Comparison of Unlike Fractions

In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare.

Let us compare two fractions \(\frac{4}{7}\) and \(\frac{4}{9}\) which have same numerator.

Since 4 shaded parts of 7 is bigger than the 4 shaded parts of 9 therefore \(\frac{4}{7}\) > \(\frac{4}{9}\).

To compare two fractions with different numerators and different denominators, we multiply by a number to convert them to like fractions.

Let us consider some of the examples on comparing fractions (i.e. unlike fractions).

1. Which one is greater, \(\frac{4}{7}\) or \(\frac{3}{5}\)?

First we convert these fractions into like fractions. To convert unlike fraction into like fraction first of all find the L.C.M. of their denominators.

L.C.M. of 7 and 5 = 35

Now, divide this L.C.M. by the denominator of both the fractions.

35 ÷ 7 = 5

35 ÷ 5 = 7

Multiply both the numerator and denominator with the number you get after dividing.

i.e., \(\frac{4 × 5}{7 × 5}\) = \(\frac{20}{35}\)

\(\frac{3 × 7}{5 × 7}\) = \(\frac{21}{35}\)

because \(\frac{21}{35}\) > \(\frac{20}{35}\)

So, \(\frac{3}{5}\) > \(\frac{4}{7}\)

We can compare two fractions by cross multiplication also.

Let us solve the above example by cross multiplication. Here, we cross multiply as follows.

4 × 5 = 20

3 × 7 = 21

Since, 21 > 20

Therefore, \(\frac{3}{5}\) > \(\frac{4}{7}\)

2. Compare 3\(\frac{2}{5}\) and 2\(\frac{3}{4}\).

First we convert these mixed numbers into improper fractions.

2\(\frac{3}{4}\) = \(\frac{4 × 2 + 3}{4}\) = \(\frac{11}{4}\)

3\(\frac{2}{5}\) = \(\frac{5 × 3 + 2}{5}\) = \(\frac{17}{5}\)

Now, we compare \(\frac{11}{4}\) and \(\frac{17}{5}\) by cross multiplication.

11 × 5 = 55 and 17 × 4 = 68

We see that 68 > 55.

Therefore, \(\frac{17}{5}\) > \(\frac{11}{4}\)  or, 3\(\frac{2}{5}\) > 2\(\frac{3}{4}\)

3. Let us compare \(\frac{5}{7}\) and \(\frac{3}{5}\).

\(\frac{5}{7}\) = \(\frac{5 × 5}{7 × 5}\) = \(\frac{25}{35}\)

Multiply the numerator and denominator by 5.

\(\frac{3}{5}\) = \(\frac{3 × 7}{5 × 7}\) = \(\frac{21}{35}\)

Multiply the numerator and denominator by 7.

Hence, \(\frac{25}{35}\) > \(\frac{21}{35}\)

Therefore, \(\frac{5}{7}\) > \(\frac{3}{5}\)

We will learn an alternative method i.e. cross multiply to compare the given fractions.

4. Let us compare \(\frac{2}{3}\) and \(\frac{4}{5}\).

2 × 5 = 10 and 3 × 4 = 12

Since, 12 > 10, hence \(\frac{4}{5}\) > \(\frac{2}{3}\)

Comparison of Fraction with Different Numerators and Denominators:

1. Compare \(\frac{3}{4}\) and \(\frac{5}{11}\)

Step I: Find the least common denominator by finding the L.C.M. of the denominators 4 and 11.

L.C.M. of 4 and 11 = 4 × 11 = 44

Step II: Change the given fractions into equivalent fractions with denominator 44.

\(\frac{3 × 11}{4 × 11}\) = \(\frac{33}{44}\); \(\frac{5 × 4}{11 × 4}\) = \(\frac{20}{44}\);

\(\frac{3}{4}\) = \(\frac{33}{44}\) \(\frac{5}{11}\) = \(\frac{20}{44}\)

\(\frac{33}{44}\) > \(\frac{20}{44}\)

Therefore, \(\frac{3}{4}\) > \(\frac{5}{11}\)

2. Compare \(\frac{6}{8}\) and \(\frac{14}{16}\)

L.C.M. of 8 and 16 is 16. \(\frac{6 × 2}{8 × 2}\) = \(\frac{12}{16}\); \(\frac{6}{8}\) = \(\frac{12}{16}\) \(\frac{14 × 1}{16 × 1}\) = \(\frac{14}{16}\) \(\frac{12}{16}\) < \(\frac{14}{16}\) Therefore, \(\frac{6}{8}\) < \(\frac{14}{16}\)

3. Compare \(\frac{6}{8}\) and \(\frac{14}{16}\) by using the method of cross multiplication.

3 × 4 = 12 16 × 2 = 32

\(\frac{3}{16}\) < \(\frac{2}{4}\) because 12 < 32

4. Compare 6\(\frac{1}{4}\) and \(\frac{12}{2}\)

Change 6\(\frac{1}{4}\) to an improper fraction.

6\(\frac{1}{4}\) = \(\frac{(6 × 4) + 1}{4}\) = \(\frac{25}{4}\)

25 × 2 = 50 4 × 12 = 48

\(\frac{25}{4}\) > \(\frac{12}{2}\) because 50 > 48

Questions and Answers on Comparison of Unlike Fractions

1. Put the appropriate sign >, < or = in the box.

(i) \(\frac{4}{25}\) _____ \(\frac{16}{100}\)

(ii) \(\frac{1}{8}\) _____ \(\frac{3}{32}\)

Answer:

1. (i) =

(ii) >

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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