# Unitary method

Unitary method is the process of finding the value of a single unit from the value of multiple units or vice versa.

Method to solve

Method 1:

• To find the value of the multiples articles when the unit value is given, we use multiplication.

Example 1:

The cost of 1 almirah is Rs 15,790. Find the cost of 5 such almirahs.

Solution:

The cost of 1 almirah = Rs 15,790
Number of almirah = 5
Multiply 15,790 by 5 to get the cost of 5 almirahs.
15,790 × 5 = 78,950
Therefore, the cost of 5 almirahs = Rs 78,950.

Method 2:

• To find the unit value when the value of the multiple is given, we use “division”.

Example 2:

The cost of 12 sacks of rice is Rs 864. Find the cost of one sack of rice.

Solution:

The cost of 12 sacks of rice = Rs 864
Number of sacks = 12
Divide 864 by 12 to get the cost of 1 sack of rice.
864 `÷` 12 = 72
Therefore, the cost of 1 sack of rice = Rs 72.

Method 3:

• If the value of multiple units is given and we need to find the value of a particular unit then we first find the value of a single using division and then find the value of the particular unit using multiplication.

Example 3:

A restaurant uses 504 kg of rice in 9 days. How much rice will be used in 18 days?

Solution:

Step 1: Quantity of rice used in 9 days = 504

Number of days = 9

Divide 504 by 9 to get the quantity of rice used in 1 day.

504 `÷` 9 = 56

Step 2: Quantity of rice used in 1 day = 56
Number of days = 18
Multiply 56 by 18 to get the quantity of rice used in 18 days.
56 × 18 = 1,008
Therefore, the quantity of rice used in 18 days is 1,008 Kg.

Method 4:

• If the value is expected to increase then we multiply and if the value is expected to decrease then we divide.

Example:

If 12 men can complete the work in 144 days. Find the number of days 18 men will require to complete the same work.

Solution:

Step 1: 12 men can complete the work in 144 days.

If one man will work alone then he will take more number of days.

Therefore, to find the number of days required by 1 man to complete the work we have to multiply 12 by 144.

12 × 144 = 1,728

Step 2: If one man takes 1,728 days to complete the work, then 18 men will take less number of days. Therefore, we divide 1,728 by 18 to get the number of days required by 18 men to complete the work.

1728 `÷` 18 = 96

Common Mistakes:

Students generally divide in place of multiply and multiply in place of division.

The general flow of the unitary method is shown in the diagram below: