Proportions

Proportion
If the ratios between quantity A and quantity B is equal to the ratio between quantity C and quantity D, then the four quantities A, B, C and D, are said to be in proportion. Proportion is denoted by the signs '∷’ or ‘=’. 

Thus, the quantities 4, 16, 5 and 20 can be written as 4:16∷5:20 or 4:16 = 5:20.

The order of the terms in a proportion carries value. The quantities 4,16, 5 and 20 are in proportion, whereas 4, 20, 5 and 16 are not in proportion.

In the proportion a:b∷c:d, the quantities a and d are the extreme terms, and b and c are the middle terms.

Unitary method
The method of calculating the value of one unit and using this value to calculate the value of the required number of units is called the unitary method.

For example, suppose the cost of 8 bags is Rs 240. Now, to find the cost of 6 bags, using the unitary method, we first find out the cost of one bag. 

Cost of one bag = 240 8 = Rs 30

Now, the cost of 6 bags = 6 × 30 = Rs 180

Hence, the cost of 6 bags is Rs 180.

Summary

Proportion
If the ratios between quantity A and quantity B is equal to the ratio between quantity C and quantity D, then the four quantities A, B, C and D, are said to be in proportion. Proportion is denoted by the signs '∷’ or ‘=’. 

Thus, the quantities 4, 16, 5 and 20 can be written as 4:16∷5:20 or 4:16 = 5:20.

The order of the terms in a proportion carries value. The quantities 4,16, 5 and 20 are in proportion, whereas 4, 20, 5 and 16 are not in proportion.

In the proportion a:b∷c:d, the quantities a and d are the extreme terms, and b and c are the middle terms.

Unitary method
The method of calculating the value of one unit and using this value to calculate the value of the required number of units is called the unitary method.

For example, suppose the cost of 8 bags is Rs 240. Now, to find the cost of 6 bags, using the unitary method, we first find out the cost of one bag. 

Cost of one bag = 240 8 = Rs 30

Now, the cost of 6 bags = 6 × 30 = Rs 180

Hence, the cost of 6 bags is Rs 180.

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