Question

1. fill in the missing digits. explain how you found each digit.

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$$\begin{array}{r@{\\quad}c@{\\quad}c@{\\quad}c@{\\quad}c} & 2, & 7 & 4 & \\square \\\\ - & 1, & \\square & \\square & 4 \\\\ \\hline & \\square, & 5 & 4 & 1 \\end{array}$$

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Explanation:

Analyze the ones place

We are working with Multi-digit Subtraction.
Let the missing digits be:

• \(A\) in the ones place of the first number: \(2,74A\)
• \(B\) in the hundreds place of the second number: \(1,B C 4\)
• \(C\) in the tens place of the second number: \(1,B C 4\)
• \(D\) in the thousands place of the result: \(D,541\)

In the ones place:

$$A - 4 = 1$$

Solving for \(A\):

$$A = 5$$

Analyze the tens place

In the tens place:

$$4 - C = 4$$

Solving for \(C\):

$$C = 0$$

Analyze the hundreds place

In the hundreds place:

$$7 - B = 5$$

Solving for \(B\):

$$B = 2$$

Analyze the thousands place

In the thousands place:

$$2 - 1 = D$$

Solving for \(D\):

$$D = 1$$

Verify the subtraction

We substitute the found digits back into the problem:

$$
LATEXBLOCK0
$$

The subtraction is correct.

of how each digit was found:

• Ones place: To get \(1\) from subtracting \(4\), the missing digit must be \(5\) because \(5 - 4 = 1\).
• Tens place: To get \(4\) from subtracting a digit from \(4\), the missing digit must be \(0\) because \(4 - 0 = 4\).
• Hundreds place: To get \(5\) from subtracting a digit from \(7\), the missing digit must be \(2\) because \(7 - 2 = 5\).
• Thousands place: Subtracting \(1\) from \(2\) gives the missing digit \(1\) because \(2 - 1 = 1\).

</answer>

Answer:

The completed subtraction problem is:

$$
LATEXBLOCK0
$$

Explanation of how each digit was found:

• Ones place: To get \(1\) from subtracting \(4\), the missing digit must be \(5\) because \(5 - 4 = 1\).
• Tens place: To get \(4\) from subtracting a digit from \(4\), the missing digit must be \(0\) because \(4 - 0 = 4\).
• Hundreds place: To get \(5\) from subtracting a digit from \(7\), the missing digit must be \(2\) because \(7 - 2 = 5\).
• Thousands place: Subtracting \(1\) from \(2\) gives the missing digit \(1\) because \(2 - 1 = 1\).