Chech whether the given four numbers are in proportion. Write (T) if they are in proportion, and give the middle terms and the exterme terms.
Wrire (F) if they ar nit in proportion.
`0.16 :0.2 ::1.2 :1.5`

Answer

To determine if the numbers 0.16, 0.2, 1.2, and 1.5 are in proportion, we will follow these steps:

### Step 1: Understand the Proportion Condition
For four numbers \( a, b, c, d \) to be in proportion, the condition is:
\[ a : b :: c : d \]
This means:
\[ a \times d = b \times c \]

### Step 2: Identify the Numbers
Here, we have:
- \( a = 0.16 \)
- \( b = 0.2 \)
- \( c = 1.2 \)
- \( d = 1.5 \)

### Step 3: Calculate the Products
Now we will calculate the products of the extreme terms and the middle terms.

**Calculate \( a \times d \):**
\[ 0.16 \times 1.5 \]

To perform the multiplication:
- \( 0.16 \times 1.5 = 0.16 \times \frac{15}{10} = \frac{16 \times 15}{100} = \frac{240}{1000} = 0.240 \)

**Calculate \( b \times c \):**
\[ 0.2 \times 1.2 \]

To perform the multiplication:
- \( 0.2 \times 1.2 = 0.2 \times \frac{12}{10} = \frac{2 \times 12}{100} = \frac{24}{100} = 0.240 \)

### Step 4: Compare the Products
Now, we compare the two products:
- \( a \times d = 0.240 \)
- \( b \times c = 0.240 \)

Since both products are equal:
\[ 0.240 = 0.240 \]

### Step 5: Conclusion
Since the products of the extreme terms and the middle terms are equal, the numbers are in proportion.

**Final Answer:**
- Write (T) for True, as they are in proportion.
- Middle terms: 0.2 and 1.2
- Extreme terms: 0.16 and 1.5