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Rational Numbers

Question
CBSEENMA8002189
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What should be subtracted from <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre> to get space space fraction numerator negative 17 over denominator 12 end fraction ?

Solution

space space space space open parentheses fraction numerator negative 3 over denominator 4 end fraction close parentheses- (The required rational number) = space space fraction numerator negative 17 over denominator 12 end fraction

∴         <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre> = (The required rational number)

∴           (The required rational number) = space space open parentheses fraction numerator negative 3 over denominator 4 end fraction close parentheses minus open parentheses fraction numerator negative 17 over denominator 12 end fraction close parentheses equals open parentheses fraction numerator negative 3 over denominator 4 end fraction close parentheses plus 17 over 12

                           
                                                       space space space space space space space open square brackets because space Additive space inverse space of space open parentheses fraction numerator negative 17 over denominator 12 end fraction close parentheses space is space 17 over 12 close square brackets
                            
                                                   =space space space open parentheses fraction numerator negative 3 over denominator 4 end fraction cross times 3 over 3 close parentheses plus 17 over 12 (∵ LCM of 4 and 12 is 12)
                                                   = space space fraction numerator negative 9 over denominator 12 end fraction plus 17 over 12
                                                   = space space fraction numerator negative 9 plus 17 over denominator 12 end fraction
                                                   =  space space space 8 over 12 space or space 2 over 3
                                                    

                                                                                                                      
                     

 

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Some More Questions From Rational Numbers Chapter

The reciprocal of –5 is ______.

The reciprocal of 1/x, where x # 0 is

The product of two rational numbers is always a ___________.

The reciprocal of a positive rational number is _________.

Complete the following table:

Numbers

Commutative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

Yes

    

...

Integers

  

No

    

Whole numbers

    

Yes

  

Natural numbers

      

No

Complete the following table:

Numbers

Associative for
 

Addition

Subtraction

Multiplication

Division

Rational numbers

      

No

Integers

    

Yes

  

Whole numbers

Yes

      

Natural numbers

  

No

If a property holds for rational numbers, will it also hold for integers? For whole Numbers? Which will? Which will not?

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