Multiplication Patterns Across Place Values

Look at these equations.

1

10

100

1,000

Do you think they follow a certain **pattern****?**

Yes, they do! π

We've discovered many different patterns in multiplication.

In this lesson, we're going to explore how patterns help us easily multiply large numbers. π

Let's take a look at these equations.

10 x 6=?100 x 6=?1,000 x 6=?

Did you notice these? πΒ

- They are all multiplied by 6.
- All the numbers multiplied by 6 begin with 1.
- The number of zeros increase by 1 in each equation. This means that the place value of number 1 increases in each equation.
- In the 1st equation, the value of 1 is
**1 Ten.**

10

- In the 2nd equation, the value of 1 is
**1 Hundred.**

100

- In the 3rd equation, the value of 1 is
**1 Thousand.**

1,000

π Now, let's figure out the answer to the **1st equation.** π

What is 10 x 6?

If we think about our observation,Β

10 x 6 = 1 Ten x 6

π So, we know that:

1 Ten x 6=6 Tens

10 x 6=60

Now, let's figure out the answer to the **2nd equation.**

100 x 6=?

What can we do to get our answer?

We think of it as:

1 hundred x 6=6 Hundreds

100 x 6=600

π Did you see how **a zero was added **from the answer of the 1st equation?

As the place value of the number that's being multiplied increases, the number of zeros also increase.

Have you figured out the answer to the **3rd equation**?

Nice work! π

The third equation should look like this:

1 thousand x 6=6 Thousands

1000 x 6=6000

Now, our pattern is complete.Β

10 x 6=60100 x 6=6001,000 x 6=6,000

See how easy it is to multiply large numbers? π

Let's try another example.

3 x 7=?3 x 70=?3 x 700=?3 x 7,000=?

Can you complete the pattern?

First, you have to figure out the** rule for the pattern** by looking at the first equation.

π What is **3 x 7?**

Correct! π

It's 21!

π To figure out the missing numbers in the next equation, we justincrease the valueof the digits 2 and 1by adding zeros.

Now, let's complete the pattern!

3 x 7=213 x 70=2103 x 700=2,1003 x 7,000=21,000

π The increase in place value means an increase in the number of zeros.

Whencompleting patterns in multiplication,always look for the rule based on the place values of the numbers.

πGreat job!

Now, you can move on to practice! πͺ

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