Factors are the numbers you multiply together to get a product.
So far, you've learned about addition patterns across place values and subtraction patterns too.
Do you remember what patterns are?
Patterns are the way that numbers or things are arranged based on a rule. They help us predict what comes next.
Most of the time, we think of patterns in designs like fabrics. 🎨
But as we've seen in earlier lessons, we also see patterns in math. 😀
In this lesson, we're going to explore multiplication patterns across increasing place values.
Let's look at this example:
What did you notice? 🧐
Yes! The digits used (3, 2, and 6) are the same in each equation.
First, we see 3 × 2 = 6.
If we add one zero at the end of 3, we also add one zero to the product.
In the third row, we add two zeros at the end of 3.
We can predict the answer will be 600, because we know we can just add two zeros to the 6.
What do you think the product is when you multiply 3,000 by 2?
That's right! It's 6,000! 👍
If we extend this pattern further to 30,000 × 2, can you guess what the answer is?
Yes! It is 60,000. 👍
We just used the pattern to help us multiply a huge number! 😀
What's the rule of this pattern?
When you add a zero to one of the factors, you also add a zero to the product.
Let's make our own multiplication pattern.
We start the pattern with 6 × 4 = 24.
Can you use this to figure out 60 × 4? 🤔
Since we've added one zero to one of the factors, we just add one zero to the product as well.
60 × 4 = 240
So far, this is what our pattern looks like:
6 × 4 = 24
60 × 4 = 240
Let's keep going by adding two zeros after 6. 👇
600 × 4 = ?
Just by following the rule of the pattern, can you guess the answer? 🤔
Fantastic! It's 2,400.
Just add two zeros after 24 to get the answer.
600 × 4 = 2,400
Let's grow the pattern even more.
Add 3 zeros to 6.
6,000 × 4 = ?
What do you think is the answer?
Awesome! It's 24,000!
6,000 × 4 = 24,000
What is 60,000 × 4? 🤔
Correct! It's 240,000.
Factors can end with lots of zeros.
Numbers that end in 0 are called multiples of 10.
Take a look. 👇
What's the product of 6,000 × 400?
How many zeros are there in the factors?
There are 3 zeros in 6,000 and 2 zeros in 400.
There are 5 zeros in total.
To find the answer, we can just add five zeros at the end of the product of 6 and 4.
6 × 4 = 24
If we add five zeros at the end of 24, we get 2,400,000.
6,000 × 400 = 2,400,000
Why does this work? 🤔
Because you're really doing this math. 👇 🧙♂️
6,000 × 400 =
6 × 1,000 × 4 × 100 =
6 × 4 × 1,000 × 100 =
6 × 4 × 100,000 =
Tip: If you don't understand this yet 👆, don't worry about it. You'll learn more in a later lesson.
Excellent work! 👏
Now, ace the practice.