Fractions in Descending Order

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

Solved examples for arranging in descending order:

1. Arrange the following fractions 5/6, 7/10, 11/20 in descending order.

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

L.C.M. of 6, 10 and 20

L.C.M. of 6, 10 and 20 = 2 × 5 × 3 × 1 × 2 = 60

5/6 = 5 × 10/6 × 10 = 50/60 (because 60 ÷ 6 = 10)

7/10 = 7 × 6/10 × 6 = 42/60 (because 60 ÷ 10 = 6)

11/20 = 11 × 3/20 × 3 = 33/60 (because 60 ÷ 20 = 3)

Now we compare the like fractions 50/60, 42/60 and 33/60

Comparing numerators, we find that 50 > 42 > 33.

Therefore, 50/60 > 42/60 > 33/60 or 5/6 > 7/10 > 11/20

The descending order of the fractions is 5/6, 7/10, 11/20.


2. Arrange the following fractions 1/2, 3/4, 7/8, 5/12 in descending order.

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

L.C.M. of 2, 4, 8 and 12 = 24

1/2 = 1 × 12/2 × 12 = 12/24 (because 24 ÷ 2 = 12)

3/4 = 3 × 6/4 × 6 = 18/24 (because 24 ÷ 10 = 6)

7/8 = 7 × 3/8 × 3 = 21/24 (because 24 ÷ 20 = 3)

5/12 = 5 × 2/12 × 2 = 10/24 (because 24 ÷ 20 = 3)

Now we compare the like fractions 12/24, 18/24, 21/24 and 10/24.

Comparing numerators, we find that 21 > 18 > 12 > 10.

Therefore, 21/24 > 18/24 > 12/24 > 10/24 or 7/8 > 3/4 > 1/2 > 5/12

The descending order of the fractions is 7/8 > 3/4 > 1/2 > 5/12.


3. Arrange the following fractions in descending order of magnitude.

\(\frac{3}{4}\), \(\frac{5}{8}\), \(\frac{4}{6}\), \(\frac{2}{9}\)

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

= 2 × 2 × 3 × 2 × 3 = 72

Arrange the Following Fractions

\(\frac{3 × 18}{4 × 18}\) = \(\frac{54}{72}\)

Therefore, \(\frac{3}{4}\) = \(\frac{54}{72}\)

\(\frac{5 × 9}{8 × 9}\) = \(\frac{45}{72}\)

Therefore, \(\frac{5}{8}\) = \(\frac{45}{72}\)

\(\frac{4 × 12}{6 × 12}\) = \(\frac{48}{72}\)

Therefore, \(\frac{4}{6}\) = \(\frac{48}{72}\)

\(\frac{2 × 8}{9 × 8}\) = \(\frac{16}{72}\)

Therefore, \(\frac{2}{9}\) = \(\frac{16}{72}\)  

Descending order: \(\frac{54}{72}\), \(\frac{48}{72}\), \(\frac{45}{72}\), \(\frac{16}{72}\)

i.e., \(\frac{3}{4}\), \(\frac{4}{6}\), \(\frac{5}{8}\), \(\frac{2}{9}\)


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

4\(\frac{1}{2}\), 3\(\frac{1}{2}\), 5\(\frac{1}{4}\), 1\(\frac{1}{6}\), 2\(\frac{1}{4}\)

Observe the whole numbers.

4, 3, 5, 1, 2

1 < 2 < 3 < 4 < 5

Therefore, descending order: 5\(\frac{1}{4}\), 4\(\frac{1}{2}\), 3\(\frac{1}{2}\), 2\(\frac{1}{4}\), 1\(\frac{1}{6}\)

 

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

3\(\frac{1}{4}\), 3\(\frac{1}{2}\), 2\(\frac{1}{6}\), 4\(\frac{1}{4}\), 8\(\frac{1}{9}\)

Observe the whole numbers.

3, 3, 2, 4, 8

Since the whole number part of 3\(\frac{1}{4}\) and 3\(\frac{1}{2}\) are same, compare them.

Which is bigger? 3\(\frac{1}{4}\) or 3\(\frac{1}{2}\)? \(\frac{1}{4}\) or \(\frac{1}{2}\)?

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

\(\frac{1 × 1}{4 × 1}\) = \(\frac{1}{4}\)                 \(\frac{1 × 2}{2 × 2}\) = \(\frac{2}{4}\)

Therefore, 3\(\frac{1}{4}\) = 3\(\frac{1}{4}\)       3\(\frac{1}{2}\) = 3\(\frac{2}{4}\)

Therefore, 3\(\frac{2}{4}\) > 3\(\frac{1}{4}\)       i.e., 3\(\frac{1}{2}\) > 3\(\frac{1}{4}\)

Therefore, descending order: 8\(\frac{1}{9}\), 4\(\frac{3}{4}\), 3\(\frac{1}{2}\), 3\(\frac{1}{4}\), 2\(\frac{1}{6}\)

 


Questions and Answers on Comparison of Like Fractions:

1. Arrange the given fractions in descending order:

(i) \(\frac{7}{27}\), \(\frac{10}{27}\), \(\frac{18}{27}\), \(\frac{21}{27}\)

(ii) \(\frac{15}{39}\), \(\frac{7}{39}\), \(\frac{10}{39}\), \(\frac{26}{39}\)


Answers:

1. (i) \(\frac{21}{27}\), \(\frac{18}{27}\), \(\frac{10}{27}\), \(\frac{7}{27}\)

(ii) \(\frac{26}{39}\), \(\frac{15}{39}\), \(\frac{10}{39}\), \(\frac{7}{39}\)


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

(i) \(\frac{5}{23}\), \(\frac{12}{23}\), \(\frac{4}{23}\), \(\frac{17}{23}\), \(\frac{45}{23}\), \(\frac{36}{23}\)

(ii) \(\frac{3}{4}\), \(\frac{2}{3}\), \(\frac{4}{3}\), \(\frac{6}{4}\), \(\frac{1}{2}\), \(\frac{1}{4}\)


Answers:

2. (i) \(\frac{45}{23}\), \(\frac{36}{23}\), \(\frac{17}{23}\), \(\frac{12}{23}\), \(\frac{5}{23}\)

(ii) 

\(\frac{6}{4}\), \(\frac{4}{3}\), \(\frac{3}{4}\), \(\frac{2}{3}\), (\frac{1}{2}\), \(\frac{1}{4}\)



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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