Mathematics Long Multiplication

The aim of this powerpoint is to teach you pencil & paper methods for multiplying large numbers together. 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 Calc6b

Traditional Method Write the largest value on the top and the smallest value underneath; Working from right to left, multiply each of the digits in the top number by the ‘UNITS’ digit of the number below; If any product comes to more than 10, carry the tens value into the next column and add it on to the next product. Now repeat the above, working from right to left, multiply each of the digits in the top number by the ‘TENS’ digit of the number below (remembering to put a ZERO in the units column first) Put the answer to this below the one to the units column answer. Repeat the above multiplying by the ‘HUNDREDS’ digit (if applicable) – remembering to put a ZERO in the units and tens columns first, and write the answer below the two previous ones. Now add all the units, tens and hundreds products together for the final answer!

Example 1 23 × 1674 1 6 7 4 × 2 3 + Step 1: Write 1674 on top × 2 3 + Step 1: Write 1674 on top Write 23 underneath it Line up numbers in the correct column values, i.e. from right to left Because 23 has 2 digits there will be 2 products to add together for the final answer so 2 working lines and an answer line are needed.

Example 1 23 × 1674 1 6 7 4 × 2 3 + 5 2 2 Step 2: From right to left multiply each top digit (4 then 7 then 6 then 1) by the 3 2 2 1

Example 1 23 × 1674 1 6 7 4 × 2 3 + 5 0 2 2 Step 3: From right to left multiply each top digit (4 then 7 then 6 then 1) by the 2 3 3 4 8 1 1 Remember the 2 in 23 is worth 2 tens so your answer to this will end in zero!

Example 1 23 × 1674 1 6 7 4 × 2 3 + 5 0 2 2 Step 4: Now add both products together for the final answer 3 3 4 8 0 3 8 5 2 1 Mental Check: The answer should be around 20 x 2,000 = 40,000

Grid / Area Method Draw a grid… number of columns = number of digits in one of the numbers; number of rows = number of digits in the other number; Partition each number separating the hundreds, tens, units etc. and write these above each column and on the left hand side of each row; Fill-in the products of the resultant multiplication grid; Add all the values inside the grid to find your answer.

Example 2 71 × 358 (Split 71 into 70 + 1 & Split 358 into 300 + 50 + 8) × 300 50 8 70 21000 3500 560  25060 1 300 50 8  358 25418 1 + Mental check: The answer should be around 70 × 400 = 28000

Gelosia Method Draw a grid… number of columns = number of digits in one of the numbers number of rows = number of digits in the other number Draw UPHILL diagonal lines (bottom left to top right) in every square of the grid. Write the ‘column’ number across the top (1 digit above each column) and the ‘row’ number down the right hand side. Multiply each pair of digits together putting the tens value in the right half and the units value in the left half of each square of the grid Once the grid is completely filled in, add down the diagonals to get the final answer (see example on next slide).

Example 3 203 × 45 2 2 3 3 × 1 4 4 8 2 1 1 5 5 5

Example 3 203 × 45 2 3 × 1 4 8 2 1 1 5 5 Mental Check: The answer should be about 200 x 50 = 10,000 9 1 3 5

Practice Showing all your workings in your books (using whichever method you prefer), work out the answers to the following calculations, and after each, show what mental calculation you used to check your answer! 1) 57 × 16 = 2) 35 × 84 = 3) 142 × 39 = 4) 45 × 206 = 5) 318 × 422 = When you have worked out your answers, move on to the next slide and mark your work.

Answers 5 7 x 1 6 3 4 2 5 7 0 9 1 2 1 1) 57 × 16 = 912 (Check: It will be less than 60 x 20 = 1200)   2) 35 × 84 = 2940 (Check: It will be about 40 x 80 = 3200) 3) 142 × 39 = 5538 (Check : It will be around 100 x 40 = 4,000) 4) 45 × 206 = 9270 (Check : It will be around 50 x 200 = 10,000) 5) 318 × 422 = 134196 (Check : It will be more than 300 x 400 = 120,000) x 100 40 2 30 3000 1200 60 9 900 360 18 4260 + 1278 = 5538 3 1 8 x 1 2 0 4 3 2 4 0 6 0 2 1 6 2 ________________________ 1 3 4 1 9 6 1

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 Calc6b. Read through them and make sure you answer any questions. Work through the MyMaths lesson (and then the online homework) called Multiply Double Digits found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiply2&taskID=1025 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiply2OH&taskID=1025 Continued on next slide

What next? (Page 2 of 2) Work through the MyMaths lesson (and then the online homework) called Multiply Triple Digits found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=numbops/multiply3&taskID=1026 http://www.mymaths.co.uk/tasks/library/loadTask.asp?title=numbops/multiply3OH&taskID=1026 Save and complete the worksheet called LongM-S1.xlsx Now move on to the Calc7c-LongD powerpoint