The ratio `1/2 : 1/3 : 1/5` is the same as-

Options

A. `2:3:5`
B. `5:3:2`
C. `15:10:6`
D. `6:10:15`

Answer

To solve the problem of finding the equivalent ratio for \( \frac{1}{2} : \frac{1}{3} : \frac{1}{5} \), we can follow these steps:

### Step 1: Identify the Ratios
We start with the given ratio:
\[ \frac{1}{2} : \frac{1}{3} : \frac{1}{5} \]

### Step 2: Find the LCM of the Denominators
Next, we need to eliminate the fractions by finding the least common multiple (LCM) of the denominators (2, 3, and 5).
- The LCM of 2, 3, and 5 is calculated as follows:
- Since 2, 3, and 5 are all prime numbers, the LCM is simply their product:
\[ \text{LCM} = 2 \times 3 \times 5 = 30 \]

### Step 3: Multiply Each Term by the LCM
Now, we multiply each term of the ratio by the LCM (30) to eliminate the denominators:
\[ 30 \times \frac{1}{2} : 30 \times \frac{1}{3} : 30 \times \frac{1}{5} \]

### Step 4: Calculate Each Term
Calculating each term gives us:
- For \( \frac{1}{2} \):
\[ 30 \times \frac{1}{2} = 15 \]
- For \( \frac{1}{3} \):
\[ 30 \times \frac{1}{3} = 10 \]
- For \( \frac{1}{5} \):
\[ 30 \times \frac{1}{5} = 6 \]

### Step 5: Write the Simplified Ratio
Now we can write the simplified ratio:
\[ 15 : 10 : 6 \]

### Step 6: Check for Further Simplification
We can simplify this ratio further by finding the greatest common divisor (GCD) of 15, 10, and 6, which is 1. Thus, the ratio remains:
\[ 15 : 10 : 6 \]

### Conclusion
The equivalent ratio of \( \frac{1}{2} : \frac{1}{3} : \frac{1}{5} \) is:
\[ 15 : 10 : 6 \]