# Comparison of Fraction

Compare which fraction is smaller out of 1/4 and 2/3

To compare fractions do the following steps.

Step 1: Calculate the LCM (Least Common Multiples or Lowest common multiple) of denominators.

In the given fractions 4 and 3 are denominators.
LCM of 4 and 3 = 12
LCM of denominator is also called Least common denominator.

Step 2: Consider one of the fractions, i.e. ¼

Divide the LCM from its denominator.
12 ÷ 4 = 3
Now, multiply the numerator and denominator of the fraction with the quotient you got.
1/4=(1xx3)/(4xx3)=(3)/(12)

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Step 3: Consider the second fraction, i.e. 2/3

Divide the LCM from its denominator
12 ÷ 3 = 4
Now multiply the denominator and numerator of the fraction with result (quotient).
2/3=(2xx4)/(3xx4)=(8)/(12)

Step 4: Now we have two fractions:
(3)/(12) and (8)/(12)
Both of the fractions have equal denominator.

Now compare the numerator. The fraction with greater numerator is greater than the fraction with smaller numerator. Here, 8 is greater than 3.

Therefore; (8)/(12)>(3)/(12)

Or, 2/3>1/4

Question 1: Compare the following fractions and put < or > sign between them accordingly:

(a) 1/4 and 3/4

Solution: Here, denominator of both the fractions is same. Numerator 1 < 3

Hence, 1/4<3/4

(b) 2/3 and 3/4

Solution: The LCM of denominators 3 and 4 = 12

Hence, 2/3=(2xx4)/(3xx4)=(8)/(12)

And, 3/4=(3xx3)/(4xx3)=(9)/(12)

Since 8 < 9

Hence, (8)/(12)<(9)/(12)

Or, 2/3<3/4

(c) 3/4 and 5/6

Solution: The LCM of 4 and 6 = 12

So, 3/4=(3xx3)/(4xx3)=(9)/(12)

And, 5/6=(5xx2)/(6xx2)=(10)/(12)

Since, 9 < 10

Hence, (9)/(12)<(10)/(12)

Or, 3/4<5/6

(d) 6/7 and 5/6

Solution: LCM of 7 and 6 = 42

Hence, 6/7=(6xx6)/(7xx6)=(36)/(42)

And, 5/6=(5xx7)/(6xx7)=(35)/(42)

Here, 36 > 35

Hence, (36)/(42)>(35)/(42)

Or, 6/7>5/6

(e) 7/8 and 8/7

Solution: LCM of 8 and 7 = 56

Hence, 7/8=(7xx7)/(8xx7)=(49)/(56)

And, 8/7=(8xx8)/(7xx8)=(64)/(56)

Since, 49 < 64

Hence, (49)/(56)<(64)/(56)

Or, 7/8<(8)/7

Note: Numerator is less than denominator in 7/8while numerator is more than denominator in 8/7. When numerator is less than denominator, the number is less than 1. When numerator is more than denominator, the number is greater than 1. So, 7/8<8/7

(f) 3/5 and 5/3

Solution: LCM of 5 and 3 = 15

Hence, 3/5=(3xx3)/(5xx3)=(9)/(15)

And, 5/3=(5xx5)/(3xx5)=(25)/(15)

Since, 9 < 25

Hence, (9)/(15)<(25)/(15)

Or, 3/5<5/3

(g) (16)/(12) and (3)/(12)

Solution: Here, denominator is same in both the fractions, and 16 > 3

Hence, (16)/(12)>(3)/(12)

(h) 3/2 and 4/3

Solution: LCM of 2 and 3 = 6

Hence, 3/2=(3xx3)/(2xx3)=9/6

And, 4/3=(4xx2)/(3xx2)=8/6

Here, 9 > 8

Hence, 9/6>8/6

Or, 3/2>4/3

(i) (12)/(11) and 7/6

Solution: LCM of 11 and 6 = 66

Hence, (12)/(11)=(12xx6)/(11xx6)=(72)/(66)

And, 7/6=(7xx11)/(6xx11)=(77)/(66)

Since, 72 < 77

Hence, (72)/(66)<(77)/(66)

Or, (12)/(11)<7/6

(j) 4/7 and 5/9

Solution: LCM of 7 and 9 = 63

Hence, 4/7=(4xx9)/(7xx9)=(36)/(63)

And, 5/9=(5xx7)/(9xx7)=(35)/(63)

So, (36)/(63)>(35)/(63)

Or, 4/7>5/9

Question 2: Arrange the following in ascending order:

(a) 1/2, 1/4, ¾

Solution: LCM of 2, 4 and 4 = 4

Hence, 1/2=(1xx2)/(2xx2)=2/4

Numerator is 4 in remaining fractions. Now, the rational numbers can be arranged in ascending order as follows:

1/4<2/4<3/4

Or, 1/4<1/2<3/4

(b) 3/5, 3/7, (9)/(25)

Solution: LCM of 5, 7 and 25 = 175

Hence, 3/5=(3xx35)/(5xx35)=(105)/(175)

3/7=(3xx25)/(7xx25)=(75)/(175)

(9)/(25)=(9xx7)/(25xx7)=(63)/(175)

It is clear that:

(63)/(175)<(75)/(175)<(105)/(175)

Or, (9)/(25)<3/7<3/5

(c) 2/5, 4/7, 5/6

Solution: LCM of 5, 7 and 6 = 210

Hence, 2/5=(2xx42)/(5xx42)=(84)/(210)

4/7=(4xx30)/(7xx30)=(120)/(210)

5/6=(5xx35)/(6xx35)=(175)/(210)

Or, 2/5<4/7<5/6

(d) 1/3, 6/9, (9)/(18)

Solution: LCM of 3, 9 and 18 = 18

Hence, 1/3=(1xx6)/(3xx6)=(6)/(18)

6/9=(6xx2)/(9xx2)=(12)/(18)

It is clear that:

(6)/(18)<(9)/(18)<(12)/(18)

Or, 1/3<(9)/(18)<6/9

(e) 3/9, (9)/(25), (5)/(20)

Solution: LCM of 4, 20 and 25 = 100

Hence, 3/4=(3xx25)/(4xx25)=(75)/(100)

(9)/(25)=(9xx4)/(25xx4)=(36)/(100)

(5)/(20)=(5xx5)/(20xx5)=(25)/(100)

It is clear that:

(25)/(100)<(36)/(100)<(75)/(100)

Or, (5)/(20)&t;(9)/(25)<3/4

(f) (2)/(15), (3)/(18), (9)/(10)

Solution: LCM of 15, 18 and 10 = 90

Hence, (2)/(15)=(2xx6)/(15xx6)=(12)/(90)

(3)/(18)=(3xx5)/(18xx5)=(15)/(90)

(9)/(10)=(9xx9)/(10xx9)=(81)/(90)

Hence, (2)/(15)<(3)/(18)<(9)/(10)

(g) (16)/(15), (15)/(14), (14)/(12)

Solution: LCM of 15, 14 and 12 = 420

Hence, (16)/(15)=(16xx28)/(15xx28)=(448)/(420)

(15)/(14)=(15xx30)/(14xx30)=(450)/(420)

(14)/(12)=(14xx35)/(12xx35)=(490)/(420)

It is clear that:

(448)/(420)<(450)/(420)<(490)/(420)

Or, (16)/(15)<(15)/(14)<(14)/(12)

(h) (11)/(12), (9)/(15), 8/9

Solution: LCM of 12, 15 and 9 = 180

Hence, (11)/(12)=(11xx15)/(12xx15)=(165)/(180)

(9)/(15)=(9xx12)/(15xx12)=(108)/(180)

8/9=(8xx20)/(9xx20)=(160)/(180)

It is clear that:

(108)/(180)<(160)/(180)<(165)/(180)

Or, (9)/(15)<8/9<(11)/(12)

(i) 2/3, ¾, 4/5

Solution: LCM of 3, 4 and 5 = 60

Hence, 2/3=(2xx20)/(3xx20)=(40)/(60)

3/4=(3xx15)/(4xx15)=(45)/(60)

4/5=(4xx12)/(5xx12)=(48)/(60)

It is clear that:

(40)/(60)<(45)/(60)<(48)/(60)

Or, 2/3<3/4<4/5

(j) 2/4, 4/6, 6/8

Solution: LCM of 4, 6 and 8 = 24

Hence, 2/4=(2xx6)/(4xx6)=(12)/(24)

4/6=(4xx4)/(6xx4)=(16)/(24)

6/8=(6xx3)/(8xx3)=(18)/(24)

It is clear that:

(12)/(24)<(16)/(24)<(18)/(24)

Or, 2/4<4/6<6/8