Topics
3. Multiplication and division
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AustraliaNSW
Stage 3

3.07 Dividing of three and four digit numbers

Lesson
Practice
Lesson

Are you ready?

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.

\displaystyle 78\div 6\displaystyle =\displaystyle 60\div6+18\div6Divide each part by 6
\displaystyle =\displaystyle 10+3Find the divisions
\displaystyle =\displaystyle 13Add 10 and 3
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.

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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
\displaystyle 6000\div2\displaystyle =\displaystyle 1000\times6\div2Rewrite 6000 as 1000\times 6
\displaystyle =\displaystyle 1000\times3Divide 6 by 2
\displaystyle =\displaystyle 3000Multiply 1000 by 3
b

Find 1000\div2.

Worked Solution
Create a strategy

Write 1000 as a multiple of 100.

Apply the idea
\displaystyle 1000\div2\displaystyle =\displaystyle 100\times10\div2Rewrite 1000 as 100\times 10
\displaystyle =\displaystyle 100\times5Divide 10 by 2
\displaystyle =\displaystyle 500Multiply 100 by 5
c

Find 120\div2.

Worked Solution
Create a strategy

Write 120 as a multiple of 10.

Apply the idea
\displaystyle 120\div2\displaystyle =\displaystyle 10\times12\div2Rewrite 120 as 10\times 12
\displaystyle =\displaystyle 10\times 6Divide 12 by 2
\displaystyle =\displaystyle 60Multiply 10 by 6
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

Add the answers found in the previous parts.

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.

ThousandsHundredsTensOnes
3000
500
60
+ 5
=3565

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.

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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
\displaystyle 400\div 2\displaystyle =\displaystyle 100\times4\div2Rewrite 400 as 100\times4
\displaystyle =\displaystyle 100\times2Divide 4 by 2
\displaystyle =\displaystyle 200Multiply 100 by 2
b

Find 60\div2

Worked Solution
Create a strategy

Write 60 as a multiple of 10.

Apply the idea
\displaystyle 60\div2\displaystyle =\displaystyle 10\times6\div2Rewrite 60 as 10\times6
\displaystyle =\displaystyle 10\times3Divide 6 by 2
\displaystyle =\displaystyle 30Multiply 10 by 3
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
\displaystyle 465 \div 2 \displaystyle =\displaystyle 400 \div 2 +60\div 2+4\div 2+1\div 2Divide by 2
\displaystyle =\displaystyle 200+30+2 + 1\div 2Use the previous results
\displaystyle =\displaystyle 232+1\div 2Add the whole numbers

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.

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Examples

Example 4

Find the value of 1145\div 6.

Worked Solution
Create a strategy

Use the division algorithm.

Apply the idea
1145 divided by 6 in a short division algorithm. Ask your teacher for more information.

Set up the algorithm.

1145 divided by 6 in a short division algorithm. Ask your teacher for more information.

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.

1145 divided by 6 in a short division algorithm. Ask your teacher for more information.

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.

1145 divided by 6 in a short division algorithm. Ask your teacher for more information.

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

1145 divided by 6 in a short division algorithm. Ask your teacher for more information.

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

MA3-5NA

selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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