# 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 = 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
 $$\frac{3 × 18}{4 × 18}$$ = $$\frac{54}{72}$$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) $$\frac{15}{39}$$, $$\frac{7}{39}$$, $$\frac{10}{39}$$, $$\frac{26}{39}$$

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

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}\), $$\frac{1}{4}$$

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