# Inserting a Fraction between Two Given Fractions

Inserting a fraction between two given fractions are discussed below:

If a/b and c/d are two given fractions and a/b < c/d then

a/b < (a+c)/(b+d) < c/d.

Example:

1. Insert a fraction between 2/3 and 5/6, given 2/3 < 5/6.

Solution:

Required fraction between 2/3 and 5/6 is (2+5)/(3+6)=7/9

Therefore, 2/3 < 7/9 < 5/6.

2. Insert a fraction between 1/2 and 3/4, given 1/2 < 3/4.

Solution:

Required fraction between 1/2 and 3/4 is (1+3)/(2+4)=4/6=2/3.

3. Insert a fraction between 2/3 and 3/4, given 2/3 3/4.

Solution:

Required fraction between 2/3 and 3/4 is (2+3)/(3+4) = 5/7.

4. Insert a fraction between 5/7 and 3/4, given 5/7 < 3/4.

Solution:

Required fraction between 5/7 and 3/4 is (5+3)/(7+4) = 8/11.

5. Insert a fraction between 5/7 and 8/11, given 5/7 < 8/11.

Solution:

Required fraction between 5/7 and 8/11 is (5+8)/(7+11) = 13/18.

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions