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Fractions in Ascending Order

We will discuss here how to arrange the fractions in ascending order.


Solved examples for arranging in ascending order:

1. Let us arrange the fractions 516, 916, 816 and 716 in ascending order.

We know that above fractions are like fractions. We can arrange them in ascending order by comparing the numerators of each fraction. We can also compare these fractions by comparing the shaded parts in the given figures.

Comparison Fractions

916 > 816 > 716 > 516.

Hence, the ascending order is 516, 716, 816 and 916.

2. Arrange the following fractions 56, 89, 23 in ascending order.

First we find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. of 3, 6 and 9



L.C.M. = 3 × 2 × 3 × 1 = 18

Now to make the fraction as like fractions divide the L.C.M. by the denominator of fractions, then multiply both the numerator and denominator of fraction with the number get after dividing L.C.M.

As in fraction 56 denominator is 6.

Divide 18 ÷ 6 = 3

Now, multiply both numerator and denominator by 3 = 5×36×3 = 1518

Similarly, 89 = 8×29×2 = 1618 (because 18 ÷ 9 = 2)

and 23 = 2×63×6 = 1218 (because 18 ÷ 3 = 6)

Now, we compare the like fractions 1518, 1618 and 1218

Comparing numerators, we find that 16 > 15 > 12

Therefore, 1618 > 1518 > 1218

or, 89 > 56 > 23

or, 23 < 56 < 89

The ascending order of the fractions is 23, 56, 89.


3. Arrange the following fractions 12, 38, 23, 45 in ascending order.

First we find the L.C.M. of the denominators of the fractions to make the denominators same.

L.C.M. of 2, 8, 3 and 5 = 120

Now to make the fraction as like fractions divide the L.C.M. by the denominator of fractions, then multiply both the numerator and denominator of fraction with the number get after dividing L.C.M.

As in fraction 12 denominator is 2.

Divide 120 ÷ 2 = 60

Now, multiply both numerator and denominator by 60 = 1×602×60 = 60120

Similarly, 38 = 3×158×15 = 45120 (because 120 ÷ 8 = 15)

23 = 2×403×40 = 80120 (because 120 ÷ 3 = 40)

and 45 = 4×245×24 = 96120 (because 120 ÷ 5 = 24)

Now, we compare the like fractions 60120, 45120, 80120 and 96120

Comparing numerators, we find that 96 > 80 > 60 > 45

Therefore, 96120 > 80120 > 60120 > 45120

or 45 > 23 > 12 > 38 

or 38  < 12 < 23 < 45

The ascending order of the fractions is 38 < 12 < 23 < 45.


4. Arrange the following fractions in ascending order of magnitude.

34, 58, 46, 29

L.C.M. of 4, 8, 6 and 9

= 2 × 2 × 3 × 2 × 3 = 72

Arrange the following fractions

3×184×18 = 5472

Therefore, 34 = 5472

5×98×9 = 4572

Therefore, 58 = 4572

4×126×12 = 4872

Therefore, 46 = 4872

2×89×8 = 1672

Therefore, 29 = 1672

Ascending order: 1672, 4572, 4872, 5472

                    i.e., 29, 58, 46, 34   


5. Arrange the following fractions in ascending order of magnitude.

412, 312, 514, 116, 214

Observe the whole numbers.

4, 3, 5, 1, 2

1 < 2 < 3 < 4 < 5

Therefore, ascending order: 116, 214, 312, 412, 514

 

6. Arrange the following fractions in ascending order of magnitude.

314, 312, 216, 414, 819

Observe the whole numbers.

3, 3, 2, 4, 8

Since the whole number part of 314 and 312 are same, compare them.

Which is bigger? 314 or 312? 14 or 12?

L.C.M. of 4, 2 = 4

1×14×1 = 14                 1×22×2 = 24

Therefore, 314 = 314       312 = 324

Therefore, 324 > 314       i.e., 312 > 314

Therefore, Ascending order: 216, 314, 312, 434, 819 


Worksheet on Fractions in Ascending Order:

1. Arrange the given fractions in ascending order:

(i) 1322, 1822, 1022, 322

(ii) 3342, 1642, 3942, 942


Answers:

1. (i) 322, 1022, 1322, 1822

(ii) 942, 1642, 3342, 3942


2. Arrange the following fractions in ascending order of magnitude:

(i) 77, 37, 17, 47, 27, 57

(ii) 12, 32, 83, 46, 92, 13


Answer:

2. (i) 1727, 37, 47, 57, 77

(ii) 1312, 46, 32, 83, 92


3. Arrange the following fractions in ascending order:

(i) 235313 

(ii) 14, 16, 512

(iii) 315, 715, 415, 915

(iv) 38, 116, 74, 518


Answer:

3. (i) 13 < 23 < 53 

(ii) 512 < 16 < 14

(iii) 315 < 415 < 715 < 915

(iv) 116 < 518 < 38 < 74

You might like these

Related Concept

Fraction of a Whole Numbers

Representation of a Fraction

Equivalent Fractions

Properties of Equivalent Fractions

Like and Unlike Fractions

Comparison of Like Fractions

Comparison of Fractions having the same Numerator

Types of Fractions

Changing Fractions

Conversion of Fractions into Fractions having Same Denominator

Conversion of a Fraction into its Smallest and Simplest Form

Addition of Fractions having the Same Denominator

Subtraction of Fractions having the Same Denominator

Addition and Subtraction of Fractions on the Fraction Number Line





4th Grade Math Activities

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