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
8 years ago
11 months ago
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.