Question

what should be subtracted from the sum of -5/12 and -5/18 to get -71/72​

Answer 1

Answer:

$\large{\boxed{\sf \frac{21}{72}}}$

Step-by-step explanation:

Let the required number be x.

Now, sum of (-5/12) and (-5/18):

$\sf \implies \frac{ - 5}{12} + ( \frac{ - 5}{18} ) \\ \\ \sf \implies \frac{ - 15 + ( - 10)}{36} \\ \\ \implies \sf \frac{ - 25}{36}$

According to the question ;

$\implies \sf \frac{ - 25}{36} - x = \frac{ - 71}{72} \\ \\ \implies \sf - x = \frac{ - 71}{72} + \frac{25}{36} \\ \\ \implies \sf - x = \frac{ - 71 + 50}{72} \\ \\ \implies \sf - x = - \frac{ 21}{72} \\ \\ \implies \sf x = \frac{21}{72}$

Hence, the required number is 21/72.

Answer 2

Solution

Let 'x' should be subtracted from the sum of $\dfrac{-5}{12}$ and $\dfrac{-5}{18}$ to get $\dfrac{-71}{72}$

Firstly we have to find the sum of $\dfrac{-5}{12}$ and $\dfrac{-5}{18}$

$\dfrac{-5}{12}+\dfrac{-5}{18}\\\\\\=\dfrac{-15+ (-10)}{36}\\\\\\=\dfrac{-25}{36}$

We get the sum =     $\dfrac{-25}{36}$

Now we have to subtract 'x' from  $\dfrac{-25}{36}$  to get $\dfrac{-71}{72}$

According to the question -

$\implies\dfrac{-25}{36}-x=\dfrac{-71}{72}\\\\\\\implies-x=\dfrac{-71}{72}+\dfrac{25}{36}\\\\\\LCM\:of\:72\:and\:36\:is\:72\\\\\\\implies-x=\dfrac{(-71)+50}{72}\\\\\\\implies-x=\dfrac{-21}{72}\:(Here\:'-'\:and\:'-'\:will\:be\:cancelled)\\\\\\\implies x=\bold{\dfrac{21}{72}}$