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# Long Division

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1. Long Division by One-Digit Numbers

2. ) 5 36,987 What is this problem asking us? If we divided 36,987 into 5groups of equal size, how many would be in each group?

3. ) 5 36,987 Real Life Example If Janice has5 years to repay a small business loan for\$36,987, how much will she need to pay each year?

4. ) 5 36,987 divisor How do we solve it? • 5 is our divisor • Look at the first number and ask how many 5’s are in 3 • There are none, so we ask how many 5’s are in 36

5. ) 5 36,987 • How many 5’s are in 36? • Recall your multiplication facts to find the one that will give an answer near 36. • 5 x 7 = 35

6. ) 5 36,987 • 5 x 7 = 35 7 35 • Place the 7 above the division bar • Subtract 35 from 36 • Bring down the next digit in the dividend 9 1 • Now ask how many 5’s are in 19

7. ) 5 36,987 • 5 x 3 = 15 7 3 • Place the 3 above the division bar • Subtract 15 from 19 • Bring down the next digit in the dividend 35 9 1 15 4 8 • Now we ask how many 5’s are in 48

8. ) 5 36,987 • 5 x 9 = 45 7 3 9 • Place the 9 above the division bar • Subtract 45 from 48 • Bring down the next digit in the dividend 35 1 9 15 48 45 • Now we ask how many 5’s are in 37 3 7

9. ) 5 36,987 remainder 7 3 9 7 • Place the 7 above the division bar • Subtract 35 from 37 • There are no more numbers to bring down • The remainder is 2, which means 2 are left over • The quotient or answer to our problem is 7,397 with a remainder of 2 35 1 9 15 48 45 5 x 7 = 35 3 7 35 2

10. ) 5 36,987 Our Real Life Example 7,397 about If Janice has5 years to repay a small business loan for\$36,987, how much will she need to pay each year?

11. ) 6 8,437 What is this problem asking us? If we divided 8,437 into 6groups of equal size, how many would be in each group?

12. ) 6 8,437 Real Life Example Can you think of a word problem that can be expressed as the division problem written above?

13. ) 6 8,437 divisor How do we solve it? • 6 is our divisor • Look at the first number and ask how many 6’s are in 8 • There is one, so we multiply and begin to work through the steps to solve the problem.

14. ) 6 8,437 1 • 6 x 1 = 6 • Place the 1 above the division bar • Subtract 6 from 8 • Bring down the next digit in the dividend 6 4 2 • Now ask how many6’s are in 24

15. ) 6 8,437 1 4 • 6 x 4 = 24 • Place the 4 above the division bar • Subtract 24 from 24 • Bring down the next digit in the dividend 6 24 24 0 3 • Now ask how many6’s are in 3

16. ) 6 8,437 1 4 0 • 6 x 0 = 0 • Place the 0 above the division bar • Subtract 0 from 3 • Bring down the next digit in the dividend 6 24 24 3 0 0 • Now ask how many6’s are in 37 3 7

17. ) 6 8,437 remainder 1 4 0 6 • 6 x 6 = 36 • Place the 6 above the division bar • Subtract 36 from 37 • There are no more numbers to bring down • The remainder is 1, which means there is one left over • The quotient or answer to our problem is 1,406 with a remainder of 2 6 24 24 3 0 0 7 3 36 1

18. ) • 25 ÷ 7 or how many groups of 7 are in 25 • Think of a your seven facts • 7x3=21 • Place the 3 above the bar • Subtract 21 from 25 • Bring down the next digit in the dividend ~ THREE • 43 ÷ 7 or how many 7’s are in 43 3 6 2,538 7 -21 4 3 -42 7 x 6 = 42

19. 3 • 7 x 6 = 42 ~ Place the 6 above the division bar • Subtract 42 from 43 • Bring down the next number in the dividend ~ EIGHT • How many 7’s are in 18 • 7 x 2 = 14 • Place the 2 above the bar • Subtract 14 from 18 • Our quotient is 362with a remainder of 4 ) remainder 6 2 2,538 7 -21 4 3 -42 1 8 -14 4

20. ) • 37 ÷ 8 or how many groups of 8 are in 37 • Think of a your eight facts • 8 x 4 = 32 • Place the 4 above the bar • Subtract 32 from 37 • Bring down the next digit in the dividend ~ NINE • 59÷ 8 or how many 8’s are in 59 4 7 8 3,792 -32 5 9 -56 8 x 7 = 56

21. 4 • 8 x 7 = 56 ~ Place the 7 above the division bar • Subtract 56 from 59 • Bring down the next number in the dividend ~ TWO • How many 8’s are in 32 • 8 X 4 = 32 • Place the 4 above the bar • Subtract 32 from 32 • Our quotient is 474 ) no remainder 7 4 3,792 8 -32 5 9 -56 3 2 -32 0

22. ) • 17 ÷ 3 or how many groups of 3 are in 17 • Think of a your three facts • 3 x 5 = 15 • Place the 5 above the bar • Subtract 15 from 17 • Bring down the next digit in the dividend ~ SIX • 26 ÷ 3 or how many 3’s are in 26 5 8 1,763 3 -15 2 6 -24 8 X 3 = 24

23. 5 • 3 x 8 = 24 ~ Place the 8 above the division bar • Subtract 24 from 26 • Bring down the next number in the dividend ~ THREE • How many 3’s are in 23 • 3 x 7 = 21 • Place the 7 above the bar • Subtract 21 from 23 • Our quotient is 587with a remainder of 2 ) remainder 8 7 1,763 3 -15 2 6 -24 2 3 -21 2

24. ) • 24 ÷ 9 or how many groups of 9 are in 24 • Think of a your nine facts • 9 x 2 = 18 • Place the 2 above the bar • Subtract 18 from 24 • Bring down the next digit in the dividend ~ SEVEN • 67 ÷ 9 or how many 9’s are in 67 2 7 9 2,473 -18 6 7 -63 9 x 7 = 63

25. 2 • 9 X 7 = 63 ~ Place the 7 above the division bar • Subtract 63 from 67 • Bring down the next number in the dividend ~ THREE • How many 9’s are in 43 • 9 x 4 = 36 • Place the 4 above the bar • Subtract 36 from 43 • Our quotient is 274with a remainder of 7 ) remainder 7 4 2,473 9 -18 6 7 -63 4 3 -36 7

26. ) • 14 ÷ 2 or how many groups of 2 are in 14 • Think of your doubles • 2 x 7 = 14 • Place the 7 above the bar • Subtract 14 from 14 • Bring down the next digit in the dividend ~ NINE • 9 ÷ 2 or how many 2’s are in 9 7 4 1,499 2 -14 0 9 - 8 2 x 4 = 8

27. 7 • 2 x 4 = 8 ~ Place the 4 above the division bar • Subtract 8 from 9 • Bring down the next number in the dividend ~ NINE • How many 2s are in 19 • 2 x 9 = 18 • Place the 9 above the bar • Subtract 18 from 19 • Our quotient is 749with a remainder of 1 ) remainder 4 9 1,499 2 -14 0 9 - 8 1 9 -18 1

28. ) 2 2 • 6 ÷ 3 or how many groups of 3 are in 6 • Recall your multiplication facts 3 x 2 = 6 • Place the 2 above the bar • Subtract 6 from 6 • Bring down the next digit in the dividend ~ EIGHT • 8 ÷ 3 or how many 3’s are in 8 3 6,843 -6 0 8 - 6 3 x 2 = 6

29. ) no remainder • 3 x 2 = 6 or how many groups of 3 are in 6 • Place the 2 above the bar • Subtract 6 from 8 • Bring down the next digit in the dividend ~ FOUR • How many 3’s are in 24 • Place the 8 above the bar • Subtract 24 from 24 • Bring down the THREE • 3 x 1 = 3 ~ Now subtract • Our quotient is 2,281 2 2 8 1 3 6,843 -6 0 8 - 6 2 4 -24 0 3 - 3 0

30. ) ) ) ) ) Try These On Your Own • We will check them using webmath.com b. 6 4 a. 3,927 8,146 d. 9 c. 8 3,506 4,468 7 8,338 e.