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Comparing fractions (I)

© Vidya Narayan Wadadekar

The ability to obtain equivalent fractions is very useful in acquiring many higher-level concepts related to fractions. Let us first learn to compare fractions. On many occasions we need to compare fractions. Especially, if we are asked to provide the difference between two fractional numbers, we need to know which one is to be subtracted from the other fractional number. Understanding of comparison is also useful to check if the answer of the problem we have solved is the likely one!

While understanding fractional numbers we have indirectly learned to compare some fractions. These were the fractions with one in their numerator. We will revise comparisons of numbers with one as a numerator, using different tools.

Comparing fractions using fractions wall:

Refer to the fractions wall we have. This wall has one complete strip on top, which represents the fraction 1/1. Subsequently we kept dividing this strip into an increasing number of parts. Thus, we obtained fractions like half, one-thirds, one-fourths...etc.

Just by looking at the fractions wall, we can compare fractions 1/1, 1/2, 1/3, 1/4, etc. We can see that 1/1 is greater than 1/2 or 1/3 or 1/4, etc. We can also see that the fraction 1/2 is greater than 1/3 or 1/4 ...etc. In short, we can see that the fractions which appear in the upper part of the fractions wall are greater than those appearing in the lower part of the fractions wall.

Comparing fractions using fractions chart:

Similar observations are possible with our fractions chart.

Let us compare 1/1 with ½ using our chart. 1/1 in our fractions chart is equivalent to 24 objects.

1/2 of 24 in the chart is equivalent to 12 objects.

Therefore, comparing 1/1 and 1/2 can now be managed by comparing 24 objects with 12 objects! 24 is greater than 12. Using arithmetic signs, we can write 24 > 12

Hence, 1/1 must be greater than 1/2. The same can now be translated to arithmetic language as 1/1 > ½. In a similar fashion you can compare different fractions like 1/2, 1/3, 1/4 ...etc. with each other using fractions chart.

Comparisons between fractions with one as a numerator using a fractions chart also reveal that as we distribute the objects into more numbers of parts, the number of objects in each part keeps reducing.

In other words, a set of 24 objects if divided into two parts each part will have more numbers of objects compared to those in each of its four parts. Therefore, lesser is the number of parts (indicated by the number in the denominator) into which the objects of a set get distributed; greater is the value of the fraction, provided the numerators of the fractions are equivalent or same.

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