Using the Standard Method to Multiply a Two-Digit Number by a One-Digit Number

Question

Find the product of 22 × 3.
Write it vertically. The number with more digits goes on top, and the ____values should be lined up.
22
X 3
____

Now, write the problem in expanded form

Answer 1

To find the product of 22 × 3 using the standard method and writing it vertically, you would set it up like this:

  22
x  3
____

Now, let's proceed with the steps of multiplying.

1. Multiply the bottom digit (3) by each digit of the top number (22), starting from the rightmost digit.
   • \(2 \times 3 = 6\)
   • \(2 \times 3 = 6\)

So, we write that down:

  22
x  3
____
  66

The final product is 66.

Now, let's write the problem in expanded form:

The number 22 can be expressed in expanded form as: \[ 20 + 2 \]

So, when we multiply it by 3, we have: \[ (20 + 2) × 3 \]

Using the distributive property, we can expand this to: \[ 20 × 3 + 2 × 3 \]

Calculating each part:

• \(20 × 3 = 60\)
• \(2 × 3 = 6\)

Now, combining those two results: \[ 60 + 6 = 66 \]

Thus, the expanded form of the multiplication problem is: \[ (20 + 2) × 3 = 60 + 6 = 66 \]