Topic C: Dividing Larger Numbers by One-Digit Divisors

Wendy Tagami; Liz Girard

Topic C: Dividing Larger Numbers by One-Digit Divisors

Several methods are used to divide larger numbers. This book will only teach one method. If you have learned a different method for dividing, ask your instructor to review it with you. You can use the practice exercises in this workbook using whichever method you prefer.

One-Digit Divisors without Remainders

Division has four steps which are repeated until the dividend is completely divided. Work through the three examples which show these steps.

Divide.
Multiply
Subtract and compare the remainder to the divisor.
Bring down the next digit in the dividend and repeat.

Example A

294 ÷ 7 =
Rewrite as $7\enclose{longdiv}{294}$

Step 1: Divide. Find a trial quotient using multiplication tables or division facts. Look at the dividend one digit at a time. The first digit is a 2, which is really 2 hundreds. Will 7 go into 2? Can you divide 2 by 7? No. Look at the first 2 digits, 29, which is really 29 tens. Will 7 go into 29? Yes. 4 × 7 = 28. The first number in the quotient is 4. Place the 4 in the quotient directly above the 9 tens. The 4 is 4 tens in the quotient.	$\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\end{array}$

Step 2: Multiply. Multiply 4 × 7 = 28. Write the 28 under the 29. Draw a line.	$\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\28\hspace{0.8em}\\\hline\end{array}$

Step 3: Subtract. Subtract 29 − 28 = 1 (ten). Check 1 < 7.	$\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline1\hspace{0.8em}\end{array}$

Step 4: Bring down the next number in the dividend.

Bring down the next number in the dividend (4), and put it beside the result of the subtraction you just completed (1).

Together, they make 14. This 14 is the number that you must now divide.

$\begin{array}{r}4\hspace{0.8em}\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\end{array}$

Repeat Step 1: Divide.

Divide 14 ÷ 7 = 2
Put the 2 in the quotient right after the 4 in the ones place.

$\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\end{array}$

Repeat Step 2: Multiply.

Multiply 2 × 7 = 14.
Write the 14 under the 14. Draw a line.

$\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\\14\\\hline\end{array}$

Repeat Step 3: Subtract.

Subtract 14 − 14 = 0. There is 0 remainder.
Check 0 < 7.

$\begin{array}{r}42\\7 \enclose{longdiv}{294}\\-28\hspace{0.8em}\\\hline14\\-14\\\hline0\end{array}$

There are no more numbers in the dividend to bring down, so you are done.

294 ÷ 7 = 42

Example B

128 ÷ 2 =

$\begin{array}{r}64\\2 \enclose{longdiv}{128}\\-12\hspace{0.8em}\\\hline08\\-8\\\hline0\end{array}$

Step 1: Divide.

Can 2 go into 1? No.
Can 2 go into 12? Yes.
How many times?
- 2 × 6 = 12; 12 ÷ 2 = 6
The first number in the trial quotient is 6. Put the 6 in the quotient directly above the 2 tens dividend.

Step 2: Multiply.

6 × 2 = 12.
Write the 12 under the 12. Draw a line.

Step 3: Subtract.

12 − 12 = 0
Check 0 < 12

Step 4: Bring down the next number in the dividend.

Bring down the next number in the dividend (8), and put it beside the result of the subtraction you just completed (0).
8 is now the number to be divided.

Repeat

Divide: 8 ÷ 2 = 4
Multiple: 4 × 2 = 8
Subtract: 8 − 8 = 0
1. Check 0 < 2
Bring down the next digit. There are no more digits in the dividend.

128 ÷ 2 = 64

Exercise 1

Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.

$4\enclose{longdiv}{364}$
$2\enclose{longdiv}{144}$
$5\enclose{longdiv}{455}$
$7\enclose{longdiv}{651}$
$8\enclose{longdiv}{144}$
$2\enclose{longdiv}{166}$
$7\enclose{longdiv}{588}$
$2\enclose{longdiv}{196}$
$5\enclose{longdiv}{230}$
$8\enclose{longdiv}{584}$
$6\enclose{longdiv}{366}$
$4\enclose{longdiv}{244}$
$5\enclose{longdiv}{375}$
$8\enclose{longdiv}{200}$
$2\enclose{longdiv}{628}$
$7\enclose{longdiv}{357}$
$9\enclose{longdiv}{837}$
$8\enclose{longdiv}{248}$
$8\enclose{longdiv}{312}$
$7\enclose{longdiv}{462}$
$5\enclose{longdiv}{295}$
$6\enclose{longdiv}{384}$
$2\enclose{longdiv}{276}$
$4\enclose{longdiv}{372}$

Answers to Exercise 1

91
72
91
93
18
83
84
98
46
73
61
61
75
25
314
51
93
31
39
66
59
64
138
93

Example C

856 ÷ 8 =

$8\enclose{longdiv}{856}$

Divide Does 8 go into 8? Yes. 8 ÷ 8 = 1.	$\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\end{array}$

Multiply 1 × 8 = 8	$\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\8\hspace{1.2em}\end{array}$

Subtract 8 − 8 = 0. Check 0 < 8.	$\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline0\hspace{1.2em}\end{array}$

Bring down the next digit 5 is now the number to be divided.	$\begin{array}{r}1\hspace{1.2em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\end{array}$

Now repeat.

Divide Does 8 go into 5? No. You must put a zero to hold the place in the quotient. If a digit is brought down, a digit must be placed in the quotient.	$\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\end{array}$

Multiply 0 × 8 = 0	$\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline\hspace{0.8em}\end{array}$

Subtract 5 − 0 = 5. Check 5 < 8.	$\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline5\hspace{0.8em}\end{array}$

Bring down the next digit 56 is now the number to be divided.	$\begin{array}{r}10\hspace{0.8em}\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\end{array}$

Now repeat.

Divide Does 8 go into 56? Yes. 56 ÷ 8 = 7. Write 7 in the quotient in the ones place above the 6 in the dividend.	$\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\end{array}$

Multiply 7 × 8 = 56	$\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\\56\end{array}$

Subtract 56 − 56 = 0. Check 0 < 8.	$\begin{array}{r}107\\8 \enclose{longdiv}{856}\\-8\hspace{1.2em}\\\hline05\hspace{0.8em}\\-0\hspace{0.8em}\\\hline56\\-56\\\hline0\end{array}$
Bring down the next digit. No more digits.

856 ÷ 8 = 107

Exercise 2

Find the quotients (divide, multiply, subtract, compare). Check your work using the answer key at the end of the exercise.

$7\enclose{longdiv}{721}$
$9\enclose{longdiv}{954}$
$3\enclose{longdiv}{927}$
$3\enclose{longdiv}{621}$
$4\enclose{longdiv}{824}$
$9\enclose{longdiv}{972}$
$7\enclose{longdiv}{714}$
$2\enclose{longdiv}{416}$
$5\enclose{longdiv}{540}$
$6\enclose{longdiv}{654}$
$8\enclose{longdiv}{832}$
$4\enclose{longdiv}{436}$
$5\enclose{longdiv}{515}$
$2\enclose{longdiv}{814}$
$6\enclose{longdiv}{648}$
$8\enclose{longdiv}{856}$
$5\enclose{longdiv}{525}$
$7\enclose{longdiv}{763}$
$9\enclose{longdiv}{945}$
$3\enclose{longdiv}{315}$
$8\enclose{longdiv}{872}$
$4\enclose{longdiv}{416}$
$6\enclose{longdiv}{618}$
$2\enclose{longdiv}{612}$

Answers to Exercise 2

103
106
309
207
206
108
102
208
108
109
104
109
103
407
108
107
105
109
105
105
109
104
103
306

One-Digit Divisors with Remainders

Do the division exactly the same way that you have been learning. Often there is a remainder after the last subtraction. Write it with the quotient as you already know how to do.

Example D

259 ÷ 8 =

$\begin{array}{l}\hspace{1.5em}32\text{ R}3\\8 \enclose{longdiv}{259}\\\hspace{0.3em}-24\\\hline\hspace{1.7em}19\\\hspace{1em}-16\\\hline\hspace{2.3em}3\end{array}$

259 ÷ 8 = 32 R3

Exercise 3

Divide and show any remainders. Check your work using the answer key at the end of the exercise.

$2\enclose{longdiv}{93}$
$3\enclose{longdiv}{52}$
$5\enclose{longdiv}{94}$
$7\enclose{longdiv}{74}$
$4\enclose{longdiv}{95}$
$9\enclose{longdiv}{96}$
$6\enclose{longdiv}{97}$
$8\enclose{longdiv}{99}$
$9\enclose{longdiv}{98}$
$4\enclose{longdiv}{59}$
$6\enclose{longdiv}{76}$
$3\enclose{longdiv}{79}$
$7\enclose{longdiv}{96}$
$5\enclose{longdiv}{57}$
$2\enclose{longdiv}{47}$
$8\enclose{longdiv}{91}$
$7\enclose{longdiv}{89}$
$6\enclose{longdiv}{82}$
$5\enclose{longdiv}{67}$
$2\enclose{longdiv}{85}$
$4\enclose{longdiv}{71}$
$3\enclose{longdiv}{65}$
$9\enclose{longdiv}{92}$
$8\enclose{longdiv}{94}$

Answers to Exercise 3

46 R1
17 R1
18 R4
10 R4
23 R3
10 R6
16 R1
12 R3
10 R8
14 R3
12 R4
26 R1
13 R5
11 R2
23 R1
11 R3
12 R5
13 R4
13 R2
42 R1
17 R3
21 R2
10 R2
11 R6

Check Division by Multiplying

To check your division, do this:

Multiply the quotient by the divisor.
Add on any remainder.

The product will equal the dividend if your arithmetic is correct.

Example E

$\begin{array}{l}\hspace{1.5em}52\text{ R}1\\9 \enclose{longdiv}{469}\\\hspace{0.3em}-45\\\hline\hspace{1.7em}19\\\hspace{1em}-18\\\hline\hspace{2.3em}1\end{array}$ $\begin{array}{rr}&52\\\times&9\\\hline&468\end{array}$ $468+1=469$

Exercise 4

Divide and check your answer by multiplying. Check your work using the answer key at the end of the exercise.

$7\enclose{longdiv}{709}$
$2\enclose{longdiv}{423}$
$5\enclose{longdiv}{538}$
$4\enclose{longdiv}{609}$
$9\enclose{longdiv}{406}$
$6\enclose{longdiv}{125}$
$3\enclose{longdiv}{605}$
$9\enclose{longdiv}{928}$
$3\enclose{longdiv}{962}$
$4\enclose{longdiv}{805}$
$8\enclose{longdiv}{301}$
$2\enclose{longdiv}{807}$
$6\enclose{longdiv}{725}$
$7\enclose{longdiv}{320}$
$9\enclose{longdiv}{140}$
$8\enclose{longdiv}{483}$
$2\enclose{longdiv}{197}$
$6\enclose{longdiv}{307}$
$5\enclose{longdiv}{504}$
$8\enclose{longdiv}{709}$
$7\enclose{longdiv}{876}$
$4\enclose{longdiv}{101}$
$3\enclose{longdiv}{269}$
$5\enclose{longdiv}{473}$

Answers to Exercise 4

101 R2
211 R1
107 R3
152 R1
45 R1
20 R5
201 R2
103 R1
320 R2
201 R1
37 R5
403 R1
120 R5
45 R5
15 R5
60 R3
98 R1
51 R1
100 R4
88 R5
125 R1
25 R1
89 R2
94 R3

Topic C: Self-Test

Mark /24 Aim 19/24

A. Find the quotient. (6 marks)

$6\enclose{longdiv}{96}$
$4\enclose{longdiv}{92}$
$7\enclose{longdiv}{91}$
$2\enclose{longdiv}{93}$
$5\enclose{longdiv}{94}$
$3\enclose{longdiv}{52}$

B. Divide. (6 marks)

$7\enclose{longdiv}{182}$
$8\enclose{longdiv}{736}$
$6\enclose{longdiv}{162}$
$5\enclose{longdiv}{295}$
$4\enclose{longdiv}{184}$
$9\enclose{longdiv}{576}$

C. Divide and show your check for each answer (12 marks – 1 mark for question, 1 mark for check).

$9\enclose{longdiv}{705}$
$4\enclose{longdiv}{257}$
$7\enclose{longdiv}{899}$
$5\enclose{longdiv}{538}$
$8\enclose{longdiv}{876}$
$6\enclose{longdiv}{628}$

Answers to Topic C Self-Test

Find the quotient.
1. 16
2. 23
3. 13
4. 46 R1
5. 18 R4
6. 17 R1
Divide.
1. 26
2. 92
3. 27
4. 59
5. 46
6. 64
Divide and show your check for each answer.
1. 78 R3
2. 64 R1
3. 128 R3
4. 107 R3
5. 109 R4
6. 104 R4

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