Question

Solve 13 x 17 in expanded form. Fill in the blanks
(10 + 3) x (10 + 7)
(10 x 10) + (10 x ?) + (3 x 10) + (3 x 7)
100 + 70 + ? + 21 = 221

Answer 1

To solve \(13 \times 17\) in expanded form, we can fill in the blanks as follows:

We start with the expression:
\[
(10 + 3) \times (10 + 7)
\]
We can expand this using the distributive property:
\[
(10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7)
\]
Now, let's calculate each part:
- \(10 \times 10 = 100\)
- \(10 \times 7 = 70\)
- \(3 \times 10 = 30\)
- \(3 \times 7 = 21\)

So, we replace the question marks:
\[
(10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7) = 100 + 70 + 30 + 21
\]

Thus, filling in the blanks, we get:
\[
(10 + 3) \times (10 + 7) = (10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7) \implies 100 + 70 + 30 + 21
\]

Finally, when you add these all together:
\[
100 + 70 + 30 + 21 = 221
\]

So, the answer to fill in the blanks is \(30\) for the missing value in the expression.