Write the ratio of `45` seconds to `2` minutes in simplest form .

Options

A. `3:7`
B. `8:3`
C. `3:5`
D. `3:8`

Answer

To find the ratio of 45 seconds to 2 minutes in its simplest form, follow these steps:

### Step 1: Convert minutes to seconds
First, we need to convert 2 minutes into seconds. We know that:
1 minute = 60 seconds

So, to convert 2 minutes to seconds:
\[ 2 \text{ minutes} = 2 \times 60 \text{ seconds} = 120 \text{ seconds} \]

### Step 2: Write the ratio
Now that we have both quantities in seconds, we can write the ratio of 45 seconds to 120 seconds:
\[ \text{Ratio} = 45 : 120 \]

### Step 3: Simplify the ratio
To simplify the ratio, we need to find the greatest common divisor (GCD) of 45 and 120.

- The factors of 45 are: 1, 3, 5, 9, 15, 45
- The factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 120

The greatest common factor is 15.

Now, we divide both terms of the ratio by their GCD (15):
\[ \frac{45}{15} : \frac{120}{15} = 3 : 8 \]

### Final Answer
Thus, the ratio of 45 seconds to 2 minutes in simplest form is:
\[ \text{Ratio} = 3 : 8 \]

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