Unit 2: Division
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 72947294
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.
4729447294
Step 2: Multiply.
- Multiply 4 × 7 = 28.
- Write the 28 under the 29. Draw a line.
47294284729428
Step 3: Subtract.
- Subtract 29 − 28 = 1 (ten).
- Check 1 < 7.
47294−28147294−281
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.
47294−281447294−2814
Repeat Step 1: Divide.
- Divide 14 ÷ 7 = 2
- Put the 2 in the quotient right after the 4 in the ones place.
427294−2814427294−2814
Repeat Step 2: Multiply.
- Multiply 2 × 7 = 14.
- Write the 14 under the 14. Draw a line.
427294−281414427294−281414
Repeat Step 3: Subtract.
- Subtract 14 − 14 = 0. There is 0 remainder.
- Check 0 < 7.
427294−2814−140427294−2814−140
There are no more numbers in the dividend to bring down, so you are done.
294 ÷ 7 = 42
Example B
128 ÷ 2 =
642128−1208−80642128−1208−80
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
- 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.
- 43644364
- 21442144
- 54555455
- 76517651
- 81448144
- 21662166
- 75887588
- 21962196
- 52305230
- 85848584
- 63666366
- 42444244
- 53755375
- 82008200
- 26282628
- 73577357
- 98379837
- 82488248
- 83128312
- 74627462
- 52955295
- 63846384
- 22762276
- 43724372
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 =
88568856
Divide
Does 8 go into 8? Yes. 8 ÷ 8 = 1.
1885618856
Multiply
1 × 8 = 8
188568188568
Subtract
8 − 8 = 0. Check 0 < 8.
18856−8018856−80
Bring down the next digit
5 is now the number to be divided.
18856−80518856−805
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.
Multiply
0 × 8 = 0
108856−805108856−805
Subtract
5 − 0 = 5. Check 5 < 8.
108856−805−05108856−805−05
Bring down the next digit
56 is now the number to be divided.
108856−805−056108856−805−056
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.
1078856−805−0561078856−805−056
Multiply
7 × 8 = 56
1078856−805−056561078856−805−05656
Subtract
56 − 56 = 0. Check 0 < 8.
1078856−805−056−5601078856−805−056−560
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.
- 77217721
- 99549954
- 39273927
- 36213621
- 48244824
- 99729972
- 77147714
- 24162416
- 55405540
- 66546654
- 88328832
- 44364436
- 55155515
- 28142814
- 66486648
- 88568856
- 55255525
- 77637763
- 99459945
- 33153315
- 88728872
- 44164416
- 66186618
- 26122612
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 =
32 R38259−2419−16332 R38259−2419−163
259 ÷ 8 = 32 R3
Exercise 3
Divide and show any remainders. Check your work using the answer key at the end of the exercise.
- 20932093
- 352352
- 594594
- 774774
- 495495
- 996996
- 697697
- 899899
- 998998
- 459459
- 676676
- 379379
- 796796
- 557557
- 247247
- 891891
- 789789
- 682682
- 567567
- 285285
- 471471
- 365365
- 992992
- 894894
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
52 R19469−4519−18152 R19469−4519−181 52×946852×9468 468+1=469468+1=469
Exercise 4
Divide and check your answer by multiplying. Check your work using the answer key at the end of the exercise.
- 77097709
- 24232423
- 55385538
- 46094609
- 94069406
- 61256125
- 36053605
- 99289928
- 39623962
- 48054805
- 83018301
- 28072807
- 67256725
- 73207320
- 91409140
- 84838483
- 21972197
- 63076307
- 55045504
- 87098709
- 78767876
- 41014101
- 32693269
- 54735473
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
- Find the quotient. (6 marks)
- 696696
- 492492
- 791791
- 293293
- 594594
- 352352
- Divide. (6 marks)
- 71827182
- 87368736
- 61626162
- 52955295
- 41844184
- 95769576
- Divide and show your check for each answer (12 marks – 1 mark for question, 1 mark for check).
- 97059705
- 42574257
- 78997899
- 55385538
- 88768876
- 66286628
Answers to Topic C Self-Test
- Find the quotient.
- 16
- 23
- 13
- 46 R1
- 18 R4
- 17 R1
- Divide.
- 26
- 92
- 27
- 59
- 46
- 64
- Divide and show your check for each answer.
- 78 R3
- 64 R1
- 128 R3
- 107 R3
- 109 R4
- 104 R4