INSERTION OF FRACTIONS BETWEEN TWO GIVEN FRACTIONS
y z y + z
A fraction between -------- and ------- is -----------
z w z + w
2 3 2 + 3
Example.- A fraction between ------- and ------- is --------- for
5 7 5 + 7
5
= -----------
12
y y + z y + ( y + z )
Similarly a fraction between ------ and -------- is --------------
z z + w z + ( z + w )
2y + z
= ----------
2z + w
2y + z z ( 2y + z ) + z
a fraction between ---------- and ------ is ----------------
2z + w w ( 2z + w ) + w
2w + 2z
= ------------
2z + 2w
y 2y + z y + ( 2y + z )
a fraction between ------- and ---------- is -----------------
z 2z + w z + ( 2z + w )
3y + z
= ------------
3z + w
y z
thus, some of the fractions lying between ------ and ------- are
z w
y + z 2y + z 2w + 2z 3y + z
---------, --------- , ---------- and -----------
z + w 2z + w 2z + 2w 3z + w
There are some example has been given below for your better understanding –
2 3
Example.1) Find three fractional number between ------ and ------
7 11
Answer) As per the condition we have only two fractional number these
2 3
are ------- and ------- 7 11
2 3 2 + 3 5
So, Number between ------- and ------- is ---------- = -------
7 11 7 + 11 18
2 5 2 + 5 7
Number between ------ and ------ is ---------- = -------
7 18 7 + 18 25
5 3 5 + 3 8
Number between -------- and ------- is ---------- = -------
18 11 18 + 11 29
2 3 5 7 8
Number between ------ and ------ are ------, ------, -------
7 11 18 25 29
It has been seen that, there are an infinite number of fractions between any two fractions. (Ans.)
4 7
Example.2) Find three fractional number between ------- and ------
11 15
Answer) As per the condition we have only two fractional number these
4 7
are ------ and -------
11 15
4 7 4 + 7 11
So, number between ------ and ------- is ---------- = --------
11 15 11 + 15 26
4 11 4 + 11 15
Number between ------- and ------ is ---------- = --------
11 26 11 + 26 37
15 7 15 + 7 22
Number between ------- and ------- is ---------- = --------
37 15 37 + 15 52
4 7 11 15 22
Number between ------ and ------ are -------, -------, -------
11 15 26 37 52
It has been seen that, there are an infinite number of fractions between any two fractions. (Ans.)