Two ratios are equivalent, if the ________ corresponding to them are equivalent
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Two angles are equivalent, if the angles corresponding to them are equivalent.
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fraction
2explaining ;
In certain situations, comparison by division makes better sense than comparison by taking the difference. The comparison by division is called the ratio of the two numbers. For example, for most mammals the ratio of legs to noses is 4:1, but for humans, the ratio of legs to noses is 2:1.
We come across Ratios everywhere in life like sports, finance, medicine, cooking, you name it! In this topic, we learn what ratios are and how to use them.
Ratios
A ratio is a relationship between two quantities of the same kind with same unit and is obtained on dividing first quantity by the second. The ratio between 3 and 4 is written as 3 : 4.
In the ratio 2 : 3, first term 2 is called antecedent and the second term 4 is called consequent.
A ratio has no unit.
To calculate ratio, the two quantities have to be measured using the same unit. If not, they should be converted to the same unit before ratio is taken.
The same ratio can occur in different situations. For example, the ratio 4 : 5 is different from 5 : 4.
A ratio can be treated as a fraction. For example, 5 : 6 can be treated as 5/65/6
Two ratios are said to be equivalent if the fractions corresponding to them are equivalent.
To calculate equivalent ratio, convert the ratio into a fraction, and then multiply or divide the numerator and the denominator by the same number. Ex : 4 : 5 is equivalent to 8 : 10 or 12 : 15 and so on.
A ratio can be expressed in its lowest form. For example, the ratio 40 : 20 in its lowest form can be written as follows: 40 : 20 = 40/2040/20 = (2×2×10)/(2×10)(2×2×10)/(2×10) = 2/12/1 = 2 : 1. Thus, the lowest form of 40 : 20 is 2 : 1.
Proportions
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 3, 12, 5, and 20 can be written as 3:12: :5:20 or 3 : 12 = 5 : 20.
The order of the terms in a proportion carries value.
The quantities 3, 12, 5, 20 are in proportion, whereas 3, 20, 5 and 12 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. For every proportion, the product of the extremes is always equal to the product of the means.
Three quantities (a, b, c) are said to be in continued proportion if the ratio between the first and the second quantity is equal to the ratio between the second and third quantity, if a : b = b : c.