Download Division Algorithms

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Whole Numbers
Division Algorithms
Different symbols may be used to indicate division. For example,
94
4
, 94 / 6, or 6.
“94 divided by 6” may be written as 94 6, 69
Four ways to show
“123 divided by 4”
♦ The number that is being divided is called the dividend.
123 4
123 / 4
41
2
3
123
4
♦ The number that divides the dividend is called the divisor.
♦ The answer to a division problem is called the quotient.
♦ Some numbers cannot be divided evenly. When this happens,
the answer includes a quotient and a remainder.
123 is the dividend.
4 is the divisor.
Partial-Quotients Method
In the partial-quotients method, it takes several steps to find
the quotient. At each step, you find a partial answer (called a
partial quotient). These partial answers are then added to
find the quotient.
Study the example below. To find the number of 6s in 1,010, first
find partial quotients and then add them. Record the partial
quotients in a column to the right of the original problem.
1,010 / 6 ?
Write partial quotients in this column.
61
,0
1
0
600
↓
100
410
300
50
The second partial quotient is 50. 50 ∗ 6 300
Subtract. At least 10 [6s] are left in 110.
10
50
The third partial quotient is 10. 10 ∗ 6 60
Subtract. At least 8 [6s] are left in 50.
48
8
2
168
↑
↑
Remainder
The first partial quotient is 100. 100 ∗ 6 600
Subtract 600 from 1,010. At least 50 [6s] are left in 410.
110
60
Think: How many [6s] are in 1,010? At least 100.
The fourth partial quotient is 8. 8 ∗ 6 48
Subtract. Add the partial quotients.
Quotient
168 R2
The answer is 168 R2. Record the answer as 61
,0
1
0
or write 1,010 / 6 → 168 R2.
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Whole Numbers
The partial-quotients method works with a 2-digit or a 1-digit
divisor. It may help to write some easy facts for the divisor.
Divide 800 by 22.
Some facts for 22
(to help find partial quotients):
1 ∗ 22 22
2 ∗ 22 44
5 ∗ 22 110
10 ∗ 22 220
228
0
0
440
360
220
140
110
30
22
8
20
(20 [22s] in 800)
10
(10 [22s] in 360)
5
(5 [22s] in 140)
1
36
(1 [22s] in 30)
36 R8
Record the answer as 228
0
0
or write 800 / 22 → 36 R8.
There are different ways to find partial quotients. Study the
example below. The answer is the same for each way.
The national debt is the
total amount of money
owed by the U.S.
government.
On June 30, 2005, the
national debt was about
7.85 * 1012 dollars
($7,850,000,000,000),
and the U.S. population
was about 296,500,000.
If each American were
asked to pay an equal
share of this debt, he or
she would owe $7.85 *
1012 296,500,000 $26,475.55, or about
$26,500.
391 / 4 ?
One way:
A second way:
A third way:
43
9
1
43
9
1
43
9
1
200 50
200 50
360 90
191
191
31
120 30
160 40
20 5
71
31
11
40 10
20 5
8 2
31
11
3 97
20 5
8 2
11
3 97
8 2
3 97
The answer, 97 R3, is the same for each way.
Divide.
1. 69
2
2. 645 / 5
3. 637 ÷ 7
4. 48
3
4
Check your answers on page 415.
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