Add Multiples of 10 and 100

There are secret tricks for adding multiples of 100 and multiples of 10 quickly.π

Do you want to know the tricks?

I'm sure you do! π

But first, let's review.

What numbers are **multiples of 10?**

They're numbers that **end with a zero**. They're made up of Tens.

Here are some examples:

10, 20, 30, 50, 90, 140, 270, 380, 460, 570

What about **multiples of 100?**

They're numbers that **end with two zeros**. They're made up of Hundreds.

Are these multiples of 100?

100, 200, 300, 400, 500, 600, 700, 800, 900

Yes! Because they all end in two zeros.

How do you add a multiple of 10 to a multiple of 100?

Let's try adding these:

400 + 70 = ?

π Let's add it the long way before we learn the secret trick.

π We write the numbers in **column form **before adding.

Write the 3-digit number at the top, and the 2-digit number at the bottom.Β

Make sure to **align the columns **correctly.Β

Important Tip: The Tens should be aligned with the Tens, and the Ones with the Ones. Write 7 under 0 in the Tens place, not under 4. π

Now, we can start adding.

**First,** we add the **Ones.**

What's 0 + 0? That's right. It's 0.

Write 0 in the Ones place.

**Next,** we add the **Tens.**

What is 0 + 7?

Remember the rule about adding zero?

When we **add zero to a number**, nothing changes. The answer is still the same number.Β

So, our answer is 7!

We'll write 7 in the Tens place.

**Finally,** we add the **Hundreds.**Β

π There's nothing below 4, so we just bring it down.

So, 400 + 70 = **470**.

π Here's a **secret trick **for adding a multiple of 100 and a 2-digit multiple of 10.Β

π First, write the Hundreds digit of the first addend.

The digit in the Hundreds place of 400 is 4.Β

4____

Then, write the Tens and Ones digits of the second addend after it.

If we write 70 after 4, we get 470.

470

Wasn't that quick and easy? π

How about we add two multiples of 10?

270 + 310 = ?

π 270 and 310 are multiples of 10 because they end in zero.

There's **no secret trick** for adding these numbers.

But there are two ways to solve this.

The first one is how we usually add numbers.Β

π We write the numbers in **column form.**

Then, we start adding.

**First,** we add the **Ones.**

They're both zeros. So, we know that their sum is zero.

Let's write zero in the Ones place.

**Next,** we add the **Tens.**

What is 7 + 1?

Remember the rule about adding 1?

We just count up 1 from 7. We get 8!

Write 8 in the Tens place.

**Finally,** we add the **Hundreds.**

When we add 2 and 3, we get 5.

Write 5 in the Hundreds place.

So, 270 + 310 = **580.**

π Another way to solve this is by **expanding the numbers.**Β

**Expanding a number** means to show the value of each digit.

Now, we add the values.Β

π First, we add the Hundreds.Β

200 + 300 is 500.

Do you remember the trick about adding multiples of 100?

π Ignore the Tens and Ones, and just add the Hundreds.

Add two zeros after your answer.

It's easy, right? π

π Next, we add the Tens.

70 + 10 is 80.

Do you know the trick for adding 2-digit multiples of 10!

You guessed it right!

Just add the Tens and write a zero after the answer.

7 + 1 is 8.Β

If we write a zero after 8, we get 80.

π Lastly, add the Ones.Β

There's nothing to add here because they're both zeros. Our answer is 0.

Let's put all our answers together, and we get 580.

Try the practice exercises now. π

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