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.
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. = 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.
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
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) 17, 27, 37, 47, 57, 77
(ii) 13, 12, 46, 32, 83, 92
3. Arrange the following fractions in ascending order:
(i) 23, 53, 13
(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
Related Concept
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● 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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