EM2007SRB_G4_WHO_ccc.qxd 1/26/06 7:55 PM Page 22
Whole Numbers
Division Methods
Different symbols may be used to indicate division. For
example, “94 divided by 6” may be written as 94 ! 6, 6!9
"4
",
94
"
"
94 / 6, or 6 .
♦ The number that is being divided is called the dividend.
♦ The number by which it is divided is called the divisor.
♦ The answer to a division problem is called the quotient.
Four ways to show
“123 divided by 4”
123 ! 4 123 / 4
4!""
123
123
""
4
123 is the dividend.
4 is the divisor.
♦ Some numbers cannot be divided evenly. When this
happens, the answer includes a quotient and a remainder.
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.
The ! symbol is called
an obelus. It was first
used as a symbol for
division by Johann Rahn,
in 1659.
Study this example. To find the number of 6s in 94, first find
partial quotients, then add them. Record the partial quotients
in a column to the right of the original problem.
94 / 6 # ?
Write partial quotients in this column.
6!9
"4
"
$ 60
?
10
34
$ 30
Think: How many [6s] are in 94? At least 10.
The first partial quotient is 10. 10 * 6 # 60 Subtract 60 from 94.
At least 5 [6s] are left in 34.
5
4
15
B
B
Remainder Quotient
The second partial quotient is 5. 5 * 6 # 30 Subtract 30 from 34.
Add the partial quotients.
15 R4
"4
"
or write 94 / 6 A 15 R4.
The answer is 15 R4. Record the answer as 6!9
22
twenty-two
EM2007SRB_G4_WHO_ccc.qxd 1/26/06 7:55 PM Page 23
Whole Numbers
The partial-quotients method works the same whether you divide by a 2-digit or
a 1-digit divisor. It often helps to write down some easy facts for the divisor first.
400 / 22 " ?
"0
"0
"
22!4
# 220
Some facts for 22
(to help find partial quotients):
10
(10 [22s] in 400)
5
(5 [22s] in 180)
2
(2 [22s] in 70)
# 22
1
(1 [22] in 26)
4
18
180
# 110
1 * 22 " 22
2 * 22 " 44
5 * 22 " 110
10 * 22 " 220
70
# 44
26
18 R4
Record the answer as 22!4
"0
"0
"
, or write 400 / 22 A 18 R4.
There are different ways to find partial quotients when you use the partialquotients method. Study the different ways in the example below. Each is correct.
371 / 4 " ?
One way:
Another way:
4!3
""
7"
1
# 200
4!3
""
7"
1
50
171
# 120
# 200
4!3
""
7"
1
50
# 360
171
30
51
# 40
Still another way:
# 160
11
40
11
10
#8
2
3
92
11
#8
2
3
92
90
#8
2
3
92
The answer, 92 R3, is the same for each way.
Divide.
1. 2!7
"5
"
2. 110 / 6
3. 121 ! 5
4. 3!4
"1
"6
"
Check your answers on page 340.
twenty-three
23