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)

Comparison of Fractions having the same Numerator

Shaded portion = 3/10


(ii)

Comparison of Fractions

Shaded portion = 3/5


(iii)

Comparison of Fractions

Shaded portion = 3/4


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

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)

comparing fractions





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)

comparing fractions









          1/2

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

We write it as 1/2.

comparing Fraction

              \(\frac{1}{3}\)                          \(\frac{1}{4}\)                         \(\frac{1}{5}\)                         \(\frac{1}{6}\)

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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