The lowest fraction in 1/2,3/4,5/6,7/12,2/5 is

Options

A. (1/2
B. (7/12)
C. (5/6)
D. (2/5)

Answer

To find the lowest fraction among the given fractions \( \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{12}, \frac{2}{5} \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Fractions:**
We have the following fractions:
\[ \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{12}, \frac{2}{5} \]

2. **Find the Denominators:**
The denominators of the fractions are:
\[ 2, 4, 6, 12, 5 \]

3. **Calculate the LCM of the Denominators:**
To compare the fractions, we need a common denominator. We will find the least common multiple (LCM) of the denominators \( 2, 4, 6, 12, 5 \).

- The prime factorization of each number is:
- \( 2 = 2^1 \)
- \( 4 = 2^2 \)
- \( 6 = 2^1 \times 3^1 \)
- \( 12 = 2^2 \times 3^1 \)
- \( 5 = 5^1 \)

- The LCM is obtained by taking the highest power of each prime:
- For \( 2 \): \( 2^2 \)
- For \( 3 \): \( 3^1 \)
- For \( 5 \): \( 5^1 \)

Therefore, the LCM is:
\[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \]

4. **Convert Each Fraction to Have the Common Denominator:**
Now we will convert each fraction to have a denominator of 60:

- For \( \frac{1}{2} \):
\[ \frac{1}{2} = \frac{1 \times 30}{2 \times 30} = \frac{30}{60} \]

- For \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60} \]

- For \( \frac{5}{6} \):
\[ \frac{5}{6} = \frac{5 \times 10}{6 \times 10} = \frac{50}{60} \]

- For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60} \]

- For \( \frac{2}{5} \):
\[ \frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60} \]

5. **Compare the Converted Fractions:**
Now we have:
\[ \frac{30}{60}, \frac{45}{60}, \frac{50}{60}, \frac{35}{60}, \frac{24}{60} \]

The numerators are \( 30, 45, 50, 35, 24 \).

6. **Identify the Lowest Fraction:**
The smallest numerator is \( 24 \), which corresponds to the fraction:
\[ \frac{2}{5} \]

### Conclusion:
The lowest fraction among \( \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{12}, \frac{2}{5} \) is:
\[ \frac{2}{5} \]