Expert Answers
mwmovr40 eNotes educator| Certified Educator

The number line is smooth and continuous.  Therefore between any two points on the number line there can be found an infinite number of other points.

If one of the points on the number line is labelled as `1/3`  and the other `1/4` , there must be an infinite number of values which can lie between them.

If one wishes to know the midpoint between the two point, you would get the two fractions over a common denominator, add them together, and then divide by two:

`1/3 = 4/12` ,  `1/4 = 3/12`

`(4/12 + 3/12)*1/2 = 7/24`

However, one needs to remember that this is just one of an infinite number of choices for numbers between 1/3 and 1/4.  (Parenthetically, there must be an infinite number of points between 1/3 and 7/24 as well.)

Wiggin42 | Student

We want a number between 1/3 and 1/4. 

There are an infinite number of points between these to lines because the infinite set of decimal numbers is larger than the infinite set of whole numbers. There is a great TED talk on this which I encourage you to check out! 

If we convert 1/3, it becomes .33
And 1/4 becomes .25

We want a number between .25 and .33 . 

As you can see we can come with all sorts of numbers such as 

.2518794546 , .28 , . etc. 

zumba96 | Student

What is between 1/3 and 1/4.

1/3 is approx .33333333 and 1/4 is .25 to There can be fractions such as 

3/10    5/16     7/24   and decimal places ranging from .25 to .333333

atyourservice | Student

7/25 is between  1/3 and 1/4

lilahrose8248 | Student

Well, a lot of fractions are between 1/3 and 1/4, but I'll give you some examples.





7/24 (that's right in the middle)




Hope that helps!