State True or False:
`475xx(16-:4)=(475xx16)-:(475xx4)`

Answer

To determine whether the statement \( 475 \times (16 \div 4) = (475 \times 16) \div (475 \times 4) \) is true or false, we will evaluate both sides of the equation step by step.

### Step 1: Calculate the Left-Hand Side (LHS)
The left-hand side of the equation is:
\[ 475 \times (16 \div 4) \]
First, we need to calculate \( 16 \div 4 \):
\[ 16 \div 4 = 4 \]
Now substitute this back into the equation:
\[ 475 \times 4 \]
Now calculate \( 475 \times 4 \):
\[ 475 \times 4 = 1900 \]
So, the LHS is:
\[ \text{LHS} = 1900 \]

### Step 2: Calculate the Right-Hand Side (RHS)
The right-hand side of the equation is:
\[ (475 \times 16) \div (475 \times 4) \]
First, calculate \( 475 \times 16 \):
\[ 475 \times 16 = 7600 \]
Next, calculate \( 475 \times 4 \):
\[ 475 \times 4 = 1900 \]
Now substitute these values back into the RHS:
\[ 7600 \div 1900 \]
Now calculate \( 7600 \div 1900 \):
\[ 7600 \div 1900 = 4 \]
So, the RHS is:
\[ \text{RHS} = 4 \]

### Step 3: Compare LHS and RHS
Now we compare the results from both sides:
\[ \text{LHS} = 1900 \quad \text{and} \quad \text{RHS} = 4 \]
Since \( 1900 \neq 4 \), we conclude that:
\[ \text{LHS} \neq \text{RHS} \]

### Final Answer
Thus, the statement \( 475 \times (16 \div 4) = (475 \times 16) \div (475 \times 4) \) is **False**.

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