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How to get all rational numbers between two rational numbers?
Getting all the rational numbers between two rational numbers is a simple process that involves finding the lowest common multiple (LCM) of the denominators of the two numbers and then creating equivalent fractions with that LCM as the denominator.
Step-by-step process:
- Find the LCM of the denominators of the two numbers.
- Multiply each fraction by the appropriate form of 1 so that each denominator equals the LCM. This will create equivalent fractions with the same denominator.
- Write out all the fractions between the two original fractions, in order from smallest to largest.
- Simplify any fractions that can be simplified.
Example:
Find all the rational numbers between 2/3 and 4/5.
- The LCM of 3 and 5 is 15.
- 2/3 x 5/5 = 10/15 and 4/5 x 3/3 = 12/15
- The fractions between 2/3 and 4/5 with denominator 15 are:
- 7/15
- 8/15
- 9/15 = 3/5
- 10/15 = 2/3
- 11/15
- 12/15 = 4/5
- The simplified fractions between 2/3 and 4/5 are:
- 7/15
- 8/15
- 3/5
- 2/3
- 11/15
- 4/5
Therefore, the rational numbers between 2/3 and 4/5 are 7/15, 8/15, 3/5, 2/3, 11/15, and 4/5.
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