Find the ratio of the first quantity to second quantity in the reduced form . 7 years 3 months 12 years 1 month.

Answer

To find the ratio of the first quantity (7 years 3 months) to the second quantity (12 years 1 month) in reduced form, we will follow these steps:

### Step 1: Convert both quantities into months.
- **First Quantity:**
- 7 years = 7 × 12 months = 84 months
- 3 months = 3 months
- Total for the first quantity = 84 + 3 = 87 months

- **Second Quantity:**
- 12 years = 12 × 12 months = 144 months
- 1 month = 1 month
- Total for the second quantity = 144 + 1 = 145 months

### Step 2: Write the ratio of the two quantities.
- The ratio of the first quantity to the second quantity is:
\[ \text{Ratio} = \frac{87}{145} \]

### Step 3: Simplify the ratio.
- To simplify the ratio, we need to find the greatest common divisor (GCD) of 87 and 145.
- The prime factorization of 87 is \(3 \times 29\) and for 145 is \(5 \times 29\).
- The GCD is 29.

### Step 4: Divide both the numerator and the denominator by the GCD.
- Dividing both by 29:
\[ \frac{87 \div 29}{145 \div 29} = \frac{3}{5} \]

### Final Answer:
- The ratio of the first quantity to the second quantity in reduced form is:
\[ 3 : 5 \]

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