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

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