How to Multiply Two-Digit by Three-Digit Numbers

In the last lesson, you learned how to multiply 2-digit by 2-digit numbers.

For example:

36 × 27 = ?

You solved this using column form:

You split the problem into two simpler multiplication steps and an addition.

Now, let's learn how to multiply 2-digit numbers by 3-digit numbers. We'll follow the same steps. 🏄‍♀️

2-Digit by 3-Digit Multiplication

Let's learn with an example:

413 × 32 = ?

First, write the numbers in column form, one below the other, starting with the bigger number.

Now, multiply 413 × 2.

Well done! 👍

Now, let's multiply 413 × 30.

Because 30 is a multiple of 10, we can just find 413 × 3 and put a '0' at the end of the product.

Let's place the '0' first.

And now, let's multiply 413 × 3.

Very good! Pause and review those steps slowly if you need to.

Finally, let's add the two products to get the final answer.

So,

413 × 32 = 13,216 ✅

Nice work. 👏

Example 2

895 × 57 = ?

Let's follow the steps again.

First, let's write the numbers in column form, starting with the bigger number.

Now, let's multiply 895 × 7.

Next, let's place a '0' at the Ones place of the next product. 

Also, let's clear-out all previous carries, to avoid any confusion.

Now, let's multiply 895 × 5.

Lastly, let's add the two products to get the final answer.

So,

895 × 57 = 51,015

Way to go!

Let's Review

Here are the steps one more time:

✅ STEP 1: Write the numbers in column form, one below the other, starting with the bigger number.

✅ STEP 2: Multiply the top factor by the Ones place digit of the bottom factor and write the product.

✅ STEP 3: Put a '0' at the Ones place of the next product. Also, clear-out all previous carries, to avoid confusion.

✅ STEP 4: Multiply the top factor by the Tens place digit of the bottom factor and write the product.

✅ STEP 5: Add the two products together to get the final answer.

Congratulations! 🎉 You now know how to multiply 2-digit numbers by 3-digit numbers.

Now, let's practice.