If `(2)/(3), (23)/(30), (9)/(10), (11)/(15) and (4)/(5)` are written in ascending order, then the fraction in the middle most will be

Options

A. `(23)/(30)`
B. `(4)/(5)`
C. `(2)/(3)`
D. `(11)/(15)`

Answer

To find the fraction in the middle when the fractions \( \frac{2}{3}, \frac{23}{30}, \frac{9}{10}, \frac{11}{15}, \frac{4}{5} \) are arranged in ascending order, we can follow these steps:

### Step 1: Convert all fractions to have a common denominator
To compare the fractions easily, we can convert them to have a common denominator. The least common multiple (LCM) of the denominators (3, 30, 10, 15, and 5) is 30.

### Step 2: Rewrite each fraction with the common denominator
Now, we convert each fraction:

- \( \frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30} \)
- \( \frac{23}{30} = \frac{23}{30} \) (already has the common denominator)
- \( \frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30} \)
- \( \frac{11}{15} = \frac{11 \times 2}{15 \times 2} = \frac{22}{30} \)
- \( \frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30} \)

### Step 3: List the fractions with the common denominator
Now we have the following fractions:

- \( \frac{20}{30} \)
- \( \frac{23}{30} \)
- \( \frac{27}{30} \)
- \( \frac{22}{30} \)
- \( \frac{24}{30} \)

### Step 4: Arrange the fractions in ascending order
Now we can arrange these fractions in ascending order:

1. \( \frac{20}{30} \)
2. \( \frac{22}{30} \)
3. \( \frac{23}{30} \)
4. \( \frac{24}{30} \)
5. \( \frac{27}{30} \)

### Step 5: Identify the middle fraction
Since there are 5 fractions, the middle fraction is the 3rd one in the ordered list.

Thus, the middle fraction is \( \frac{23}{30} \).

### Final Answer:
The fraction in the middle most is \( \frac{23}{30} \).

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