expenditure is given by
\begin{align}\frac{\text{Ram’s monthly expenditure}}{\text{Shyam’s monthly expenditure}}&=\frac{3700}{2800}\\&=\frac{37}{28}\end{align}

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

## Solved Examples

 Example 1

Karan goes to a stationery shop to buy some notebooks.

The shopkeeper informs him that $$2$$ notebooks would cost $$\text{Rs.}\;90$$.Can you find the cost of $$5$$ notebooks?

Solution

In this example, the number of books corresponds to the “unit” and the cost of the books corresponds to the “value”.

STEP 1:

First, we will find the cost of $$1$$ notebook.

\begin{align}\text {Cost of 1 notebook }&=\frac{\text{Total cost of books}}{\text{Total number of books}}\\&=\frac{90}{2}\\&=45\end{align}

STEP 2:

Now, we will find the cost of $$5$$ notebooks.

\begin{align}\!\text {Cost of 5 notebooks }&=\!\text{Cost of 1 book}\! \times\! \text{Number of books}\\&\!=\!45 \!\times\! 5\\&\!=\!225\end{align}

 $$\therefore$$Cost of 5 notebooks = Rs 225
 Example 2

Edwin wants to buy a bottle of ink. At the stationery shop, he was given two options:

a)    Bottle A costing him $$\textbf{Rs. } \bf{55}$$ for $$\bf{2} \textbf{ Litres}$$
b)    Bottle  B costing him $$\textbf{Rs. } \bf{70}$$ for $$\bf{3}\textbf{ Litres}$$

Can you help him decide which option would be the best buy?

Solution

To help him decide the best buy, we can find the cost of 1 litre of ink.

For Bottle A : Cost of 1 litre ink = $$\dfrac{55}{2} = \text {Rs. }27.5$$

For Bottle B : Cost of 1 litre ink = $$\dfrac{70}{3} = \text {Rs. }23.3$$

We observe that 1 litre ink of type B costs less than 1 litre ink of type A.

 $$\therefore$$ Bottle B is the best buy.
 Example 3

Priya can type 540 words in half an hour. How many words will she able to type in 20 minutes with same efficiency?

Solution

Number of words typed in half an hour i.e. $$30$$ min = $$540$$

$$\therefore$$ Number of words typed in $$1$$ min = $$\dfrac{540}{30}=18$$

Number of words typed in $$20$$ min = $$20 \times 18 = 360$$

 $$\therefore$$Priya will be able to type 360 words in 20 minutes
 Example 4

If 36 labourers can construct a road in 12 days, how many days will it take for 16 labourers to construct same road?

Solution

We have here: More labourers, less days required.

$$36$$ labourers can construct the road in $$12$$ days.

So, $$1$$ labourers can construct the road in $$12\times36$$ days.

$$\therefore 16$$ labourers can construct the road in $$\dfrac{12\times36}{16}=27$$ days.

 $$\therefore$$16 labourers will construct the road in 27 days

Challenging Questions
1. If Rijo can complete a work in 30 days and Soham finishes same work in 60 days, then how many days they would require to finish the work working together?

2. 18 binders bind 900 diaries in 10 days. How many binders would be required to bind 660 diaries in 12 days? Use unitary method to solve this.

## Interactive Questions

Here are a few activities for you. Select/Type your answer and click the "Check answer" button to see the results.

## Let’s Summarize

The mini-lesson was aimed at helping you learn about Unitary method and how to apply this method in real life. Hope you enjoyed learning about them and exploring this method and its application to real life situations.

We would love to hear from you. Drop us your comments in the chat and we would be happy to help.

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

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Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we at Cuemath believe in.

## 1. What is the formula for unitary method?

The formula for 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.

## 2. What is the unitary method for percentage?

To find the $$100%$$ amount or the value of an object, unitary method is used. Consider the following example.

In a hospital, $$10%$$ of the monthly consumption of milk of patients is $$1540 \text{L}$$. 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.

## 3. What is the unitary ratio?

When either side of the ratio is equal to $$1$$ it is called unitary ratio.

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.

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UNitary MEthod Worksheet
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