Those Fractions in Between

Find three different fractions in between 3/ 5 and 2/ 3 whose numerators and denominators are all whole numbers.

There are many fractions in between 3/5 and 2/3 whose numerators and denominators are all whole numbers. All you need to do for this problem is to find some common denominators of 5 and 3...they include 15, 30, 45, 60, 75, 90, 105, 120, 135, ...210, ...300...etc.

For example:

When I find the least common denominator of 5 and 3, which is 15, my numerators are 9 and 10, respectively. In this particular case, there are no fractions whose numerators and denominators are both whole numbers but when I change my denominators to 30, I get 3/5 = 18/30 and 2/3 = 20/30. In this case, I have 19/30 in between 3/5 and 2/3. When I enlist 45 as my denominator, I have 3/5 = 27/45 and 2/3 = 30/45...here I have 28/45 and 29/45 in between 3/5 and 2/3. When I have 60 as my denominator, 3/5 = 36/60 and 2/3 = 40/60, so I have 37/60, 38/60, and 39/60 in between 3/5 and 2/3. If I continue this pattern, I have the following: 3/5 = 45/75 = 54/90 = 63/105 = 72/120; and 2/3 = 50/75 = 60/90 = 70/105 = 80/120...

Now if I have 3 different fractions in between 3/5 and 2/3, they may be:

37/60, 28/45, and 19/30

There are soooo many fractions in between 3/5 and 2/3....in fact, there are infinite possibilities!!

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