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.

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.


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 10chocolate = $ 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


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.




5th Grade Math Problems

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