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

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\div2	Rewrite 6000 as 1000\times 6
	\displaystyle =	\displaystyle 1000\times3	Divide 6 by 2
	\displaystyle =	\displaystyle 3000	Multiply 1000 by 3

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\div2	Rewrite 1000 as 100\times 10
	\displaystyle =	\displaystyle 100\times5	Divide 10 by 2
	\displaystyle =	\displaystyle 500	Multiply 100 by 5

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\div2	Rewrite 120 as 10\times 12
	\displaystyle =	\displaystyle 10\times 6	Divide 12 by 2
	\displaystyle =	\displaystyle 60	Multiply 10 by 6

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

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.

	Thousands	Hundreds	Tens	Ones
	3	0	0	0
		5	0	0
			6	0
+				5
=	3	5	6	5

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:

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\div2	Rewrite 400 as 100\times4
	\displaystyle =	\displaystyle 100\times2	Divide 4 by 2
	\displaystyle =	\displaystyle 200	Multiply 100 by 2

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\div2	Rewrite 60 as 10\times6
	\displaystyle =	\displaystyle 10\times3	Divide 6 by 2
	\displaystyle =	\displaystyle 30	Multiply 10 by 3

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

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 2	Divide by 2
	\displaystyle =	\displaystyle 200+30+2 + 1\div 2	Use the previous results
	\displaystyle =	\displaystyle 232+1\div 2	Add 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.

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

ACMNA101

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

ACMNA291

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

3.06 Dividing of three and four digit numbers

Ideas

Are you ready?

Examples

Example 1

Strategies for division

Examples

Example 2

Division with remainders

Examples

Example 3

Division algorithm with remainders

Examples

Example 4

Outcomes

ACMNA101

ACMNA291

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