Check whether the following numbers are in proportion or not :
0.8, 3, 2.4, 9

Answer

To determine whether the numbers 0.8, 3, 2.4, and 9 are in proportion, we can follow these steps:

### Step 1: Identify the numbers
The numbers given are:
- First number (a) = 0.8
- Second number (b) = 3
- Third number (c) = 2.4
- Fourth number (d) = 9

### Step 2: Understand the condition for proportion
The condition for four numbers \( a, b, c, d \) to be in proportion is:
\[ a : b :: c : d \]
This means that the product of the extremes (first and last numbers) should be equal to the product of the means (the middle two numbers):
\[ a \times d = b \times c \]

### Step 3: Calculate the product of the extremes
Calculate the product of the extremes:
\[ a \times d = 0.8 \times 9 \]
\[ = 7.2 \]

### Step 4: Calculate the product of the means
Now calculate the product of the means:
\[ b \times c = 3 \times 2.4 \]
\[ = 7.2 \]

### Step 5: Compare the products
Now we compare the two products:
- Product of extremes = 7.2
- Product of means = 7.2

Since both products are equal:
\[ 7.2 = 7.2 \]

### Conclusion
Since the product of the extremes is equal to the product of the means, the numbers 0.8, 3, 2.4, and 9 are in proportion.

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