The numbers 3,6,8,12 are in proportion. Is it true or false?

Answer

To determine whether the numbers 3, 6, 8, and 12 are in proportion, we will follow these steps:

### Step 1: Understand the definition of proportion
Proportion means that two ratios are equal. For four numbers a, b, c, and d to be in proportion, the following condition must hold:
\[ \frac{a}{b} = \frac{c}{d} \]

### Step 2: Assign the numbers to a, b, c, and d
Let:
- \( a = 3 \)
- \( b = 6 \)
- \( c = 8 \)
- \( d = 12 \)

### Step 3: Set up the equation
We need to check if:
\[ \frac{3}{6} = \frac{8}{12} \]

### Step 4: Simplify both ratios
1. Simplify \( \frac{3}{6} \):
\[ \frac{3}{6} = \frac{1}{2} \]

2. Simplify \( \frac{8}{12} \):
\[ \frac{8}{12} = \frac{2}{3} \]

### Step 5: Compare the simplified ratios
Now we compare the two simplified ratios:
\[ \frac{1}{2} \quad \text{and} \quad \frac{2}{3} \]

### Step 6: Determine if they are equal
Since \( \frac{1}{2} \) is not equal to \( \frac{2}{3} \), we conclude that:
\[ \frac{3}{6} \neq \frac{8}{12} \]

### Conclusion
Since the two ratios are not equal, the numbers 3, 6, 8, and 12 are **not in proportion**. Therefore, the statement is **false**.

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