Concepts

Multiplying by a two-digit number requires multiplying each digit in every place value being multiplied by every digit in the two-digit factor. The numbers that are multiplied are called FACTORS, and the answer is called the PRODUCT.

Rules

The FACTORS are written on top of each other. Usually, we write the bigger number on the top, and it’s called the MULTIPLICAND, and the smaller number below is called the MULTIPLIER.
Multiply the multiplicand by each of the digits of the multiplier, moving from right to left. The digits of the product are written below the line.

Example

Multiply. Complete the missing steps.

Solution

Work through the problem to find the missing digits.
1. Multiply the ones (3 x 1 = 3). Write the 3 in the ones place under the line. 

2. Multiply the tens (3 x 60 = 180). Write the 8 in the tens place below the line and carry the 1 forward to the hundreds.

3. Multiply the hundreds and add what was carried forward (3 x 500 = 1,500 and then 1,500 +100 = 1,600).  Write the 6 in the hundreds place. Carry the 1 over and write it in the thousands place.
The 3 from this product is the missing digit in the first row.

4. Multiply 20 x 1 = 20. Write the 2 in the tens place and 0 in the ones place.

5. Multiply the tens (20 x 60 = 1,200). Write the 2 in the hundreds place and carry the 1 over to the thousands place.

6. Multiply the hundreds and add what was carried forward (20 x 500 = 10,000 and then 10,000 + 1,000 = 11,000). Write 1 in the thousands place and 1 in the ten thousand’s place. The 1 in the thousands place is the missing number in the second row.

7. Add the two products to get the final answer and finish finding the missing digits.

561 x 23 = 12,903

Prerequisite Skills

Basic Multiplication Facts

Place Value (4.1.4 value of digits)

Place Value (4.1.8 value of digits)

Expanded Numbers (4.1.3 Convert between Standard and Expanded Form)

Expanded Numbers (4.1.7 Convert between Standard and Expanded Form)