How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
There are infinitely many fractions between 0 and 1.
Reasoning: For any two fractions, we can always find another fraction between them by taking their average or by using a common denominator.
Examples:
- Between 0 and 1/2 lies 1/4
- Between 1/4 and 1/2 lies 3/8
- And so on endlessly
∴ There are infinitely many fractions between 0 and 1.
Explanation
The chapter introduces the concept that fractions can be marked on a number line between 0 and 1. Since we can always divide a unit into more equal parts (denominators can be any number), there is no limit to how many fractions exist between 0 and 1.
Solution Steps
There are infinitely many fractions between 0 and 1.
For any two fractions, we can always find another fraction between them by taking their average or by using a common denominator.
For example, between 0 and 1/2 lies 1/4, between 1/4 and 1/2 lies 3/8, and so on endlessly.