Division patterns over increasing place values

key notes:

💎Patterns with zero💎

You can also use patterns with zero to divide multiples of 10. Look at the examples below. Compare the number of zeros in the quotient to the number of zeros in the dividend and the divisor. What pattern do you see?

• 8,000 ÷ 2= 4,000
• 8,000 ÷ 20= 400
• 8,000 ÷ 200= 40
• 8,000 ÷ 2,000 = 4

To divide a multiple of 10, follow these steps:

1. Find a division fact to start with.
2. Look at the remaining zeros.
3. Subtract the number of remaining zeros in the divisor from the number of remaining zeros in the dividend. The result tells you how many zeros should be in the quotient.

Look at example 8,000÷200.

First, find a division fact to start with. You can start with 8÷2.

8 ÷ 2 = 4

Now, count the number of remaining zeros.8,000÷200

• There are 3 zeros in 8,000.
• There are 2 zeros in 200.

Subtract the number of zeros. There will be 3–2=1 zero in the quotient.

• 8 ÷ 2 = 4
• 8,000 ÷ 200=40
• So, 8,000 ÷ 200 = 40!

But be careful!

For some problems, you need to be careful with the zero tricks.

Look at example 4,000 ÷ 80. Find a division fact to start with. You can start with 40 ÷ 8.

4,000÷80

40 ÷ 8 = 5

Keep in mind that 40 has a zero in it. Look just at the remaining zeros.

4,000 ÷ 80

Subtract those remaining zeros. There will be 2–1=1 zero in the quotient. Now put it all together.

• 40 ÷ 8 = 5
• 4,000 ÷ 80 = 50
• So, 4,000 ÷ 80 = 50!

✒️Learn with an example✒️

Let’s practice!