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 $\frac{5}{6}$, $\frac{7}{10}$, $\frac{11}{20}$ 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 = 2 × 5 × 3 × 1 × 2 = 60

$\frac{5}{6}$ = $\frac{5 × 10}{6 × 10}$ = $\frac{50}{60}$ (because 60 ÷ 6 = 10)

$\frac{7}{10}$ = $\frac{7 × 6}{10 × 6}$ = $\frac{42}{60}$ (because 60 ÷ 10 = 6)

$\frac{11}{20}$ = $\frac{11 × 3}{20 × 3}$ = $\frac{33}{60}$ (because 60 ÷ 20 = 3)

Now we compare the like fractions $\frac{50}{60}$, $\frac{42}{60}$  and $\frac{33}{60}$ 

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

Therefore, $\frac{50}{60}$ > $\frac{42}{60}$ > $\frac{33}{60}$ or $\frac{5}{6}$ > $\frac{7}{10}$ > $\frac{11}{20}$

The descending order of the fractions is $\frac{5}{6}$, $\frac{7}{10}$, $\frac{11}{20}$.

2. Arrange the following fractions $\frac{1}{2}$, $\frac{3}{4}$, $\frac{7}{8}$, $\frac{5}{12}$ 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

$\frac{1}{2}$ = $\frac{1 × 12}{2 × 12}$ = $\frac{12}{24}$ (because 24 ÷ 2 = 12)

$\frac{3}{4}$ = $\frac{3 × 6}{4 × 6}$ = $\frac{18}{24}$ (because 24 ÷ 10 = 6)

$\frac{7}{8}$ = $\frac{7 × 3}{8 × 3}$ = $\frac{21}{24}$ (because 24 ÷ 20 = 3)

$\frac{5}{12}$ = $\frac{5 × 2}{12 × 2}$ = $\frac{10}{24}$ (because 24 ÷ 20 = 3)

Now we compare the like fractions $\frac{12}{24}$, $\frac{18}{24}$, $\frac{21}{24}$ and $\frac{10}{24}$.

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

Therefore, $\frac{21}{24}$ > $\frac{18}{24}$ > $\frac{12}{24}$ > $\frac{10}{24}$ or $\frac{7}{8}$ > $\frac{3}{4}$ > $\frac{1}{2}$ > $\frac{5}{12}$

The descending order of the fractions is $\frac{7}{8}$ > $\frac{3}{4}$ > $\frac{1}{2}$ > $\frac{5}{12}$.

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

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$\frac{1}{6}$

Worksheet on Fractions in Descending Order:

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) $\frac{13}{17}$, $\frac{12}{17}$, $\frac{11}{17}$, $\frac{16}{17}$

Answers:

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

(ii) $\frac{16}{17}$ > $\frac{13}{17}$ > $\frac{12}{17}$ > $\frac{11}{17}$

Comparison of Unlike Fractions:

3. Arrange the following fractions in descending order:

(i) $\frac{1}{6}$, $\frac{5}{12}$, $\frac{2}{3}$, $\frac{5}{18}$

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

(iⅲ) $\frac{3}{6}$, $\frac{3}{4}$, $\frac{3}{5}$, $\frac{3}{8}$

(iv) $\frac{4}{7}$, $\frac{6}{7}$, $\frac{3}{14}$, $\frac{5}{21}$

Answers:

3. (1) $\frac{2}{3}$ > $\frac{5}{12}$ > $\frac{5}{18}$ > $\frac{1}{6}$

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

(iⅲ) $\frac{3}{4}$ > $\frac{3}{5}$ > $\frac{3}{6}$ > $\frac{3}{8}$

(iv) $\frac{6}{7}$ > $\frac{4}{7}$ > $\frac{5}{21}$ > $\frac{3}{14}$

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

From Fractions in Descending Order to HOME PAGE