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The unitary method provides an alternative approach to solving problems in various topics interrelated by ratios such as fractions, percentages, rates, interest, etc. Its appeal lies in its transparent logic, which often allows problems to be solved by mental arithmetic.

In the unitary method, 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.

Let’s understand what the unitary method is and how it is used.

## What is Unitary Method?

Let’s start with the unitary method definition which states that “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.”

For example, if the price of $32$ pens is ₹ $480$, and we want to find the price of $15$ pens. It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit. This method can be widely used for solving ratio and proportion problems.

## When Do We Use Unitary Method?

Whenever we’ve problems where the value of many things is given and we need to find either of the following

- the value of more things
- the value of fewer things

Following are some of the examples where we can use the unitary method.

- If $4$ bananas cost ₹$28$, how much do $7$ bananas cost?
- If $20$ tiles weigh $5$ kg. How much do $11$ tiles weigh?
- A tank that is \frac{2}{5} full contains $1200$ litres. What is its capacity?

## Steps to Use Unitary Method

Let’s understand the unitary method step by step.

First, make a note of the information given in the problem. In our problem above there are $32$ pens and their price is ₹$480$.

**Step 1:** Find the price of $1$ pen. In order to do that, divide the price of pens by the number of pens. This gives the price of $1$ pen.

$\text{Price of} 1 \text{ pen } =\frac{\text{Price of pens}}{\text{Number of pens}} = \frac{480}{32} = 15$. Therefore, the price of $1$ pen is ₹$15$.

**Step 2:** To find the price of $15$ pens, multiply the price of $1$ pen by the required number of pens. The $\text{price of} 15 \text{ pens is price of } 1 \text{ pen} \times \text{number of pens } = 25 \times 3 = 75$. Finally, we get the price of $15$ pens which is ₹$225$.

## Examples

**Ex 1:** If the annual rent of a flat is ₹ $1,44,000$, calculate the rent of $7$ months.

Annual rent of a flat = ₹ $1,44,000$ => Rent of flat for $12$ months = ₹ $1,44,000$

Rent of flat for $1$ month = $\frac{1,44,000}{12} = $₹ $12,000$

Rent of flat for $7$ months = $12,000 \times 7 =$₹ $84,000$

**Ex 2:** If weight of $75$ books is $12 \text{kg}$, find the weight of $35$ similar books.

Weight of $75$ books = $12 \text{kg} = 12000 \text{gram}$

Weight of $1$ book = $\frac{12000}{75} = 160 \text{gram}$

Weight of $35$ books = $160 \times 35 = 5600 \text{gram} = 5.6 \text{kg}$.

**Ex 3:** A shopowner is selling apples at $4$ for ₹$72$, and oranges at $11$ for ₹$154$. Which costs more, $10$ apples or $10$ oranges, and by how much?

Apples:

Cost of $4$ apples = ₹$72$

Cost of $1$ apple = $\frac{72}{4} =$₹ $18$

Cost of $10$ apples = $18 \times 10 =$₹ $180$

Oranges:

Cost of $11$ oranges = ₹$154$

Cost of $1$ orange = $\frac{154}{11} =$₹ $14$

Cost of $10$ oranges = $14 \times 10 =$₹ $140$

$180 – 140 = 40$

Therefore, the cost of $10$ apples is ₹$40$ more than that of the cost of $10$ oranges.

## Advantages of Unitary Method

The unitary method provides two important advantages over other methods.

- The unitary method often allows problems to be solved mentally, in contrast to the standard written algorithms. Thus the unitary method is an important part of learning mental arithmetic, and once grasped, can be used quickly for all sorts of calculations in everyday life and in financial situations.
- Fluency in the unitary method can often lead to a better understanding of the way in which a fraction is made up of two whole numbers, the numerator, and the denominator.

## Points to Remember

## Conclusion

The unitary method is based on converting an amount for $1$ unit and then converting an amount for the desired number of units. While converting from many to one, operation division is used while converting from one to many, and operation multiplication is used.

## Practice Problems

- The weight of $56$ books is $8 \text{kg}$. What is the weight of $152$ such books? How many such books weigh $5 \text{kg}$?
- Manoj types $450$ words in half an hour. How words would he type in $7$ minutes?
- A worker is paid ₹ $750$ for $6$ days’ work. If he works for $23$ days, how much will he get?
- A water tank can be filled in $7$ hours by $5$ equal-sized pumps working together. How much time will $7$ pumps take to fill it up?
- $15$ masons can build the wall in $20$ days. How many masons will build the wall in $12$ days?
- $76$ persons can complete the job in $42$ days. In how many days will $56$ persons do the same job?
- The freight for $75$ quintals of goods is ₹ $375$. Find the freight for $42$ quintals.

## Recommended Reading

- What is Percentage – Meaning, Formula & Examples
- What is Proportion? (With Meaning & Examples)
- What is Ratio(Meaning, Simplification & Examples)
- Factors and Multiples (With Methods & Examples)
- Fractions On Number Line – Representation & Examples
- Reducing Fractions – Lowest Form of A Fraction
- Comparing Fractions (With Methods & Examples)
- Like and Unlike Fractions
- Improper Fractions(Definition, Conversions & Examples)
- How To Find Equivalent Fractions? (With Examples)
- 6 Types of Fractions (With Definition, Examples & Uses)
- What is Fraction? – Definition, Examples & Types
- Mixed Fractions – Definition & Operations (With Examples)
- Multiplication and Division of Fractions
- Addition and Subtraction of Fractions (With Pictures)

## FAQs

### How do you solve unitary method questions?

There are two steps involved while solving questions using the unitary method.

(1) Convert the amount for $1$ unit by dividing

(2) Convert the amount for the desired number of units by multiplying

For example, if the cost of $7$ chocolates is ₹$175$, then to find the cost of $4$ chocolates, the first cost of $1$ chocolate is calculated by dividing $175$ by $7$, and then the cost of $1$ chocolate is multiplied by $4$ to get the cost of $4$ chocolates.

### What is the formula for the 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 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.