If the following fractions are arranged from smallest to largest, then which fraction would be in the middle? Explain. Show all work using fractions(NOT DECIMALS).

2/3, 4/5, 3/7, 5/9, 3/4

Change all these fractions to equivalent fractions with the same denominators.

To arrange the fractions from smallest to largest, we need to compare their values. Here's how you can do it step by step:

Step 1: Find a common denominator.
In this case, the common denominator for these fractions is 3 * 5 * 7 * 9 = 945. Multiply each fraction by the appropriate value to get the same denominator:
- 2/3 = (2/3) * (315/315) = 630/945
- 4/5 = (4/5) * (189/189) = 756/945
- 3/7 = (3/7) * (135/135) = 405/945
- 5/9 = (5/9) * (105/105) = 525/945
- 3/4 = (3/4) * (236.25/236.25) = 708.75/945

Step 2: Compare the fractions.
Now, we have the fractions with the same denominator, so we can compare their numerators:
- 630/945, 756/945, 405/945, 525/945, 708.75/945

Step 3: Arrange the fractions.
By comparing the numerators, we can see that the fractions in ascending order are:
- 405/945, 525/945, 630/945, 708.75/945, 756/945

Therefore, the fraction that would be in the middle is 630/945.