Fill in the blank
The simplest form of the ratio `8:12` is …. Whereas simplest form of the ratio ` 1/8 : 1/12 ` is ….

Answer

To find the simplest form of the ratios given in the question, we will go through the steps systematically.

### Step 1: Simplifying the ratio 8:12
To simplify the ratio 8:12, we need to find the greatest common divisor (GCD) of the two numbers.

- **Finding the GCD of 8 and 12:**
- The factors of 8 are: 1, 2, 4, 8
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The common factors are: 1, 2, 4
- The greatest common factor is 4.

- **Dividing both numbers by their GCD:**
- 8 ÷ 4 = 2
- 12 ÷ 4 = 3

Thus, the simplest form of the ratio 8:12 is **2:3**.

### Step 2: Simplifying the ratio 1/8 : 1/12
To simplify the ratio 1/8 : 1/12, we can use the method of cross multiplication.

- **Cross multiplying:**
- The ratio can be rewritten as (1/8) : (1/12) = (1/8) ÷ (1/12).
- This is equivalent to (1/8) × (12/1) = 12/8.

Now we have the ratio 12:8.

- **Finding the GCD of 12 and 8:**
- As previously determined, the GCD is 4.

- **Dividing both numbers by their GCD:**
- 12 ÷ 4 = 3
- 8 ÷ 4 = 2

Thus, the simplest form of the ratio 1/8 : 1/12 is **3:2**.

### Final Answers
- The simplest form of the ratio 8:12 is **2:3**.
- The simplest form of the ratio 1/8 : 1/12 is **3:2**.

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