The “traditional” algorithm Long Division The “traditional” algorithm

Steps: Divide Multiply Subtract Bring Down Repeat Long Division Steps: Divide Multiply Subtract Bring Down Repeat

2184 DIVIDED BY 24 is what number 24 goes into 2184 how many times? Long Division Example: 2184 ÷ 24 = n Read this properly! 2184 DIVIDED BY 24 is what number or 24 goes into 2184 how many times?

Long Division 2184 ÷ 24 = n Use this symbol for division: Example: 2184 ÷ 24 = n Use this symbol for division: ____ ) Call this symbol a “gazinta” Read this properly! 2184 DIVIDED BY 24 is what number or 24 goes into 2184 how many times? I do not know what it is really called, but “gazinta” works. Try saying it out loud a few times.

24 goes into 2184 how many times? Long Division Example: 2184 ÷ 24 = n Read this properly! 24 goes into 2184 how many times? Use this symbol for division: ____ ) Call this symbol a “gazinta” _______ 24) 2184 24 goes into 2184 n times. n

Long Division: Step 1: DIVIDE _______ 24) 2184 Work the DIVIDEND (2184) from LEFT to right. 24 does not go into 2. 24 does not go into 21. 24 DOES go into 218. How many times does 24 go into 218? 10 x 24 = 240…too much. 9 x 24 = 216. This works.

Long Division Step 2: Multiply _______ 24) 2184 9 216 2 9 x 24 = 216. 1. Place a 9 over the 8 (because 24 will go into 218.) 2. Place a 216 under the 218 (because 9 x 24 = 216) Step 3: Subtract 3. Write a 2 under the 6 (because 218 – 216 = 2) Mathematical note: This is actually PARTIAL DIVISION. We are actually dividing 2184 by 24 and getting 90. 90 x 24 = 2160. We write it in this manner so that we may continue with the next step.

Long Division: Step 4: Bring Down 24 1 9 _______ 24) 2184 9 x 24 = 216. 4 216 2 4. Bring down the next digit (4). Write it next to the 2 on the bottom line. 5. Repeat the entire process, only now, do 24 divided by 24 (which = 1). Write the 1 over the 4 in the answer. Multiply 24 x 1 to get 24. Then subtract: 24 – 24 = 0.

24) 2184 Long Division 9 1 _______ 24 x 91 2160 2184 + 216 2 2184 ÷ 24=91 Check your answer by multiplying. 24 x 91 2160 2184 _______ 24) 2184 9 216 2 24 1 +

Long Division NOTES: If there is a remainder, you can: Write it as a fraction with Continue the dividend with .000… etc. for as long as necessary. Use the remainder, when appropriate. remainder divisor

Long Division Try this: 36) 3132 36 goes into 3 zero times 36 x 9 = 324…too big. 36 x 8 = 288. So 36 goes into 313 8 times. 313 - 288= 25. Bring down the 2. 36 goes into 252 seven times. Since 7 x 36 = 252, there is no remainder. Try this: 36) 3132 2 9 288 8 252 25 7

Long Division Check: 87 x 36 = 8 7 x 3 6 6 x 7 = 4 2 6 x 80 = 4 8 0 3 1 3 2 This proves that 3132 divided by 36 = 87.

Long Division a b ) b a Tricks: All division problems can be written as fraction problems: a ÷ b = = a b ) b a This means that all fraction rules apply to division problems. This means that you can REDUCE division problems as if they were fractions!

Long Division This means that all fraction rules apply to division problems. This means that you can REDUCE division problems as if they were fractions! So: 3132 ÷ 36= (divide both by 2) becomes 1566 ÷ 18= (divide both by 2) which becomes 783 ÷ 9 = (divide both by 3) which becomes 261 ÷ 3 = 87

Long Division ÷ ÷ ÷ So: 3132 ÷ 36= (divide both by 2) becomes 1566 ÷ 18= (divide both by 2) which becomes 783 ÷ 9 = (divide both by 3) which becomes 261 ÷ 3 = 87 3132 36 2 ÷ 2 1566 18 = 783 9 ÷ = 783 9 = ÷ 3 261 3 = 87

Long Division Extra Practice: 76 ÷ 3 = 11562 ÷ 47 = 342 ÷ 24 =

Long Division Extra Practice: 76 ÷ 3 = 25.333… or 25 11562 ÷ 47 = 246 342 ÷ 24 = 14.25 1 3

Additional Resources http://www.mathsisfun.com/long_division.html http://www.coolmath4kids.com/long-division/long-division- lesson-1.html http://www.mathplayground.com/howto_longdivision.html http://www.ehow.com/video_4991171_long-division.html http://www.youtube.com/watch?v=3ULXhiJqlPs http://www.youtube.com/watch?v=8OpsFZqH2ew Math comedy sketch: http://www.youtube.com/watch?v=oti7DJ9P24M