# 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.

## You might like these

• ### Worksheet on Word Problems on Multiplication of Mixed Fractions | Frac

Practice the questions given in the worksheet on word problems on multiplication of mixed fractions. We know to solve the problems on multiplying mixed fractions first we need to convert them

• ### Word Problems on Division of Mixed Fractions | Dividing Fractions

We will discuss here how to solve the word problems on division of mixed fractions or division of mixed numbers. Let us consider some of the examples. 1. The product of two numbers is 18.

• ### Word Problems on Multiplication of Mixed Fractions | Multiplying Fract

We will discuss here how to solve the word problems on multiplication of mixed fractions or multiplication of mixed numbers. Let us consider some of the examples. 1. Aaron had 324 toys. He gave 1/3

• ### Dividing Fractions | How to Divide Fractions? | Divide Two Fractions

We will discuss here about dividing fractions by a whole number, by a fractional number or by another mixed fractional number. First let us recall how to find reciprocal of a fraction

• ### Reciprocal of a Fraction | Multiply the Reciprocal of the Divisor

Here we will learn Reciprocal of a fraction. What is 1/4 of 4? We know that 1/4 of 4 means 1/4 × 4, let us use the rule of repeated addition to find 1/4× 4. We can say that $$\frac{1}{4}$$ is the reciprocal of 4 or 4 is the reciprocal or multiplicative inverse of 1/4

• ### Multiplying Fractions | How to Multiply Fractions? |Multiply Fractions

To multiply two or more fractions, we multiply the numerators of given fractions to find the new numerator of the product and multiply the denominators to get the denominator of the product. To multiply a fraction by a whole number, we multiply the numerator of the fraction

• ### Subtraction of Unlike Fractions | Subtracting Fractions | Examples

To subtract unlike fractions, we first convert them into like fractions. In order to make a common denominator, we find LCM of all the different denominators of given fractions and then make them equivalent fractions with a common denominators.

• ### Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

• ### Subtraction of Fractions having the Same Denominator | Like Fractions

To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numerators of the fractions.

• ### Properties of Addition of Fractions |Commutative Property |Associative

The associative and commutative properties of natural numbers hold good in the case of fractions also.

• ### Addition of Unlike Fractions | Adding Fractions with Different Denomin

To add unlike fractions, we first convert them into like fractions. In order to make a common denominator we find the LCM of all different denominators of the given fractions and then make them equivalent fractions with a common denominator.

To add two or more like fractions we simplify add their numerators. The denominator remains same.

• ### Fractions in Descending Order |Arranging Fractions an 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

• ### Fractions in Ascending Order | Arranging Fractions an Ascending Order

We will discuss here how to arrange the fractions in ascending order. Solved examples for arranging in ascending order: 1. Arrange the following fractions 5/6, 8/9, 2/3 in ascending order. First we find the L.C.M. of the denominators of the fractions to make the denominators

• ### Comparison of Unlike Fractions | Compare Unlike Fractions | Comparing

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

Related Concept