Question

Find six rational numbers between 3/5 and 3/4

Answer 1

six rational number are

3/5 × 4= 12/20

3/4 ×5 =15/20

we have to find six rational number between 12/20 and 15/20, so we have to multiply numerator and denominator by 7

12×7= 84

20×7=140

15/20×7=105/140

85 ,86 , 87 ,88 89 90

140, 140, 140, 140, 140 ,140

Answer 2

`\sf (121)/(200) \ ; \ (122)/(200) \ ; \ (123)/(200) \ ; \ (124)/(200) \ ; \ (125)/(200) \ ; \ (126)/(200)`

Explanation:

To find six rational numbers between the given numbers,

• Check if both rational numbers have the same denominator. If not find the LCM of the denominators.

LCM of 5 and 4 is 20.

• Find equivalent fractions using the LCM.

`\sf (3)/(5)=(3*4)/(5*4)=(12)/(20)\\\\\\(3)/(4)=(3*5)/(4*5)=(15)/(20)`

• Now, multiply numerator and the denominator of each of the rational number by 10

`\sf (12*10)/(20*10)=(120)/(200)\\\\(15*10)/(20*10)=(150)/(200)`

`\sf \text{six rational numbers between} \ (3)/(5) \ and \ (3)/(4)\ are :`

`\sf (121)/(200) \ ; \ (122)/(200) \ ; \ (123)/(200) \ ; \ (124)/(200) \ ; \ (125)/(200) \ ; \ (126)/(200)`