Unitary Method

In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given. The method to calculate the price of the required articles is called unitary method.

Generally, first we find the value of one article from the value of a multiple and then we find the value of the desired number of articles from the value of one. Usually this method involves the operations of multiplication and division both.

Remember: 

To find the cost of a number of articles ............

● We have to first find the cost of 1 article.

● Then we have to multiply the cost of 1 article with the number of articles required. This is called Unitary Method.


To find the cost of 1 article ............

● We have to divide the total cost by the number of articles purchased.


For example,

(i) A pack of 6 balls costs $ 48 and we have to buy 4 balls.

(ii) 20 oranges cost $ 60 and we have to buy 8 oranges.

(iii) The cost of 100 kg of wheat is $ 850 and we have to buy 40 kg of wheat.

In all such cases, first we find the unit cost for calculating the cost of the desired number of articles. To find the unit cost we divide the cost of many articles by the number of articles.


Ron wanted to buy 7 notebooks. The shopkeeper told him that the price of 1 notebook is 15 rupees. He thought for a while and gave the shopkeeper 105 rupees. How?

Cost of 1 note book = 15 rupees

Cost of 7 note books = 15 × 7 (to get more we multiply)

                               = 105


Ron also wanted to buy 2 balls. The cost of 1 dozen balls is 72 rupees. How much should he pay for 2 balls?

(1 dozen = 12)

Cost of 12 balls = 72 rupees

Cost of 1 ball = 72 rupees ÷ 12 (to get less we divide)

                    = 6 rupees

Therefore, cost of 2 balls = 6 × 2

                                     = 12 rupees


Let us consider some examples on unitary method:

1. 2 balls cost $ 8. Find the cost of 3 balls.

Cost of 2 balls = $ 8

Cost of 1 ball = $ 8 ÷ 2 = $ 4

Cost of 3 balls = $ 4 × 3 = $ 12


2. Cost of 1 book is $ 20. What is the cost of 10 such books?

Cost of 1 book = $ 20

Cost of 10 books = $ 20 × 10

                       = $ 200


3. 12 oranges cost $ 72. Find the cost of 4 oranges.

Cost of 12 oranges = $ 72

Cost of 1 orange = $ 72 ÷ 12 = $ 6

Cost of 4 oranges = $ 6 × 4 = $ 24


4. Cost of 5 pens is $ 125. What is the cost of 1 pen?

Cost of 5 pens = $ 125

Cost of 1 pen = $ 125 ÷ 5

                   = $ 25


5. 6 pens cost $ 96. How much will 2 such pens cost?

Cost of 6 pens = $ 96

Cost of 1 pen = $ 96 ÷ 6 = $ 16

Cost of 2 pens = $ 16 × 2 = $ 32


6. Cost of 10 note books is $ 250. Find the cost of 15 note books.

Cost of 10 note books = $ 250

Cost of 1 note book = $ 250 ÷ 10

                            = $ 25

Cost of 15 note books = $ 25 × 15

                              = $ 375



7. Cost of 5 chocolate is $ 15. Find the cost of 10 chocolate.

Cost of 5 chocolates= $15

Cost of 1 chocolate = $15 ÷ 5

                            = $ 3

Cost of 10 chocolate = $ 3× 10

                            = $ 30



8. Cost of 8 balls is $ 16. Find the cost of 17 balls.

Cost of 8 balls = $ 16

Cost of 1 ball = $ 16 ÷ 8

                   = $ 2

Cost of 17 balls = $ 2× 17

                      = $ 34


9. The cost of 9 boxes is 108 rupees.

(i) What is the cost of 1 box?

(ii) What is the cost of 3 boxes?


Cost of 9 boxes = 108 rupees

Cost of 1 box = 108 rupees ÷ 9

                        = 12 rupees

Cost of 3 boxes = 12 rupees × 3

                             = 36 rupees

Therefore, the cost of 3 boxes is 36 rupees.


10. A man stitches 25 dresses in 5 days. How many dresses does he make in 2 days?

Number of dresses made in 5 days = 25

Number of dresses made in 1 day = 25 ÷ 5

                                                 = 5

Number of dresses made in 2 days = 5 × 2

                                                   = 10

Therefore, the man stitches 10 dresses in 2 days.


11. Derek wants to buy 20 kg of rice. How much should he pay if 1 quintal of rice costs 1200 rupees?

1 quintal = 100 kg

The cost of 100 kg of rice = 1200 rupees

The cost of 1 kg of rice = 1200 rupees ÷ 100

                                  = 12 rupees

The cost of 20 kg of rice = 12 rupees × 20

                                   = 240 rupees

Therefore, the cost of 20 kg of rice is 240 rupees.


12. A car covers a distance of 300 km in 5 hours. What is the distance covered by it in 4 hours?

Distance covered by the car in 5 hours = 300 km.

Distance covered by the car in 1 hour = 300 km ÷ 5

                                                       = 60 km.

Distance covered by the car in 4 hours = 60 km × 4

                                                        = 240 km.


Note:

(i) If the cost of one object is given, we can find the cost of many objects by multiplying the cost of one object with the number of objects.

(ii) If the cost of several objects are given, we can find the cost of one object by dividing the cost of several objects by the number of objects.



Questions and Answers on Unitary Method:

1. The cost of 10 apples is 120 rupees. What is the cost of 25 apples?

Answer: 300 rupees


2. A factory produces 5320 soaps in 4 days. How many soaps does the factory produce in 10 days?

Answer: 13300 soaps


3. A passenger train covers 60 km in one hour. How much time will it take to cover 180 km?

Answer: 3 hours


4. The cost of 20 Eveready pen cells is 180 rupees. What is the cost of 8 cells?

Answer: 72 rupees


5. A scooter needs 6 litres of petrol to run 234 km. How far does the scooter run with 5 litres of petrol?

Answer: 195 km.


6. The cost of a dozen eggs is 24 rupees. What is the cost of 15 eggs?

Answer: 30 rupees





5th Grade Math Problems

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