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Division of whole numbers September 2012. Kindly contributed by Joaquin Llorente, Trafford College. Search for Joaquin on www.skillsworkshop.org Visit the download page for this resource to find detailed teaching notes, curriculum links and related resources. Curriculum links Adult Numeracy N1/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 methods N1/L2.2 Carry out calculations with numbers of any size using efficient written and mental methods and for underpinning Functional Mathematics Entry 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 Click to advance the slide when you see this symbol Understanding Division N1/E3.6 N1/L1.3 N1/L2.2 J. Llorente Foundation Learning, Trafford College 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 3 69 PEN AND PAPER 69 ÷ 3 ... The set up 3 1 2 3 T U 6 9 69 ÷ 3 ... Sharing the Tens Each bucket has 2 Tens 3 T 2 6 U 9 There are 2 lots of 3 in 6 3 goes 2 times into 6 1 2 3 69 ÷ 3 ... Sharing the Units Each bucket has 3 Units 3 T 2 6 U 3 9 There is nothing left over 69 ÷ 3 = 23 1 2 3 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 3 75 SPREADSHEET =75 / 3 75 ÷ 3 ... The set up 3 1 2 3 T U 7 5 75 ÷ 3 ... Sharing the Tens Each bucket has 2 Tens There is 1 Ten left over... 3 1 2 3 T 2 7 U 1 5 Break down the Ten into Units 75 ÷ 3 ... Sharing the Units Each bucket has 5 Units 3 T 2 7 1 U 5 5 There is nothing left over 75 ÷ 3 = 25 1 2 3 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 4 12 SPREADSHEET =12 / 4 12 ÷ 4 ... The set up 4 1 2 3 4 T U 1 2 12 ÷ 4 ... Sharing the Tens So Wethere don’t are have 0 enough Tens in Tens each bucket T to put one each bucket... There is 1inTen left over... 4 1 2 3 4 0 1 U 1 2 Break down the left over Ten into Units 12 ÷ 4 ... Sharing the Units There are 3 Units in each bucket 4 T 0 1 U 3 1 2 There is nothing left over 12 ÷ 4 = 3 1 2 3 4 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 2 208 SPREADSHEET =208 / 2 208 ÷ 2 ... The set up 2 1 2 H T U 2 0 8 208 ÷ 2 ... Sharing the Hundreds There is 1 Hundred in each bucket 2 1 2 H 1 2 T U 0 8 208 ÷ 2 ... Sharing the Tens There are 0 noTens Tensin to share each bucket ... 2 H 1 2 T 0 0 U 8 We need to write in the 0 to hold the Tens’ place 1 2 208 ÷ 2 ... Sharing the Units There are 4 Units in each bucket 2 H 1 2 T 0 0 U 4 8 There is nothing left over 208 ÷ 2 = 104 1 2 Checkpoint 1 Try the following divisions: 1. 2. 3. 4. 5. 6. 7. 24 ÷ 2 36 divided by 3 5 85 How many 4s in 48? 99 / 9 52 ÷ 4 510 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 3 67 PEN AND PAPER 67 ÷ 3 ... The set up 3 1 2 3 T U 6 7 67 ÷ 3 ... Sharing the Tens Each bucket has 2 Tens 3 T 2 6 U 7 There are 2 lots of 3 in 6 3 goes 2 times into 6 1 2 3 67 ÷ 3 ... Sharing the Units Each bucket has 2 Units 3 T 2 6 U 2 7 r1 There is one unit left over (remainder 1) 67 ÷ 3 = 22 r1 1 2 3 Checkpoint 2 Try the following divisions: 1. 2. 3. 4. 5. 6. 7. 25 ÷ 2 34 divided by 3 5 87 How many 4s in 47? 91 / 9 54 ÷ 4 512 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 remainders 18 friends are going to a party A taxi can take only 4 people How many taxis do they need? 18 ÷ 4 = 4 r2 ANSWER: 5 taxis 4 full taxis 2 more people waiting… They need another taxi! 1 2 3 4 5 Interpreting remainders DVDs cost £7 each You have £19 How many DVDs can you buy? 19 ÷ 7 = 2 r5 ANSWER: 2 DVDs 2 DVDs £5 left over… Not enough for another DVD! 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”