Find a fraction between each pair:
4/7 & 5/9 1/3 & 1/4
Sometimes it is helpful to write the fractions as equivalent fractions with the same denominator.
For example, if I were asked to find a fraction between 1/5 and 1/6, I might say, "What would be a common multiple of 5 and 6? Oh...I know! 30!"
And then, I would rewrite each fraction so that it has a denominator of 30.
To change 1/5 to an equivalent fraction with 30 for its denominator, I'd multiply both numerator and denominator by 6: (1/5)*(6/6) = 6/30
To change 1/6 to an equivalent fraction with 30 for its denominator, I'd multiply both numerator and denominator by 5: (1/6)*(5/5) = 5/30
Well....I'm still not sure what a fraction between those two might be. Maybe I should make the denominators larger. I could multiply the numerator and denominator of each fraction by 2:
(6/30)*(2/2) = 12/60
(5/30)*(2/2) = 10/60
Aha! Now I can see that a fraction between 12/60 and 10/60 would be 11/60! So, 11/60 is a fraction between 1/5 and 1/6.
You could try this approach on your problems.....