How to find the amount of rational numbers between two numbers
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ACT Math › How to find the amount of rational numbers between two numbers
How many rational numbers are between 1 and 2?
Just one
Two: 1 and 2
None
Infinitely many
Explanation
The definition of a rational number is an integer or a fraction. We can take the fractions 3/2, 4/3, 5/4, 6/5, 7/6, 8/7,...and continue in this way to realize there are infinitely many rational numbers.
A flight from Boston to Los Angeles lasts about 6 hours. The time zone difference is such that it is 3 hours later in Boston. If the flight leaves Boston at 8:00 AM, what will be the local time in Los Angeles when the plane arrives?
5:00 PM
2:00 PM
11:00 AM
3:00 PM
1:00 PM
Explanation
The plane will land in Los Angeles at 2:00 PM Boston time (8:00 AM + 6 hours = 2:00 PM).
Going west, subtract the time zone difference. Going east, add the time zone difference.
So, 2:00 PM Boston time becomes 11:00 AM local time in Los Angeles (2:00 PM – 3 hours = 11:00 AM).
How many rational numbers are there between 0 and 5?
0
5
6
Infinitely many
Explanation
Rational numbers are written in the form 
where 
; therefore, we can write infinitely many combinations of rational numbers between 0 and 1, e.g. 1/2, 1/3, 1/4, 1/5, 1/6 . . . .