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

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) \(\frac{15}{39}\), \(\frac{7}{39}\), \(\frac{10}{39}\), \(\frac{26}{39}\)

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

Answers:

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

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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