# 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
 $$\frac{3 × 18}{4 × 18}$$ = $$\frac{54}{72}$$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$$\frac{1}{6}$$

## 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) $$\frac{15}{39}$$, $$\frac{7}{39}$$, $$\frac{10}{39}$$, $$\frac{26}{39}$$

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

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

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

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