Multiplying Multi-Digit by One-Digit Numbers

Multiplying a large number (up to four digits) by a single-digit number is an essential math skill. There are a few different strategies you can use to solve these problems, including the standard algorithm, partial products, and the area model. Let's look at how each method works!

The Standard Algorithm

The standard algorithm is a fast and common way to multiply. You multiply the single digit by each digit in the top number, starting from the right (ones place) and moving left. If a product is 10 or greater, you "carry" the extra value to the next column.

Example: $2{,}345 \times 6$

1. Multiply the ones: $5 \times 6 = 30$. Write down $0$, carry over the $3$.
2. Multiply the tens: $4 \times 6 = 24$. Add the carried $3$ to get $27$. Write down $7$, carry over the $2$.
3. Multiply the hundreds: $3 \times 6 = 18$. Add the carried $2$ to get $20$. Write down $0$, carry over the $2$.
4. Multiply the thousands: $2 \times 6 = 12$. Add the carried $2$ to get $14$. Write down $14$.

Result: $2{,}345 \times 6 = 14{,}070$

The Partial Products Method

Instead of carrying numbers, the partial products method breaks the large number into its place values. You multiply each part separately and then add all the answers together.

Example: $807 \times 9$

First, break $807$ into expanded form: $800 + 0 + 7$. Next, multiply each part by $9$:

• $800 \times 9 = 7{,}200$
• $0 \times 9 = 0$
• $7 \times 9 = 63$

Finally, add the partial products together: $7{,}200 + 0 + 63 = 7{,}263$

Result: $807 \times 9 = 7{,}263$

The Area Model

The area model is a visual way to use partial products. You draw a rectangle, break the multi-digit number into its expanded form across the top, and put the single digit on the side.

Example: $4{,}030 \times 5$

1. Break $4{,}030$ into $4{,}000 + 30$. (You can skip the hundreds and ones since they are zero).
2. Draw a box with two columns (for $4{,}000$ and $30$) and one row (for $5$).
3. Multiply to find the area of each section:
   • $4{,}000 \times 5 = 20{,}000$
   • $30 \times 5 = 150$
4. Add the areas together: $20{,}000 + 150 = 20{,}150$

Result: $4{,}030 \times 5 = 20{,}150$

Quick Tips for Success

• Always line up your numbers properly by place value when adding partial products.
• Don't forget to add the numbers you "carry" when using the standard algorithm!
• Use the method that makes the most sense to you. You can even use one method to solve and another to check your work.