Determine if the numbers are in proportion:
`33. 44. 75, 100`

Answer

To determine if the numbers 33, 44, 75, and 100 are in proportion, we will follow these steps:

### Step 1: Understand the concept of proportion
Proportion states that four numbers A, B, C, and D are in proportion if the ratio of A to B is equal to the ratio of C to D. Mathematically, this is expressed as:
\[ \frac{A}{B} = \frac{C}{D} \]

### Step 2: Identify the numbers
In our case, we have:
- A = 33
- B = 44
- C = 75
- D = 100

### Step 3: Calculate the ratio of the first pair (A and B)
We will calculate the ratio of 33 to 44:
\[ \frac{33}{44} \]

To simplify this fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 11:
\[ \frac{33 \div 11}{44 \div 11} = \frac{3}{4} \]

### Step 4: Calculate the ratio of the second pair (C and D)
Next, we calculate the ratio of 75 to 100:
\[ \frac{75}{100} \]

Again, we can simplify this fraction by dividing both the numerator and the denominator by their GCD, which is 25:
\[ \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \]

### Step 5: Compare the two ratios
Now we compare the two simplified ratios:
\[ \frac{3}{4} \text{ (from A and B)} \quad \text{and} \quad \frac{3}{4} \text{ (from C and D)} \]

Since both ratios are equal:
\[ \frac{3}{4} = \frac{3}{4} \]

### Step 6: Conclusion
Since the ratios are equal, we can conclude that the numbers 33, 44, 75, and 100 are in proportion.

### Final Answer
Yes, the numbers 33, 44, 75, and 100 are in proportion.

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