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\(\frac{1}{6}\)
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
● Representation of a Fraction
● Properties of Equivalent Fractions
● Comparison of Like Fractions
● Comparison of Fractions having the same Numerator
● 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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