** Introduction: **In the competition exams, questions related to the comparison of fractions are given in four different ways.

** (i) **What is the different smallest in the given fractions and which is the different largest ?

** (ii)** Which different groups in the given group are ascending order and what different group descending order (Descending order)?

** Note: **

** (i) Ascending order –** The smallest difference in this sequence is written first and foremost, most later.

Like ^{1}/_{16 } ^{1}/_{8 }^{1}/_{4 } ^{ 1}/_{2 }

** (ii) Descending order** – The largest difference in this sequence is the first and the smallest of the most widely written later.

Such as ^{ 7}/_{8 } ^{5}/_{8 }^{3}/_{8 }^{1}/_{8}

**Example 1. **Which of the following fractions is the smallest and the second largest?

(i) ^{ 13}/_{17} (ii) ^{ 19}/_{23} (iii) ^{37}/_{41} (iv) ^{ 29}/_{33} (v) ^{ 59}/_{63}

** Explanation: **Here are the ^{ 13}/_{17} are the smallest and ^{ 59}/_{63} There is a big difference.

** Example 2 . **What is the different ascending order in the different series below and which is in the Descending Order?

(i) ^{ 5}/_{7 } ^{3}/_{5} ^{9}/_{12} (ii) ^{ 3}/_{5} ^{5}/_{7 } ^{ 9} /_{12} (iii) ^{ 5}/_{7} ^{9}/_{12} ^{3}/_{5 }(iv) ^{ 9}/_{12} ^{3}/_{5 }^{5}/_{7 }(v) ^{ 9}/_{12} ^{5}/_{7 } ^{ 3}/_{5}

** Explanation: **here ^{ 3}/_{5} ^{5}/_{7 } ^{9}/_{12} So the different categories given in the option (2) are in ascending order. Whereas the different category given in the Option (5) is in descending order.

** Noble Suggestion:** Banking, S.S.C. and R.R.B. In other competitive exams, questions are often asked by the Comparison of Variants . Most of the questions based on this are those which can only be solved by mental action. There are some questions that require a little calculation too. Resolving such questions by short-cut methods is justified.

** How to Identify the Different Types of Fractions **

** Points to be Noted: ** Comparison of Variants Before solving all related questions, it is necessary to first consider this point as to which method can be solved as quickly as possible. Is – Difference Rule, Cross multiplication rule, LCM By Rule or Division Rule. Questions should be resolved only after this decision.

If the numerator and the denominator of the given fractions are the same, then they should be “by the difference rule, if the difference is uneven,” by the cross multiplication rule, the fraction and each of the LCM being small “by the LCM rule and the difference between being unequal Together with LCM being large “Comparison is done by Division.

** TYPE-1 DIFFERENCE RULE. **

** TRICK – **If the fraction of each of the given fractions and the difference is the same, then the smallest number formed by the smallest and the largest numbers is the largest of the largest.

**Example – 1. **Which is the highest value in a different group given below.**
**(i)

** Example – 2. **Which Descending Order is in different groups given below?**
**(i)

(iv) ^{13}/_{17} ^{7}/_{11} ^{5}/_{9} ^{3}/_{7 }(v) None of these

** Explanation: **The fraction of each fraction and the difference in each of the given fractions is 4 and the variances of the smallest and largest numbers, respectively, ^{ 3}/_{7} and ^{ 13}/_{17} . Therefore, the smallest of them are ^{ 3}/_{7} and the largest difference is ^{ 13}/_{17} . Therefore, in the alternative (4) the fractions are decorated in descending order.

** TYPE-2 CROSS MULTIPLICATION RULE **

**TYPE-3**** ****L. C. M. RULE **

** TRICK – **

** (i) **If the fraction of the given fractions is L.C.M, its LC.M. If smaller than, then by dividing all the fractions and by dividing them by the appropriate number, the fragments can be divided into L.C.M. Is equal to. Now the fraction of which is the smallest of which is the second largest and the largest of which is the largest is the smallest.

** (ii) **If all of the given fractions are L.C.M. L.C.M. of his part If you are smaller than that, by multiplying each and every fraction of all the fractions by the appropriate number, they will be given the L.C.M. Is equal to. Now the fraction of the fraction of which is the smallest, the smallest and the fraction of the fraction which is the largest is the second largest.

** TYPE-4**** ** **DIVISION RULE **

** TRICK – **There are some different series that are easy to compare with part method. Fractions of this type of series are divided by dividing each and every fraction into a given quotient by comparing it with the result

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