 # 3.06 Dividing of three and four digit numbers

Lesson

Do you recall how we were able to  divide numbers with one or two digits  ?

### Examples

#### Example 1

Find the value of 78\div 6.

Worked Solution
Create a strategy

We can partition 78 to make it easier to divide by 6.

Apply the idea

Split 78 into two numbers that are both divisible by 6.

78 = 60 + 18

Now we can divide each part of the partition by 6.

Idea summary

We can divide large numbers by partitioning the number, and then dividing each part of the partition.

## Strategies for division

How can we work with larger numbers to solve division problems? Let's take a look in this video, when we are sharing equally.

### Examples

#### Example 2

We're going to break 7130 into 6000+1000+120+10 to find 7130\div 2. Follow these steps:

a

Find 6000\div 2.

Worked Solution
Create a strategy

Write 6000 as a multiple of 1000.

Apply the idea
b

Find 1000\div2.

Worked Solution
Create a strategy

Write 1000 as a multiple of 100.

Apply the idea
c

Find 120\div2.

Worked Solution
Create a strategy

Write 120 as a multiple of 10.

Apply the idea
d

Find 10\div 2.

Worked Solution
Create a strategy

Rewrite the division as a multiplication.

Apply the idea

10\div2 can be written as 2\times⬚=10.

2\times 5=10

So:10\div2=5

e

Using the fact that 7130=6000+1000+120+10, calculate 7130 \div 2.

Worked Solution
Create a strategy

Apply the idea

The answer will be equal to the sum of the answers of the previous parts.\begin{aligned} 7130\div2 &= 6000 \div 2+1000 \div 2+120 \div 2+10 \div 2 \\ &=3000+500+60+5 \end{aligned}

Write the numbers in a place value table and add the values in each column.

7130\div2=3565

Idea summary

We can break up a number into multiples of the number that we are dividing by to make the division easier.

## Division with remainders

If we can't share our total out equally, we end up with a remainder, as we see in this video.

### Examples

#### Example 3

Find 465\div2 by doing the following:

a

Find 400\div2.

Worked Solution
Create a strategy

Write 400 as a multiple of 100.

Apply the idea
b

Find 60\div2

Worked Solution
Create a strategy

Write 60 as a multiple of 10.

Apply the idea
c

Find 4\div2.

Worked Solution
Create a strategy

Rewrite the division as a multiplication.

Apply the idea

4\div2 can be written as 2 \times ⬚ =4. Since 2\times 2 = 4:

4\div 2 = 2

d

Using the fact that 465=400+60+4+1, complete the statement with the missing numbers:

2 goes into four hundred sixty five times with a remainder of .

Worked Solution
Create a strategy

Divide both sides of the number sentence by 2.

Apply the idea

Since we can't divide 1 by 2, \,\, 1 must be the remainder. So:

2 goes into four hundred sixty five 232 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 algorithm with remainders

We can use a short division algorithm to solve division problems, especially with larger numbers. Let's see how we also take care of the remainder in this video.

### Examples

#### Example 4

Find the value of 1145\div 6.

Worked Solution
Create a strategy

Use the division algorithm.

Apply the idea

Set up the algorithm.

6 goes into 1 zero times with 1 remaining, so we put a 0 in the thousands column and carry the 1 to the hundreds column.

6 goes into 11 one time with 5 remaining, so we put a 1 in the hundreds column and carry the 5 to the tens column.

6 goes into 54 nine times, so we put a 9 in the tens column.

6 goes into 5 zero times with 5 remaining, so we put a 0 in the units column and the remainder is 5.

1145\div6=190 remainder 5.

Idea summary

As our number gets larger, we need to work through more steps in our division, but the process is still the same. If we can't share into equal groups, we end up with a remainder.

### Outcomes

#### VCMNA184

Solve problems involving division by a one digit number, including those that result in a remainder

#### VCMNA185

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems