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Chapter 1 Whole Numbers 1-7 Dividing Whole Numbers | Division is the opposite of multiplication. In mathematical terms, we say that division is the inverse of multiplication. Definitions - The number being divided is called the dividend.
- The number doing the dividing is called the divisor.
- The result of the multiplication is called the quotient.
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| The division sign ( � ) indicates the division operation. | | | | Division facts | Vertical Form Examples 6
� 3
2 | 12
� 4
3 | 7
� 7
1 | 12
� 1
12 | 0
� 2
0 | Box Division Form 
The box division form can be read as: - "Two into eight equals four"
- Eight divided by 2 equals four"
Examples 2
3 ) 6 | 4
2 ) 8 | 9
1 ) 9 | 9
2 )18 | 4
3 )12 | Horizontal ("Sentence") Form This form is also known as a number sentence. It is read as, "Six divided by three equals two." This form of division shows more directly that 6 � 3 can be more simply expressed as 2. - The division sign ( �) indicates the division operation.
- The equal sign (=) expresses the equality of the two parts of the sentence.
|  | Examples | 1. 6 � 3 = 2 | 2. 12 � 4 = 3 | 3. 7 � 7 = 1 | 4. 12 � 1 = 12 | 5. 0 � 2 = 0 | Notes - Any value divided by one is equal to the original value.
- Zero divided by any value is equal to zero
- A value cannot be divided by zero.
| - Example: 5 � 1 = 5
- Example: 0 � 2 = 0
- Example: 5 � 0 is an invalid expression
| | Division with Remainders Most combinations of whole numbers do not divide evenly. In other words, their quotient cannot be expressed as a simple whole number. - 2 divides evenly into 6: 2 ) 6 = 3
- 5 does not divide evenly into 6: 5 ) 6 = ?
5 divides into 6 one time ... with a remainder of 1 
| | | Division with remainders | Examples 2 R 1
3 ) 7 | 2 R 5
7 ) 19 | 4 R 8
9 ) 44 | 8 R 2
3 ) 26 | 7 R 0
5 ) 35 | Note - When the numbers divide evenly, the remainder is zero, and it does not have to be shown.
- The remainder must always be smaller than the divisor.
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