Ascending and Descending Order Fractions

Whenever we have a set of numbers, we compare them. Some numbers are larger than others, while some are smaller. For example, we know that 5 is smaller than 12 and greater than 2. Similarly, -4 is smaller than 0. But how can we make such comparisons with fractions? Let’s explore through some examples.

In a school test:

• Aryan got 69

• Meera got 89

• Rohan got 49

Since Meera got the highest fraction of marks, we can see that: 89 >< 69 >< 49

Here, all fractions have the same denominator, making it easy to compare them.

Two fractions are unlike if they have differentsame denominators.

For example: 13 and 15 are unlike fractions. So are 23 and 45

Unlike fractions with the same numerator.

Consider a pair of unlike fractions 13 and 15 , in which the numerator is the same.

Which is greater 13 or 15 ?

Answer : 1315

In 13, we divide the whole into equal parts and take .

In 15 we divide the whole into equal parts and take .

Note that in 13 , the whole is divided into a lessergreater number of parts than in 15.

The equal part that we get in 13 is, therefore, larger than the equal part we get in 15.

Since in both cases we take the same number of parts (i.e. one), the portion of the whole showing 13 is larger than the portion showing 15 , and therfore 13 >< 15.

In the same way we can say 23 > 25. In this case, the situation is the same as in the case above, expect that the common numerator is 2, not 1.

The whole is divided into a largersmaller number of equal parts for 25 than for 23.

Therefore, each equal part of the whole in case of 23 is largersmaller than that in case of 25.

Therefore, the portion of the whole showing 23 is larger than the portion showing 25 and hence, 23 >< 25.

We can see from the above example that if the numerator is the same in two fractions, the fraction with the smallergreater denominator is greater of the two.

Thus, 18 >< 110 , 35 >< 37 , 49 >< 411 and so on.

Let us arrange 21,213,29,25,27 in increasing order.

All these fractions are unlike, but their numerator is the same. Hence, in such case, the larger the denominator, the smaller is the fraction.

The smallest is 21325 as it has the largest denominator.

The next three fractions in order are 29 27 25. The greatest fraction is 21 (It is with the smallest denominator).

1. Arrange the following in ascending and descending order :

(a) 112, 123,15,17,150,19,17

Ascending order

Descending order

(b) 37 , 311 , 35 , 32 , 313 , 34 , 317.

Ascending order

Descending order

(c)Arrange them in ascending and descending order.

(i) 213 , 225 , 26 , 28 , 210 , 217

Ascending Order

Descending Order

(ii) 56 , 517 , 514 , 57 , 512 , 58 , 511

Ascending Order

Descending Order

(iii) 411 , 413 , 45 , 47 , 419 , 417 , 415

Ascending Order

Descending Order

Compare 45 and 56.

Instruction

Compare 56 and 1315.

Instruction

Take the product of 6 and 15 is which is 90.

Obviously 90 is also a common multiple of 6 and 15. We may use either 90 or (LCM of 6 and 15) and get the correct answer.

But we are also aware that it is easier and more convenient to work with smaller numbers. Thus, the common multiple that we take is as small as possible. This is why the LCM of the denominators of the fractions is preferred as the common denominator.