Multiplication and Division
NZ Level 3
topic badge
Divide a 4 digit number by a 1 digit number

Partitioning and renaming digits

When we want to divide a large number, such as 4402 (a four digit number) by a single digit number, such as 4, there are some techniques that can help us.   We've explored some of these with smaller two and three digit numbers, so you may wish to have a look at those topics first.

In the first video, we look at partitioning, or breaking our number into chunks, to work on smaller problems, then add our answers together at the end.


The long division algorithm

If you find long division tricky, then watching the next video might help you see it is actually a series of steps.  By working through each step, the problem becomes more manageable, and it turns out we are performing a series of smaller divisions.  The main tool we use here is renaming, when we are unable to share.   As an example, 600 can be renamed as 60 tens.

Take a look, and see how these steps are the same as what you have already been doing.  


Partitioning ,- or breaking your number into smaller chunks - can help with division of larger numbers

Renaming digits can help to divide (share) numbers


Question 1

Calculate $4000\div2$4000÷​2 by doing the following.

  1. $4\div2$4÷​2

  2. $40\div2$40÷​2

  3. $400\div2$400÷​2

  4. $4000\div2$4000÷​2

Question 2

We're going to break $7130$7130 into $6000+1000+120+10$6000+1000+120+10 to calculate $7130\div2$7130÷​2.

Follow these steps.

  1. Calculate $6000\div2$6000÷​2.

  2. Calculate $1000\div2$1000÷​2.

  3. Calculate $120\div2$120÷​2.

  4. Calculate $10\div2$10÷​2.

  5. Using the fact that $7130=6000+1000+120+10$7130=6000+1000+120+10, calculate $7130\div2$7130÷​2.

Question 3

Evaluate $1477\div7$1477÷​7.



Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality

What is Mathspace

About Mathspace