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The sum of two rational numbers is $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ . if one of them is $fraction numerator negative 11 over denominator 20 end fraction comma$ find the other.

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

∴ (The required rational number) = $fraction numerator negative 4 over denominator 5 end fraction minus open parentheses fraction numerator negative 11 over denominator 20 end fraction close parentheses$ $fraction numerator negative 4 over denominator 5 end fraction minus open parentheses fraction numerator negative 11 over denominator 20 end fraction close parentheses$

 $space equals space fraction numerator negative 4 over denominator 5 end fraction plus 11 over 20 space space space space space space open square brackets space because space space A d d i t i v e space i n v e r s e space o f space fraction numerator negative 11 over denominator 20 end fraction space i s space 11 over 20 close square brackets$

 $equals space fraction numerator negative 4 cross times 4 plus 11 over denominator 20 end fraction$ ( ∵ LCM of 5 and 20 is 20)

 $space space space space space space space space space fraction numerator negative 16 plus 11 over denominator 20 end fraction space equals space fraction numerator negative 5 over denominator 20 end fraction space o r space fraction numerator negative 1 over denominator 4 end fraction space space space space space space space T h u s comma space t h e space o t h e r space r a t i o n a l space n u m b e r space equals space open parentheses fraction numerator negative 1 over denominator 4 end fraction close parentheses$

1144 Views

Subtract $5 over 6 space i s space fraction numerator negative 5 over denominator 6 end fraction$

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

$equals open parentheses fraction numerator negative 6 over denominator 7 end fraction close parentheses equals open parentheses fraction numerator negative 5 over denominator 6 end fraction close parentheses$

$equals space fraction numerator left parenthesis negative 6 right parenthesis cross times 6 plus left parenthesis negative 5 right parenthesis cross times 7 over denominator 42 end fraction space space space space space open parentheses because space H C F space o f space 7 space a n d space 6 space i s space 42 close parentheses$

$space space space space space equals space fraction numerator negative 36 plus open parentheses negative 35 close parentheses over denominator 42 end fraction space space space space space equals space fraction numerator negative 36 minus 35 over denominator 42 end fraction space equals space fraction numerator negative 71 over denominator 42 end fraction space$

249 Views

What should be added to $fraction numerator negative 4 over denominator 4 end fraction space t o space g e t space 3 over 21 ?$

∵ (The required number) + $fraction numerator negative 4 over denominator 7 end fraction space equals space 3 over 21$

∴   (The required number) = $3 over 21 minus open parentheses fraction numerator negative 4 over denominator 7 end fraction close parentheses$

             $space space equals space 3 over 21 plus 4 over 7 space space space space space space space space space open square brackets space because space a d d i t i v e space i n v e r s e space o f space open parentheses fraction numerator negative 4 over denominator 7 end fraction close parentheses space i s space 4 over 7 close square brackets space space$

        $space space space space space space space space space equals space space space fraction numerator 3 plus 4 cross times 3 over denominator 21 end fraction space space space$ (∵ LCM of 21 and 7 is 21 and 21 +7=3)

           $space space space space space space equals fraction numerator 3 plus 12 over denominator 21 end fraction$

        $space space space space space space space space equals 15 over 21 space o r space 5 over 7$