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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 47 and 49 which have same numerator.

Comparison of Unlike Fractions

Since 4 shaded parts of 7 is bigger than the 4 shaded parts of 9 therefore 47 > 49.

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, 47 or 35?

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., 4×57×5 = 2035

3×75×7 = 2135

because 2135 > 2035

So, 35 > 47


We can compare two fractions by cross multiplication also.

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

By Cross Multiplication



4 × 5 = 20

3 × 7 = 21

Since, 21 > 20

Therefore, 35 > 47


2. Compare 325 and 234.

First we convert these mixed numbers into improper fractions.

234 = 4×2+34 = 114

325 = 5×3+25 = 175

Now, we compare 114 and 175 by cross multiplication.

Compare By Cross Multiplication



11 × 5 = 55 and 17 × 4 = 68

We see that 68 > 55.

Therefore, 175 > 114  or, 325 > 234


3. Let us compare 57 and 35.

57 = 5×57×5 = 2535

Multiply the numerator and denominator by 5.

35 = 3×75×7 = 2135

Multiply the numerator and denominator by 7.

Hence, 2535 > 2135

Therefore, 57 > 35


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


4. Let us compare 23 and 45.

Compare the Fractions

2 × 5 = 10 and 3 × 4 = 12

Since, 12 > 10, hence 45 > 23


Comparison of Fraction with Different Numerators and Denominators:

1. Compare 34 and 511

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.

3×114×11 = 3344; 5×411×4 = 2044;

34 = 3344 511 = 2044

3344 > 2044

Therefore, 34 > 511


2. Compare 68 and 1416

L.C.M. of 8 and 16 is 16.

6×28×2 = 1216; 68 = 1216

14×116×1 = 1416

1216 < 1416

Therefore, 68 < 1416

L.C.M. of 8 and 16


3. Compare 68 and 1416 by using the method of cross multiplication.

Method of Cross Multiplication


3 × 4 = 12

16 × 2 = 32

316 < 24 because 12 < 32


4. Compare 614 and 122

Change 614 to an improper fraction.

614 = (6×4)+14 = 254

Method of Cross Multiplication

25 × 2 = 50

4 × 12 = 48

254 > 122 because 50 > 48


Comparison of Fractions with Unlike Numerators and Unlike Denominators

To compare two fractions having unlike numerators and unlike denominators, we first convert them into the fractions having like (same) denominator. This can be done by multiplying the numerator and the denominator of each fraction by a suitable number. Then we compare the fractions as usual.


5. Consider 15 and 34

Solution:

15 = 1×45×4  [Multiplying the numerator and the denominator by 4]

      = 420


34 = 3×54×5   [Multiplying the numerator and the denominator by 5]

      = 1520

Clearly, 420 < 1520,   (Since 4 < 15 )

Hence, 15 < 34


Another method:

Two fractions can be compared by using the method of cross multiplication.


6. Consider 211 and 47

Solution:

Given fractions are 211 and 47

Compare Unlike Fractions

Now 2 × 7 = 14 and 4 × 11 = 44

Since angle 4 > 14, hence 211 < 47


7. Consider 415 and 213

Solution:

Given fractions are 415 and 213

Unlike Fraction Comparison

Now 4 × 13 = 52 and 15 × 2 = 30

Since 52 > 30, hence 415 > 213



Worksheet on Comparison of Unlike Fractions

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

(i) 425 _____ 16100

(ii) 18 _____ 332


Answer:

1. (i) =

(ii) >


2. Fill in each blank by putting > or < in each of the following to make the statement true:

(i) 320 _____ 720

(ii) 58 _____ 516

(iii) 1519 _____ 1219

(iv) 1415 _____ 1417

(v) 511 _____ 711

(vi) 1021 _____ 1013


Answer:

2. (i) <

(ii) >

(iii) >

(iv) >

(v) <

(vi) <


3. Which is the smaller in each of the following pairs of fractions?

(i) 715, 15

(ii) 19, 421

(iii) 1825, 25

(iv) 512, 310

(v) 920, 715

(vi) 821, 720



Answer:

3. (i) 15

(ii) 421

(iii) 1825

(iv) 512

(v) 920

(vi) 821


4. Compare each pair of fractions and write < or < in the box:

(i) 57  59

(ii) 611 □ 714

(iii) 17 □ 18

(iv) 411 □ 47

(v) 67  □ 611

(vi) 37 □ 35


Answer:

4. (i) >

(ii) >

(iii) >

(iv) <

(v) >

(vi) <

You might like these

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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