Question

Jay used the Distributive Property to find 402×6
. His work is shown.

402×6=(400+6)+(2+6) =406+8 =414

Is Jay's work correct? If so, explain why. If not, use the Distributive Property to find the answer.

(2 points)

Answer 1

Jay's work is not correct. He misapplied the Distributive Property.

The Distributive Property states that \(a(b + c) = ab + ac\). To properly apply this to \(402 \times 6\), we should break down \(402\) into \(400 + 2\) and distribute \(6\) to both parts.

Here’s how it should be done:

1. Break down \(402\) as \(400 + 2\).
2. Apply the Distributive Property:

\[
402 \times 6 = (400 + 2) \times 6
\]

3. Distribute the \(6\):

\[
= 400 \times 6 + 2 \times 6
\]

4. Calculate each term:

\[
400 \times 6 = 2400
\]
\[
2 \times 6 = 12
\]

5. Add the results:

\[
2400 + 12 = 2412
\]

So, the correct answer for \(402 \times 6\) is \(2412\).