# 4.03 Modelling division

Lesson

## Ideas

There are some great  strategies for division  , that we've used for smaller numbers, up to 3 digits long. How many can you remember?

### Examples

#### Example 1

Find 769\div3 by doing the following:

a

Find 600\div 3.

Worked Solution
Create a strategy

Write 600 as a multiple of 100.

Apply the idea
b

Find 150\div3.

Worked Solution
Create a strategy

Write 150 as a multiple of 10.

Apply the idea
c

Find 18\div3.

Worked Solution
Create a strategy

Rewrite the division as a multiplication.

Apply the idea

18\div3 can be written as 3 \times ⬚ =18. Since 3\times 6 = 18:

18\div3=6

d

Using the fact that 769=600+150+18+1, complete the statement with the missing numbers:

3 goes into seven hundred sixty nine times with a remainder of .

Worked Solution
Create a strategy

Divide both sides of the number sentence by 3.

Apply the idea

Since we can't divide 1 by 3, \,\,\, 1 must be the remainder. So:

3 goes into seven hundred sixty nine 256 times with a remainder of 1.

Idea summary

The part of a number that cannot be divided into equal groups is called the remainder.

## Division review of half and half again

Dividing by one number can often help us when we need to divide by a different number, as we see here.

### Examples

#### Example 2

Find the value of 40\div4.

Worked Solution
Create a strategy

We halve both numbers to make it easier to divide the numbers.

Apply the idea

Divide each number by 2.

40\div 2 = 20

4\div 2 = 2

By the half and half again method we can use these results in our division.

Idea summary

To make a division easier, we can divide both numbers by 2.

We can also think of dividing by 4 as dividing by 2 twice.

## Division review in other methods

Dividing by other digits means we can use things like partitioning or the area model to help us.

### Examples

#### Example 3

Let's use an area model to find the answer to 133\div 7.

a

We set up the area model using a rectangle like this:

Now if we don't know straight away what 133\div 7 is, we start with something we do know, like groups of 10.

Find the area used so far if we take out 10 groups of 7.

Worked Solution
Create a strategy

"Groups of" means multiply.

Apply the idea

10 groups of 7 can also be written as: 10\times 7.

b

How much area is remaining?

Worked Solution
Create a strategy

The area remaining is the area of the left rectangle. Subtract the area found in part (a) from the total area of the rectangle.

Apply the idea

The remaining area is 63.

c

What is the width of the second rectangle?

Worked Solution
Create a strategy

Use the area of the rectangle found in part (b).

Apply the idea

We know that the area of the second rectangle is 63 and the height is 7. So the width will be the area divided by the height, or 63\div7.

The width of the second rectangle is 9.

d

Using the area model above, what is 133\div7?

Worked Solution
Create a strategy

133\div7 is the total width of the rectangle in part (c). So we need to add the widths.

Apply the idea

133\div7=19

Idea summary