Question

Fill in the blanks!
Finding Products by "Breaking it up"
What is the product of 31 x 11?
31 and 11 can be written in expanded form.

31 = _ + 1
11 = 10 + _

Multiply each part of the expanded form together.

31 x 11 = (30 + 1) x (_ + 1)

If we were to add all these up together, we would get the prodect of _.

Answer 1

Let's break down the problem step by step.

First, we can expand 31 and 11:

- 31 can be expressed as \(30 + 1\).
- 11 can be expressed as \(10 + 1\).

Now we can write the multiplication as follows:

\[
31 \times 11 = (30 + 1) \times (10 + 1)
\]

Next, we apply the distributive property (often referred to as the FOIL method in this context):

\[
(30 + 1) \times (10 + 1) = 30 \times 10 + 30 \times 1 + 1 \times 10 + 1 \times 1
\]

Now we calculate each of these multiplications:

- \(30 \times 10 = 300\)
- \(30 \times 1 = 30\)
- \(1 \times 10 = 10\)
- \(1 \times 1 = 1\)

Now, we add all these results together:

\[
300 + 30 + 10 + 1 = 341
\]

So, the final answer is:

31 x 11 = (30 + 1) x (10 + 1)

If we were to add all these up together, we would get the product of **341**.