Are the following numbers in proportion?
22,33,42,63.

Answer

To determine if the numbers 22, 33, 42, and 63 are in proportion, we will follow these steps:

### Step 1: Understand the Proportion Condition
To check if the numbers A, B, C, and D are in proportion, we need to verify if the ratio of A to B is equal to the ratio of C to D. In mathematical terms, this means we need to check if:
\[ \frac{A}{B} = \frac{C}{D} \]

### Step 2: Assign the Values
Here, we assign:
- A = 22
- B = 33
- C = 42
- D = 63

### Step 3: Calculate the Ratios
Now, we will calculate the ratios:
1. Calculate \(\frac{A}{B} = \frac{22}{33}\)
2. Calculate \(\frac{C}{D} = \frac{42}{63}\)

### Step 4: Simplify the Ratios
1. For \(\frac{22}{33}\):
- Both 22 and 33 can be divided by 11.
- \(\frac{22 \div 11}{33 \div 11} = \frac{2}{3}\)

2. For \(\frac{42}{63}\):
- Both 42 and 63 can be divided by 21.
- \(\frac{42 \div 21}{63 \div 21} = \frac{2}{3}\)

### Step 5: Compare the Ratios
Now we compare the two simplified ratios:
- \(\frac{22}{33} = \frac{2}{3}\)
- \(\frac{42}{63} = \frac{2}{3}\)

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

### Final Conclusion
Yes, the numbers 22, 33, 42, and 63 are in proportion.

---