Multiplying One-Digit by Three-Digit Numbers

So far, you've learned how to multiply 1-digit numbers by** 2-digit **numbers.

In this lesson, we're going to learn to multiply 1-digit by** 3-digit **numbers. π

It's just like multiplying 2-digit numbers, but with an extra step at the end. π

Here are the steps summed up in one sentence:

When **multiplying **a **1-digit by a 3-digit number**, multiply the 1-digit number with each of the digits in the 3-digit number, starting at the **Ones place**.

So, let's get started.

Let's say you have an equation like this:

310 x 2=?

π The first thing you need to do is to arrange the numbers in **column form.**

It will be easier to multiply the numbers this way.

π **Tip:** Write the **3-digit number at the top,** and the **1-digit number at the bottom.**

π Make sure to **align 2 with 0.** Both digits are in the **Ones place.**

So let's review the steps again:

Whenmultiplyinga 1-digit by a3-digit number,multiply the 1-digit number with each of the digits in the 3-digit number,starting at the Ones place.

**First,** multiply **2 x 0.**

Remember our rule for **multiplying by 0?** π

The answer is always 0.

2 x 0=0

π Let's write **0 **in the **Ones place.**

**Next,** multiply **2 x 1.**

Our rule for **multiplying by 1 **is easy!

The answer is the same number.

2 x 1=2

π Let's write **2 **in the **Tens place.**

**Then,** multiply **2 x 3.**

What's the rule for **multiplying by 3?**

Yes!

Just double the number, then add 1 more group.

2 x 3=6

π We write **6 **in the **Hundreds place.**

So, **310 x 2 ****= ****620****.**

Let's solve another equation.

758 x 4=?

Before we multiply anything, we have to arrange the numbers in **column form **first.

Now, we're ready!Β

**First,** we multiply **4 x 8.**

4 x 8=32

What should we do when we have a 2-digit answer?

π We **carry **the 1st digit over to the **Tens column.**

π **2 **is in the **Ones place,** and we carried **3 **over to the **Tens column.**

π **Tip: **We want to make sure that there's space for the next answer, so we carry **over **digits. It's not "carry under" right? π

What should we do next?

**Next,** we multiply **4 x 5, **and add the **3 **we carried over **after****!**

4 x 5=20

That gives us 20.

Now that we've multiplied, we add the 3 we carried over.

20 + 3=23

π We know that we can't write 23 in the Tens place.

If we do that, then there won't be space for the next answer.

π So, we write the **3 **at the **Tens place,** and we carry **2 **over to the **Hundreds column.**

**Lastly,** we multiply **4 x 7.**

4 x 7=28

... but we carried 2 over to the Hundreds column in the last step.

π So, we have to add that to 28.

28 + 2=30

Because we don't have any other numbers to multiply later, we can write both digits in our answer.

So, **758 x 4 ****= ****3,032****.**

You can jump right into practice now! πͺ

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