Determine if the following are in proportion.
32, 48, 70, 210

Answer

To determine if the numbers 32, 48, 70, and 210 are in proportion, we can follow these steps:

### Step 1: Identify the numbers
We have the numbers:
- a = 32
- b = 48
- c = 70
- d = 210

### Step 2: Set up the proportion
To check if these numbers are in proportion, we need to compare the ratios of the first pair (a and b) and the second pair (c and d). We will write this as:
\[ \frac{a}{b} \quad \text{and} \quad \frac{c}{d} \]
This translates to:
\[ \frac{32}{48} \quad \text{and} \quad \frac{70}{210} \]

### Step 3: Simplify the fractions
Now, we will simplify both fractions.

**For the first fraction:**
\[ \frac{32}{48} \]
To simplify, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 16:
\[ \frac{32 \div 16}{48 \div 16} = \frac{2}{3} \]

**For the second fraction:**
\[ \frac{70}{210} \]
To simplify, we divide both the numerator and denominator by their GCD, which is 70:
\[ \frac{70 \div 70}{210 \div 70} = \frac{1}{3} \]

### Step 4: Compare the simplified fractions
Now we compare the two simplified fractions:
\[ \frac{2}{3} \quad \text{and} \quad \frac{1}{3} \]
Since \(\frac{2}{3} \neq \frac{1}{3}\), the two fractions are not equal.

### Step 5: Conclusion
Since the two ratios are not equal, we conclude that the numbers 32, 48, 70, and 210 are **not in proportion**.

### Final Answer:
No, the numbers 32, 48, 70, and 210 are not in proportion.

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