HALFWAY BETWEEN THE TWO RATIONAL NUMBERS

To find rational numbers between the given rational numbers, we have two different ways.

Find three rational numbers between 2/3 and 3/4.

Method 1 :

To find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. 

a = 2/3 and b = 3/4

a = 23 and b = 34First number = 23 + 342= (8+9)122= 1712×12= 1724a = 23 and b = 1724Seconnd number = 23 + 17242= (16+17)242= 3324×12= 3348a = 23 and b = 3348Third number = 23 + 33482= (32+33)482= 6548×12= 6596

Method 2 :

By creating equivalent fraction :

a = 23 and b = 34

In between 32/48 and 36/48, we have 

33/48, 34/48, 35/48

Problem 1 :

Find ten rational numbers between -2/5 and 1/2

Solution :

Since we are finding 10 rational numbers, let us use the second method.

a = -25 and b = 12We find 7 rational numbersWe find 10 rational numbers

Problem 2 :

Find five rational numbers between 2/3 and 4/5

Solution :

Since we are finding 5 rational numbers, let us use the second method.

a = 23 and b = 45We can find only one rational number. So,We find 5 rational numbers

Problem 3 :

Find five rational numbers between -3/2 and 5/3

a = -32 and b = 53We find 5 rational numbers

Problem 4 :

Find five rational numbers between 1/4 and 1/2

Solution :

a = 1/4 and b = 1/2

Let c be the halfway between a and b.

a = 14 and b = 12c = a + b2c = 14+ 122c = 1+242c = 38

a = 1/4 and b = 3/8

Let d be the halfway between a and b.

a = 14 and b = 38d = a + b2d = 14+ 382d = 2+382d = 516

a = 1/4 and b = 5/16

Let e be the halfway between a and b.

a = 14 and b = 516e = a + b2e = 14+ 5162e = 4+5162e = 932

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