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Long Division by One-Digit Numbers

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**What is this problem asking us?**

) 5 36,987 If we divided 36,987 into 5 groups of equal size, how many would be in each group?

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

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**) How do we solve it? 5 36,987 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

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) 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

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**) 7 5 36,987 35 9 1 5 x 7 = 35 Now ask how many 5’s are in 19**

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

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5 x 3 = 15 7 3 ) 5 36,987 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

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5 x 9 = 45 7 3 9 ) 5 36,987 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

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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 ) 5 36,987 35 1 9 15 48 45 5 x 7 = 35 3 7 35 remainder 2

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

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**What is this problem asking us?**

) 6 8,437 If we divided 8,437 into 6 groups of equal size, how many would be in each group?

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

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**) How do we solve it? 6 8,437 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.

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**) 1 6 8,437 6 4 2 6 x 1 = 6 Now ask how many 6’s are in 24**

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 many 6’s are in 24

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**) 1 4 6 8,437 6 24 24 3 6 x 4 = 24 Now ask how many 6’s are in 3**

Place the 4 above the division bar Subtract 24 from 24 Bring down the next digit in the dividend 6 24 24 3 Now ask how many 6’s are in 3

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**) 1 4 6 8,437 6 24 24 3 3 7 6 x 0 = 0 Now ask how many 6’s are in 37**

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

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1 4 6 6 x 6 = 36 ) 6 8,437 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 7 3 36 remainder 1

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**3 6 2,538 7 -21 4 3 -42 ) 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

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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 362 with a remainder of 4 6 2 ) 2,538 7 -21 4 3 -42 1 8 -14 4 remainder

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**4 7 8 3,792 -32 5 9 -56 ) 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

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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 7 4 ) 3,792 8 -32 5 9 -56 3 2 -32 no remainder

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**5 8 1,763 3 -15 2 6 -24 ) 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

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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 587 with a remainder of 2 8 7 ) 1,763 3 -15 2 6 -24 2 3 -21 2 remainder

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**2 7 9 2,473 -18 6 7 -63 ) 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

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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 274 with a remainder of 7 7 4 ) 2,473 9 -18 6 7 -63 4 3 -36 7 remainder

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**7 4 1,499 2 -14 9 - 8 ) 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 9 - 8 2 x 4 = 8

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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 749 with a remainder of 1 4 9 ) 1,499 2 -14 9 - 8 1 9 -18 1 remainder

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**2 2 3 6,843 -6 8 - 6 ) 6 ÷ 3 or how many groups of 3 are in 6**

Recall your multiplication facts 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 8 - 6 3 x 2 = 6

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**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 8 - 6 2 4 -24 3 - 3 no remainder

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**Try These On Your Own ) ) ) ) ) 6 4 3,927 8,146 9 8 3,506 4,468 7**

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.

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EXAMPLE 1 Use polynomial long division

EXAMPLE 1 Use polynomial long division

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