Question

Which of the following is equal to 1,057 × 675?
A.
(1,000 × 675) + (50 × 675) + (7 × 675)
B.
(1,000 + 675) + (50 + 675) + (7 + 675)
C.
(7 × 675) × (50 × 675) × (1,000 × 675)
D.
(70 × 675) + (500 × 675) + (1,000 × 675)

Answer 1

To determine which expression is equal to \(1,057 \times 675\), let's break down \(1,057\) into its components:

\[
1,057 = 1,000 + 50 + 7
\]

So we can write:

\[
1,057 \times 675 = (1,000 + 50 + 7) \times 675
\]

Using the distributive property:

\[
= (1,000 \times 675) + (50 \times 675) + (7 \times 675)
\]

Now, let's check the options:

A.
\[
(1,000 \times 675) + (50 \times 675) + (7 \times 675)
\]
This matches our derived expression.

B.
\[
(1,000 + 675) + (50 + 675) + (7 + 675)
\]
This simplifies to:
\[
(1,675) + (725) + (682) \neq 1,057 \times 675
\]

C.
\[
(7 \times 675) \times (50 \times 675) \times (1,000 \times 675)
\]
This is not equal to \(1,057 \times 675\).

D.
\[
(70 \times 675) + (500 \times 675) + (1,000 \times 675)
\]
This simplifies to:
\[
(70 + 500 + 1,000) \times 675 = 1,570 \times 675 \neq 1,057 \times 675
\]

Thus, the only correct answer is:

\[
\boxed{A}
\]

The expression A is indeed equal to \(1,057 \times 675\).