Division of whole numbers

September 2012. Kindly contributed by Joaquin Llorente, Trafford College. Search for Joaquin on www.skillsworkshop.orgVisit the download page for this resource to find detailed teaching notes, curriculum links and related resources.

Curriculum linksAdult NumeracyN1/E3.6 Divide two-digit whole numbers by single-digit whole numbers and interpret remainders N1/L1.3 Add, subtract, multiply and divide using efficient written and mental methodsN1/L2.2 Carry out calculations with numbers of any size using efficient written and mental methodsand for underpinning Functional MathematicsEntry 3: Solve practical problems involving multiplication and division by 2, 3, 4, 5 and 10. Level 1: Add, subtract, multiply and divide whole numbers using a range of strategies

Understanding Division

N1/E3.6N1/L1.3N1/L2.2

J. Llorente Foundation Learning,Trafford College

Click to advance the slide when you see this symbol

Division of whole numbers

• This presentation covers the basic division of whole numbers

• A gradual series of steps of increased complexity covers the process, from simple divisions to divisions with remainders

• The last few slides use 2 everyday situations as an introduction to interpreting the remainders

Example 1: 69 ÷ 3

• 69 divided by 3?• 69 shared between 3?• How many lots of 3 in 69?• CALCULATOR 69 ÷ 3• SPREADSHEET = 69 / 3 • PEN AND PAPER 3 6

9

69 ÷ 3 ... The set up

T U

3 6 9

1 2 3

69 ÷ 3 ... Sharing the Tens

Each bucket has 2 Tens

There are 2 lots of 3 in 6

3 goes 2 times into 6

T U

3 6 9

1 2 3

2

69 ÷ 3 ... Sharing the Units

Each bucket has 3 Units T U

3 6 9

1 2 3

2 3

There is nothing left over

69 ÷ 3 = 23

Example 2: 75 ÷ 3

• 75 divided by 3?• 75 shared between 3?• How many lots of 3 in 75?• CALCULATOR 75 ÷ 3• PEN AND PAPER• SPREADSHEET =75 / 3

3 75

75 ÷ 3 ... The set up

T U

3 7 5

1 2 3

75 ÷ 3 ... Sharing the Tens

T U

3 7 5

1 2 3

Each bucket has 2 TensThere is 1 Ten left over...

Break down the Ten

into Units

21

75 ÷ 3 ... Sharing the Units

T U

3 7 5

1 2 3

21

Each bucket has 5 Units

5

There is nothing left over

75 ÷ 3 = 25

Example 3: 12 ÷ 4

• 12 divided by 4?• 12 shared between 4?• How many lots of 4 in 12?• CALCULATOR 12 ÷ 4• PEN AND PAPER• SPREADSHEET =12 / 4

4 12

12 ÷ 4 ... The set up

T U

4 1 2

1 2 3 4

12 ÷ 4 ... Sharing the Tens

T U

4 1 2

1 2 3 4

We don’t have enough Tensto put one in each bucket...So there are 0 Tens in each bucket There is 1 Ten left over...

01

Break down the left over Ten into Units

12 ÷ 4 ... Sharing the Units

T U

4 1 2

1 2 3 4

There are 3 Units in each bucket

01

3

There is nothing left over

12 ÷ 4 = 3

Example 4: 208 ÷ 2

• 208 divided by 2?• 208 shared between 2?• How many lots of 2 in 208?• CALCULATOR 208 ÷ 2• PEN AND PAPER• SPREADSHEET =208 / 2

2 208

208 ÷ 2 ... The set up

H T U

2 2 0 8

1 2

208 ÷ 2 ... Sharing the Hundreds

H T U

2 2 0 8

1 2

There is 1 Hundred in each bucket 1

208 ÷ 2 ... Sharing the Tens

H T U

2 2 0 8

1 2

There are no Tens to share ...

1

There are 0 Tens in each bucket

0

We need to write in the 0 to hold the Tens’ place

208 ÷ 2 ... Sharing the Units

H T U

2 2 0 8

1 2

There are 4 Units in each bucket

1 0 4

There is nothing left over

208 ÷ 2 = 104

Checkpoint 1

Try the following divisions:1. 24 ÷ 22. 36 divided by 33. 5 854. How many 4s in 48?5. 99 / 96. 52 ÷ 47. 510 divided by 5

Division with remainders

• All the divisions we have seen so far have no units left over

• Sometimes after doing the division there are some units left over

• These left over units are called the remainder

• The process is the same but, at the end, we write an “r” (for remainder) followed by the number of units left over

Example 5: 67 ÷ 3

• 67 divided by 3?• 67 shared between 3?• How many lots of 3 in 67?• CALCULATOR 67 ÷ 3• SPREADSHEET = 67 / 3 • PEN AND PAPER 3 67

67 ÷ 3 ... The set up

T U

3 6 7

1 2 3

67 ÷ 3 ... Sharing the Tens

Each bucket has 2 Tens

There are 2 lots of 3 in 6

3 goes 2 times into 6

T U

3 6 7

1 2 3

2

67 ÷ 3 ... Sharing the Units

Each bucket has 2 Units T U

3 6 7

1 2 3

2 2

There is one unit left over(remainder 1)

67 ÷ 3 = 22 r1

r1

Checkpoint 2

Try the following divisions:1. 25 ÷ 22. 34 divided by 33. 5 874. How many 4s in 47?5. 91 / 96. 54 ÷ 47. 512 divided by 5

About the remainders

• The meaning and interpretation of the remainder depends on the situation

• Sometimes you need to round up to the next whole number to find the correct answer to a division problem

• Other times, you need to ignore the remainder to find the correct answer

• Whether you do one thing or the other depends on the type of problem

Interpreting remainders18 friends are going to a party

A taxi can take only 4 people

How many taxis do they need?

18 ÷ 4 =4 r2

4 full taxis2 more people waiting… They need another taxi!

1 2 3 4 5

ANSWER: 5 taxis

Interpreting remaindersDVDs cost £7 each You have £19

How many DVDs can you buy?

19 ÷ 7 =2 r5

2 DVDs£5 left over… Not enough for another DVD!

ANSWER: 2 DVDs

Interpreting remainders

• In the first example, we rounded the result to the next whole number to find the answer (5 taxis)

• In the second example we ignored the remainder to find the answer (2 DVDs)

• To find a few more problems on interpreting remainders try the worksheet “Division – Interpreting Remainders”