# Comparison of Fractions having the same Numerator

In comparison of fractions having the same numerator the following rectangular figures having the same lengths are divided in different parts to show different denominators.

(i) (ii) (iii) 3/10 < 3/5 < 3/4 or 3/4 > 3/5 > 3/10

In the fractions having the same numerator, that fraction is greater which has the smaller denominator.

5/11 > 5/17, 5/17 < 5/11, 7/15 > 7/16, 7/16 < 7/15

Comparison Fractions with same Numerator

If two fractions have the same numerator, the fraction with the smaller denominator denotes the greater fraction.

For example,

$$\frac{5}{7}$$ > $$\frac{5}{13}$$

$$\frac{9}{15}$$ < $$\frac{9}{13}$$

If there are three or more fractions having the same numerator, they may be arranged in ascending (increasing) and descending (decreasing) order. The order will be in opposite order of denominators. The bigger denominator will make the smaller fraction.

(a) Ascending order: 1/9, 1/7, 1/5, 1/4, 1/3

as 9 > 7 > 5 > 4 > 3

(b) Descending order: 5/3, 5/6, 5/9, 5/12, 5/18

as 3 < 6 < 9 < 12 < 18

Similarly again;

(a) Ascending order: 7/11, 7/9, 7/6, 7/5, 7/2

as 11 > 9 > 6 > 5 > 2

(b) Descending order: 11/1, 11/5, 11/7, 11/10, 11/15

as 1 < 5 < 7 < 10 < 15

Ordering of fraction and comparing fractions:

We know, a fraction represents an equal part of a whole thing.

(a) A whole cake = 1 cake

We can also write it as 1/1 which means in half the denominator has 1 part and numerator has taken the 1 part.

1/1 = 1.

(b) 1/2

Now the cake has been divided into two half parts and one part has been taken.

We write it as 1/2. $$\frac{1}{3}$$                          $$\frac{1}{4}$$                         $$\frac{1}{5}$$                         $$\frac{1}{6}$$

Note:

As the number of the denominator is getting bigger, the size of the part taken is getting smaller.

1 > 1/2 > 1/3 > 1/4 > 1/5 > 1/6 …..

When the numerator is 1 in a fraction number, it is called a unit fraction.

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