Fill in the blanks!

Question

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.