HOW TO FIND THE MIDWAY BETWEEN TWO FRACTIONS

Example 1 :

Find the number midway between -1/2 and 2/3

Solution :

Let a = -1/2 and b = 2/3

Midway = [-1/2 + 2/3]/2

Least common multiple of 2 and 3 is 6.

= [(-3 + 4)/6]/2

= (1/6)/2

= 1/12

Example 2 :

Find the number midway between 8/6 and 10/4

Solution :

Let a = 8/6 and b = 10/4

Midway = [8/6 + 10/4]/2

Least common multiple of 6 and 4 is 12.

= [(16 + 30)/12]/2

= (46/12)//2

= 46/24

= 23/12

So, the midway between two fractions is 23/12.

Example 3 :

Find the number midway between 2/5 and 5/10

Solution :

Let a = 2/5 and b = 5/10

Midway = [2/5 + 5/10]/2

= (4+ 5)/10)//2

= 9/20

So, the midway between the given fractions is 9/20.

Example 4 :

Find the number midway between 3/5 and 4/7

Solution :

Let a = 3/5 and b = 4/7

Mid way number = [(3/5) + (4/7)]/2

Least common multiple of 3 and 5 is 35.

= [3(7) + 4(5)]/(35 x 2)

= (21 + 20) / 70

= 41/70

So, the midway between these two fractuions is 41/70.

Example 5 :

Workout the fraction that is exactly halfway between 1/8 and 5/8.

Solution :

Let a = 1/8 and b = 5/8

Halfway between two numbers = (a + b)/2

= [(1/8) + (5/8)]/2

= [(1 + 5)/8] / 2

= 6/(8 x 2)

= 3/8

So, the halfway between these two numbers is 3/8.

Example 6 :

Find out six rational number lying between -4/8 and 3/8.

Solution :

Let a = -4/8 and b = 3/8

The rational numbers lie between the given rational numbers,

-3/8, -2/8, -1/8, 0, 1/8, 2/8

Example 7 :

Find ten rational numbers lying between 7/13 and -4/13.

Solution :

Let a = 7/13 and b = -4/13

The ten rational numbers lie between the given rational numbers,

-313, -2/13, -1/13, 0, 1/13, 2/13, 3/13, 4/13, 5/13, 6/13

Example 8 :

Find three rational numbers between -1/2 and 2/3.

Solution :

Let a = -1/2 and b = 2/3

Let c, d and e be three rational numbers between them.

c = [(-1/2) + (2/3)] / 2

LCM of 2 and 3 is 6.

= [(-3 + 4)/6]/2

= (1/6)/2

= 1/12

d = [(-1/2) + (1/12)]/2

LCM of 2 and 12 is 12.

= [(-6 + 1)/12] / 2

= (-5/12) / 2

= -5/24

e = (-5/24 + 2/3)/2

LCM of 3 and 24 is 24.

= [(-5 + 16)/24]/2

= (11/24) / 2

= 11/48

So, the three rational numbers between the given rational numbers are 

1/12, -5/24 and 11/48.

The ten rational numbers lie between the given rational numbers,

-313, -2/13, -1/13, 0, 1/13, 2/13, 3/13, 4/13, 5/13, 6/13

Example 9 :

Find seven rational numbers between -3/4 and 1/5

Solution :

Let a = -3/4 and b = 1/5

LCM of 4 and 5 is 20.

By making the denominators same,

= (-3/4) x (5/5)

= -15/20

= (1/5) x (4/4)

= 4/20

In this way, we may find many rational numbers in between the given fractions.

-14/20, -13/20, -12/20, -11/20, -10/20, -9/20, -8/20, -7/20, -6/20, -5/20, -4/20, -3/20, -2/20, -1/20, 0, 1/20, 2/20, 3/20.

We may choose any seven rational numbers.

Example 10 :

Find eight rational numbers between 2/7 and 3/4

Solution :

Let a = 2/7 and b = 3/4

LCM of 7 and 4 is 28

By making the denominators same,

= (2/7) x (4/4)

= 8/28

= (3/4) x (7/7)

= 21/28

In this way, we may find many rational numbers in between the given fractions.

9/28, 10/28, 11/28, 12/28, 13/28, 14/28, 15/28, 16/28, 17/28, 18/28, 19/28, 20/28

We may choose any eight rational numbers.

Example 11 :

Find eight rational numbers between 1/8 and 3/4

Solution :

Let a = 1/8 and b = 3/4

LCM of 8 and 4 is 8

By making the denominators same,

= (3/4) x (2/2)

= 6/8

The rational numbers are 2/8, 3/8, 4/8 and 5/8. Here we find only four rational numbers between these two fraction. By finding equivalent fractions,

1/8 x 2/2 = 2/16

6/8 x 2/2 = 12/16

Rational numbers between these two fractions are 

3/16, 4/16, 5/16, 6/16, 7/16, 8/16, 9/16, 10/16, 11/16.

We may choose any eight rational numbers.

Example 12 :

Emily and Neela think of two different fractions.

• The midpoint of the two fractions is 2/3 
• Emily says her fraction is 1/2

What fraction is Neela thinking of? 

Solution :

Let a and b be two fractions. a = 1/2 and b = ?

[(1/2) + b]/2 = 2/3

[(1/2) + b] = (2 x 2)/3

[(1/2) + b] = 4/3

b = 4/3 - (1/2)

b = (8 - 3)/6

b = 5/6

So, Neela is thinking the fraction 5/6.

Example 13 :

Otis and Cleo think of two different fractions.

• The midpoint of the two fractions is 1  5/8
• Otis says his fraction is 9/10

What fraction is Cleo thinking of ? 

Solution :

Let a and b be two fractions. a = 9/10 and b = ?

Midpoint = 1  5/8

Converting into improper fraction, we get

= 13/8

[(9/10) + b]/2 = 13/8

[(9/10) + b] = (13 x 2)/8

[(9/10) + b] = 13/4

b = 13/4 - 9/10

LCM of 4 and 10 is 20.

b = (13/4) x 5/5 - (9/10) x 2/2

= (65 - 18)/20

= 47/20

So, Cleo is thining of the fraction 47/20.