Honi, Jake and Kay play a game. Honi and Jake each choose a fraction and Kay tries to find the fraction that is half-way between Honi’s and Jake’s fractions on the number line.
If Honi chooses 1/4 and Jake chooses 5/8, what fraction should Kay choose?
Solution
Kay should choose 7/16.
Here is how you can check the answer.
7/16 – 1/4 = 7/16 – 4/16 = 3/16.
5/8 – 7/16 = 10/16 – 7/16 = 3/16.
So then 1/4 and 5/8 are both 3/16ths away from 7/16. That means that 7/16 is half-way between 1/4 and 5/8.
But is there a rule for finding halves? You might know that to find the half-way point of two whole numbers you add then and divide by 2. So to find half-way between 5 and 11 we work out (5 + 11)/2 = 16/2 = 8.
The same thing happens for 5 and 10. (5 + 10)/2 = 15/2 = 7½, and 7½ is half-way between 5 and 10.
The same thing works for fractions. How do we get the half-way point of 1/4 and 5/8? Just add them and divide by 2. So we get (1/4 + 5/8)/2 = (4/16 + 10/16)/2 = (14/16)/2 = 7/16, as Kay had already discovered.
Extension
What fraction lies half-way between 3/4 and 2/5?
You might also like to play this game with two friends.