ratio

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Ratio : A “ratio” is just a comparison between two different things. To find the ratio of the first number to the second, we find “What multiple of the second number is the first number?”. This is done by dividing the first number by the second one. For example, the ratio between 20 and 32 is = 20 / 32 = 5/8 The ratio of 60/80 = 6/8 Here you can write the phrase “the ratio of X to Y” as X : Y“. You should read it as “X is to Y” While finding out the ratio of the given numbers, you should keep the following points in your mind : 1. The quantities should be of same kind. You cant find out the ratio between 2 kg Iron and 1 liter Milk. 2. These quantities in the ratio are called Terms The first term in ratio is called Antecedent and the second term is called Consequent. 3. We represent ratios in numbers. There are no units for this. 4. If somebody says, the ratio of the two numbers is X : Y, then that doesn’t means the first number should be X and the second number should be Y. The numbers may be CX : CY (here C is a non zero constant which is a multiple of X and Y). 5. The ratio is always same. If you divide / multiple the numerator and denominator with the same number then the value should be same. 6. The ratio will change if you add or subtract a number from both numerator and denominator. 7. Percentage is a special kind of ratio. You can treat it as the ratio which is having its second term as 100. 8. Two ratios a : b and c : d (or a/b and c/d) are said to be equal if a x d = b x c. 9. If two ratios are X : Y and Y : Z, then you can simply write them as X : Y : Z. Some important points: 1) If ratio is written as A:B, it is said to be a linear form and in case it is written as A/B, it is said to be fractional form. 2) Ratio does not have any unit. It is mere number. 3) The equality of two ratios is known as proportion i.e. a/b = c/d If a/b = c/d , then it is also equal to a+c/b+d Invertendo : If a/b = c/d , then b/a = d/c Alterendo : If a/b = c/d , then a/c = b/d Componendo : If a/b = c/d , then a+b/b = c+d/d Dividendo : If a/b = c/d , then a-b/b = c-d/d Componendo and Dividendo : If a/b = c/d , then a+b/a-b = c+d/c-d

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Ratio : A ratio is just a comparison between two different things.To find the ratio of the first number to the second, we find What multiple of the second number is the first number?. This is done by dividing the first number by the second one.For example, the ratio between ! and " is#! $ "# %$&The ratio of '!$&! # '$&(ere you can write the phrase the ratio of X to Y asX : Y. )ou should read it as X is to YWhile finding out the ratio of the given numbers !ou should "eep the following points in !our mind :*. The +uantities should be of same ,ind. )ou cant find out the ratio between,g -ron and * liter .il,.. These +uantities in the ratio are called Terms The first term in ratio is called Antecedent and the second term is called #onse$uent.". We represent ratios in numbers. There are no units for this./. -f somebody says, the ratio of the two numbers is 0 1 ), then that doesn2t means the first number should be 0 and the second number should be ). The numbers may be 30 1 3) 4here 3 is a non 5ero constant which is a multiple of 0 and )6.%. The ratio is always same. -f you divide $ multiple the numerator and denominator with the same number thenthe value should be same.'. The ratio will change if you add or subtract a number from both numerator and denominator.7. 8ercentage is a special ,ind of ratio. )ou can treat it as the ratio which is having its second term as *!!.&. Two ratios a 1 b and c 1 d4or a$b and c$d6 are said to be e+ualif a x d # b x c.9. -f two ratios are 0 1 ) and ) 1 :, then you can simply write them as 0 1 ) 1 :.;ome important points1*6 -f ratio is written as