# Comparison of Fractions

Having learnt about the kinds of fractions and operations on fractions we now look at comparison of fractions. Comparison of fractions proves useful when lesser or greater of two or more fractions have to be ascertained. The sign “>” is put after a fraction which is greater than the other while the sign”<” is put after a fraction which is smaller. Just like other operations, the method of comparison of fractions varies for Like and Unlike fractions. Like Fractions: In Like fractions since the denominators are same one can easily identify the greater or lesser fraction by simply comparing the value of the numerators. For instance, in finding the larger fraction between 1/5th and 2/5th parts of a pizza, one only needs to see which numerator is greater. Likewise for 3/7 and 5/7 the fraction with the greater numerator is the is larger of the two, here being 5/7. Same is the case for 2/9 and 4/9. Unlike Fractions: For Unlike fractions to be compared they first need to be converted to Like fractions . For this the denominators of both the unlike fractions need to be equated. As illustrated in the video fraction ¼ can also be written as 2/8, 3/12 and so on. This happens when both the numerator and denominator of the fraction are multiplied by the same number. Hence ¼ *2 =2/8 and 1/4*3=3/12. Similarly 1/3 when multiplied by 2, 3 and 4 can be written as 2/6, 3/9, 4/12. Looking carefully we see that series of both fractions have a common denominator as 12. Hence to equate both fractions ¼ will be multiplied by 3 making it 3/12 and 1/3 shall be multiplied by 4 making it 4/12. It is now evident that 1/3 is a greater fraction than ¼ since 4/12 is greater than 3/12. Hence ¼ < 1/3 . Alternately one can also equate the fractions by finding the LCM to the denominators of both fractions and consequently multiplying the numerator of each fraction with the same number as the denominator of that fraction that gives the LCM number. The method of comparison of fractions is most useful in problems regarding arrangement of fractions in ascending or descending order.

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