Determine if the following are in proportion.
33, 121, 9,96

Answer

To determine if the numbers 33, 121, 9, and 96 are in proportion, we can follow these steps:

### Step 1: Identify the numbers
We have four numbers:
- a = 33
- b = 121
- c = 9
- d = 96

### Step 2: Set up the proportion
To check if these numbers are in proportion, we need to compare the ratios a/b and c/d.

### Step 3: Calculate the first ratio (a/b)
Calculate the ratio of the first two numbers:
\[ \frac{a}{b} = \frac{33}{121} \]

### Step 4: Simplify the first ratio
To simplify \(\frac{33}{121}\), we can check if both numbers have a common factor.
- 33 can be factored as \(3 \times 11\).
- 121 can be factored as \(11 \times 11\).

Now, we can simplify:
\[ \frac{33}{121} = \frac{3 \times 11}{11 \times 11} = \frac{3}{11} \]

### Step 5: Calculate the second ratio (c/d)
Now calculate the ratio of the second two numbers:
\[ \frac{c}{d} = \frac{9}{96} \]

### Step 6: Simplify the second ratio
To simplify \(\frac{9}{96}\), we can find the greatest common divisor (GCD) of 9 and 96.
- 9 can be factored as \(3 \times 3\).
- 96 can be factored as \(3 \times 32\).

Now, we can simplify:
\[ \frac{9}{96} = \frac{3 \times 3}{3 \times 32} = \frac{3}{32} \]

### Step 7: Compare the two ratios
Now we have:
- \(\frac{a}{b} = \frac{3}{11}\)
- \(\frac{c}{d} = \frac{3}{32}\)

Since \(\frac{3}{11} \neq \frac{3}{32}\), the two ratios are not equal.

### Step 8: Conclusion
Since the two ratios are not equal, we conclude that the numbers 33, 121, 9, and 96 are **not in proportion**.

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