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.
`16:56::12:42`

Answer

To determine whether the numbers 16, 56, 12, and 42 are in proportion, we will follow these steps:

### Step 1: Identify the terms
The four numbers given are:
- First term (a) = 16
- Second term (b) = 56
- Third term (c) = 12
- Fourth term (d) = 42

### Step 2: Set up the proportion
We need to check if the proportion \( a:b::c:d \) holds true. This means we need to verify if:
\[ a \times d = b \times c \]

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

1. Calculate \( a \times d \):
\[ 16 \times 42 \]
- \( 16 \times 42 = 672 \)

2. Calculate \( b \times c \):
\[ 56 \times 12 \]
- \( 56 \times 12 = 672 \)

### Step 4: Compare the products
Now we compare the two products:
- \( a \times d = 672 \)
- \( b \times c = 672 \)

Since both products are equal, we conclude that:
\[ 16 \times 42 = 56 \times 12 \]

### Step 5: Conclusion
Since the products are equal, the numbers are in proportion. We write:
- (T) for True

### Step 6: Identify the middle and extreme terms
- **Extreme terms**: 16 and 42
- **Middle terms**: 56 and 12

### Final Answer
The numbers 16, 56, 12, and 42 are in proportion. Thus, we write:
- (T)
- Extreme terms: 16 and 42
- Middle terms: 56 and 12

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