Explain the mistake. I made using distributive property for the following problem

Question

356×36
(356×3) +(356×6)
1056+2112=3,168
What era did I make?

Answer 1

Let's break down your calculation step by step to identify where the mistake occurred.

You correctly used the distributive property to break down \( 356 \times 36 \) as follows:

\[ 356 \times 36 = (356 \times 3) + (356 \times 6) \]

However, the mistake occurs in the evaluation of \( 356 \times 3 \) and \( 356 \times 6 \).

Let's calculate these separately:

1. \( 356 \times 3 \): \[ 356 \times 3 = 1068 \]

2. \( 356 \times 6 \): \[ 356 \times 6 = 2136 \]

Now, if we add these results together, we have:

\[ 1068 + 2136 = 3204 \]

So, the correct calculation of \( 356 \times 36 \) using the distributive property should yield:

\[ 356 \times 36 = 3204 \]

In your original post, you calculated \( 356 \times 3 \) as 1056 and \( 356 \times 6 \) as 2112, which are both incorrect. Thus, the total that you presented, \( 3168 \), was also incorrect.

In summary, the mistakes were in the multiplication of \( 356 \times 3 \) and \( 356 \times 6 \). The correct values are \( 1068 \) and \( 2136 \), respectively, leading to the correct sum of \( 3204 \).