# 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 = 1216 × 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 = 504 × 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) $$\frac{1}{8}$$ _____ $$\frac{3}{32}$$

1. (i) =

(ii) >

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