Comparison of Fractions
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Comparison of fractions: Suppose, some fractions are to be arranged in ascending or descending order of magnitude.
Fractions can be compared in many ways. Find below 3 differnet ways of doing it.
If denominators are same, like 56/98 and 57/98, then just compare the numerators,
So the rule is:
a b --- > --- if a > b n n
Since 56 < 57, 56/98 < 57/98. They are in the same order as their numerators.
Second, suppose the numerators are the same, as in your problem, 5/9 and 5/6. Then it works the opposite way: The bigger the denominator, the smaller the fraction. So the rule is: n n --- > --- if a < b a b
Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their denominators.
Thirdly, in general cases, you simply convert the fractions to the first case, by giving them a common denominator. You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work. Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply by 7; to convert 4/7 to 63rds, we multiply by 9:
5 4 --- ? --- 9 7
5*7 4*9 --- ? --- 9*7 7*9
35 < 36, so
5 4 --- < --- 9 7
You may not calculate the value of denominator because it will be same in both cases.
5*7=35 4*9=36; since this is bigger, 4/7 is bigger \ / 5 4 --- ? --- 9 7
If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that 81 is a multiple of 9, so I do not have to go to the trouble of multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to 44: 5 44 --- ? -- 9 81
5*9 44 --- ? -- 9*9 81
45 > 44 so
5 44 --- > -- 9 81
Finally, convert each one of the given fractions in the decimal form. Now, arrange them in ascending order
as per requirements.
Recurring Decimal: - If, in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal. In a recurring decimal, if a single figure is repeated, then it is expressed by putting a dot on it. If a set of figures is repeated, it is expressed by putting a bar on the set.
Pure Recurring Decimal: A decimal fraction, in which all the figures after the decimal point are repeated, is called a pure recurring decimal e.g. 2/3 = 0.666…=0.6.
Converting a Pure Recurring Decimal into Vulgar Fraction:-Rule: - Write the repeated figures only once in the numerator and take as many nines in the denominator as is the number of repeating figures.
Decimal: - a decimal fraction in which some figures do not repeat and some of them are repeated is called a mixed recurring decimal, e.g. 0.173333…= 0.173.
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August 10th, 2010 - 21:19
kuch kam ka likho. aise waise kuch bhi mat likho. Ye bhi koi important bat thi ratio wali. cat me ye sab use karenge
August 10th, 2010 - 21:42
Jo hukam madam!! agey se dhyan rahega!!
January 28th, 2010 - 00:22
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