Mathematics Short & Long Division

The aim of this powerpoint is to teach you pencil & paper methods for long division. EITHER Take notes as you go along, include some examples and write down any questions and your answers (which you can mark as you go along) OR At the end of the powerpoint, printout the notes called Calc7c

Symbols of Division There are THREE symbols which represent division. For simple division we use: For long division we use: For any division we can use the line in a fraction: or ÷

Review of Simple Division Before moving on to bus-shelter division, you will need to get your head into dividing mode… Work through the MyMaths lesson (and then its online homework) called Sharing found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/sharing&taskID=1391 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/sharingOH&taskID=1391 You may also wish to work through the MyMaths lesson (and then its online homework) called Dividing found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/divisionIntro&taskID=1228 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/divisionIntroOH&taskID=1228

Bus Shelter Division When you are dividing a large number, you will need to use the ‘bus shelter’ division method. Write the first number under the bus shelter Write the divisor (the second number) on the left hand side of the bus shelter. From left to right, divide each digit inside the bus shelter by the number outside. Write the answer on top of the bus shelter and write any remainder in front of the next digit on the right.

Example 1 1 5 6 2 3 What is 780 ÷ 5? 5 7 8 0 Step 1: Write 780 inside the bus shelter Step 2: Write 5 on the left hand side Step 3: Divide each digit inside from left to right so… 7 ÷ 5 = 1 r.2 (Write the 1 above and the 2 in front of the next digit on the right) 28 ÷ 5 = 5 r.3 (Write the 5 above and the 3 in front of the next digit on the right) 30 ÷ 5 = 6 (Write the 6 above)

Longer version In the first example we worked out the remainder in our head. In the longer written method, we can calculate the remainder… and instead of writing it in front of the next digit... we bring the next digit down to be next to it. Watch the next example...

Example 2 1 2 3 What is 738 ÷ 6? 6 7 3 8 6. 1 3 Step 1: Write 738 inside the bus shelter Step 2: Write 6 on the left hand side Step 3: Divide each digit inside from left to right so… 7 ÷ 6 = 1 now write 1 lot of 6 (= 6) underneath and work out the remainder Bring the next digit down to be next to this remainder so we have… 13 ÷ 6 = 2 now write 2 lots of 6 (= 12) underneath and work out the remainder 18 ÷ 6 = 3 now write 3 lots of 6 (= 18) so no remainder 1 2 1 8 1 8

What about Remainders at the end? In both of our previous examples, there was no remainder at the end – the answers were exact. If there is a remainder at the end, we can simply write r. followed by the remainder OR We can express the remainder as a fraction (by writing the remainder over the divisor) We can extend the number we are dividing, and write the decimal point after its units followed by as many zeros as needed, and then continue to divide to get a decimal answer

Example 3 3/8 What is 955 ÷ 8? 1 1 9 . r. 3 3 7 5 1 7 3 6 4 8 9 5 5 . 0 0 0 Step 1: Write 955 inside the bus shelter Step 2: Write 8 on the left hand side Step 3: Divide each digit inside from left to right… At the end either… Quote the remainder after ‘r.’ or… Quote the remainder as a fraction or… Quote the remainder as a decimal

REMEMBER… The divisor may not be a single digit so writing its times table values down the side somewhere will be useful. The answer to an individual division within the overall calculation, can never be bigger than 9. Any of the remainders can be a value up to 1 less than the divisor. Not all things will divide to an exact decimal so if you find yourself adding LOTS of zeros on the end and dividing for a long time, STOP and round your answer to 3 d.p.!

One last example (without the guide) What is 8097 ÷ 23? 23 Times Table.. 1 x 23 = 23 2 x 23 = 46 3 x 23 = 69 4 x 23 = 92 5 x 23 = 115 6 x 23 = 138 7 x 23 = 161 8 x 23 = 184 9 x 23 = 207 3 5 2 . 4 3 4 and so on 8 11 4 1 10 8 11 23 8 0 9 7 . 0 0 0 0 So the final answer is either 352 r. 1 or 352 1/23 or to 3 d.p., the answer is: 352.043

Practice In your book work out the answers to these questions before clicking on to the next slide to check your answers. 1) 428 ÷ 2 = 2) 642 ÷ 3 = 3) 3276 ÷ 9 = 4) 8137 ÷ 5 = 5) 81574 ÷ 25 =

Answers 1) 428 ÷ 2 = 214 2) 642 ÷ 3 = 214 3) 3276 ÷ 9 = 364 4) 8137 ÷ 5 = 1627 r.2 or 1627 2/5 or 1627.4 5) 81574 ÷ 25 = 3262 r.24 or 3262 24/25 or 3262.96 Even though you can mark your own work, your teacher will still need to see your workings!

What next? (Page 1 of 2) If you haven’t made any notes or copied any examples, questions and answers out during this presentation, print out the notes called Calc7c. Read through them and make sure you answer any questions. Work through the MyMaths lesson (and then the online homework) called Division Remainders found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/divisionRemainders&taskID=1022 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/divisionRemaindersOH&taskID=1022 Work through the MyMaths lesson (and then the online homework) called Long Division found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/divisionLong&taskID=1041 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/divisionLongOH&taskID=1041

What next? (Page 2 of 2) Save and complete the worksheet called ShortD-S1.xlsx Save and complete the worksheet called LongD-S1.xlsx Most of you will now move on to Negative Numbers (Calc8 powerpoint) but some of you will be asked to move on to Multiplying and Dividing Decimals (Calc7d powerpoint). Check with the VLE teacher what you should do next.