Andrew, Gill and Joe play a game. Andrew and Gill each choose a fraction and Joe tries to find a fraction that is between Andrew’s and Gill’s fractions on the number line.
If Andrew chooses 1/4 and Gill chooses 5/8, give some suggestions for what fractions Joe could choose.
Solution
There are very many fractions that Joe could have chosen. To see some of these, first recall that 1/4 = 2/8. So we are looking for a fraction between 2/8 and 5/8. You should see that 3/8 or 4/8 will do.
On the other hand, 1/4 = 4/16 and 5/8 = 10/16, so 5/16, 6/16, 7/16, 8/16 and 9/16 will work for Joe too.
You can also find equivalent fractions for some of those already listed. 8/16 = 4/8 = 1/2 = 12/24 = ...
Extension
How many more fractions can Joe find?
You might also like to play this game with two friends.