Determine if the following 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: Define the values
Let:
- A = 33
- B = 44
- C = 75
- D = 100

### Step 2: Set up the proportion
We need to check if the ratio of A to B is equal to the ratio of C to D. This can be expressed as:
\[ \frac{A}{B} = \frac{C}{D} \]

### Step 3: Substitute the values
Substituting the values we have:
\[ \frac{33}{44} = \frac{75}{100} \]

### Step 4: Simplify the fractions
Now, we simplify both fractions.

**For the left side:**
\[ \frac{33}{44} = \frac{33 \div 11}{44 \div 11} = \frac{3}{4} \]

**For the right side:**
\[ \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \]

### Step 5: Compare the simplified fractions
Now we compare the two simplified fractions:
\[ \frac{3}{4} = \frac{3}{4} \]

Since both fractions are equal, we conclude that the numbers are in proportion.

### Final Conclusion
Thus, we can write:
\[ 33 : 44 :: 75 : 100 \]
This means that the given numbers 33, 44, 75, and 100 are in proportion.

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