1-6 Multiplying and Dividing Real Numbers

Objective

To find products and quotients of real numbers

Image Long Description

The patterns in the Solve It suggest rules for multiplying real numbers.

Essential Understanding The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations.

You know that the product of two positive numbers is positive. For example, 3(5) = 15. You can think about the product of a positive number and a negative number in terms of groups of numbers. For example, 3 ( − 5 ) 3 open negative 5 close  means 3 groups of − 5 . negative 5 .  So, 3 ( − 5 ) = ( − 5 ) + ( − 5 ) + ( − 5 ) , 3 open negative 5 close equals open negative 5 close plus open negative 5 close plus open negative 5 close comma  or 3 ( − 5 ) = − 15 . 3 open negative 5 close equals negative 15 .

You can also derive the product of two negative numbers, such as − 3 ( − 5 ) . negative 3 open negative 5 close .

3 ( − 5 ) = − 15 Start with the product  3 ( − 5 ) = − 15 . − [ 3 ( − 5 ) ] = − ( − 15 ) The opposites of two equal numbers are equal. − 1 [ 3 ( − 5 ) ] = − ( − 15 ) Multiplication Property of  − 1 [ − 1 ( 3 ) ] ( − 5 ) = − ( − 15 ) Associative Property of Multiplication − 3 ( − 5 ) = − ( − 15 ) Multiplication Property of  − 1 − 3 ( − 5 ) = 15 The opposite of  − 15  is  15 . table with 6 rows and 4 columns , row1 column 1 , 3 open negative 5 close , column 2 equals negative 15 , column 3 cap start with the product . 3 open negative 5 close , column 4 equals negative 15 . , row2 column 1 , negative left bracket 3 open negative 5 close right bracket , column 2 equals negative open negative 15 close , column 3 cap the opposites of two equal numbers are equal. , row3 column 1 , negative 1 left bracket 3 open negative 5 close right bracket , column 2 equals negative open negative 15 close , column 3 cap multiplication cap property of . minus 1 , row4 column 1 , left bracket negative 1 open 3 close right bracket open negative 5 close , column 2 equals negative open negative 15 close , column 3 cap associative cap property of cap multiplication , row5 column 1 , negative 3 open negative 5 close , column 2 equals negative open negative 15 close , column 3 cap multiplication cap property of . minus 1 , row6 column 1 , negative 3 open negative 5 close , column 2 equals 15 , column 3 cap the opposite of . minus 15 , is , 15 . , end table

These discussions illustrate the following rules for multiplying real numbers.

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