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Long Division

Long Division. The “ traditional ” algorithm. Long Division. Steps: Divide Multiply Subtract Bring Down Repeat. 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. Example:

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Long Division

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  1. Long Division The “traditional” algorithm

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

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

  4. Long 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.

  5. _______ 24) 2184 24 goes into 2184 n times. n 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”

  6. 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.

  7. 9 _______ 24) 2184 216 2 Long Division Step 2: Multiply 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.

  8. 1 24 0 2 Long Division: Step 4: Bring Down 9 _______ 24) 2184 9 x 24 = 216. 4 216 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.

  9. 9 _______ 24) 2184 1 216 24 0 2 Long Division 2184 ÷ 24=91 Check your answer by multiplying. 24 x 91 24 2160 2184 +

  10. remainder divisor 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.

  11. 252 0 Long Division 2 0 • 36 goes into 3 zero times • 36 goes into 31 zero times • 36 goes into 313…. • 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 0 2 9 288 8 25 7

  12. Long Division Check: 87 x 36 = 8 7 x 3 6 6 x 7 = 4 2 6 x 80 = 4 8 0 30 x 7 = 2 1 0 30 x 80 = 2 4 0 0 3 1 3 2 This proves that 3132 divided by 36 = 87.

  13. a a b b Long Division Tricks: All division problems can be written as fraction problems: 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!

  14. 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

  15. 3132 36 2 2 1566 18 2 2 783 9 = ÷ 3 3 261 3 783 9 ÷ = = 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 ÷ =

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

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

  18. 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

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