Question

Simplify using a suitable property of integers.
\[23\times (-5)-23\times (-15)\]

Answer 1

Hint: Since we have been told to use the property of integers then we can not use BODMAS(Bracket Off Divide Multiply Addition Subtraction) rule. We will do it by normal property of integers and by taking common.

Complete step-by-step answer:
We can write the \[23\times (-5)-23\times (-15)\] in the form of \[(a\times c)-(a\times b)\] where we have two common numbers. Moreover, we can say that \[23\times (-5)\] is a separate term and \[23\times (-15)\] is a separate term since the subtraction sign comes in between (-5) and 23. Moreover from the BODMAS rule which says that we need to first open the brackets and then multiply before subtraction.
Therefore all we need to do is;
  $ 23\times (-5)-23\times (-15) $
 $ (a\times c)-(a\times b) $
 $ a\times (c-b) $
 $ \text{taking 23 common} $
 $ 23((-5)-(-15)) $
 $ 23(-5+15)=23\times (10)=230 $
 $ 230 $
The simplified answer is 230.

Note: The subtraction sign here helps us determine the expression given here in the form \[(a\times c)-(a\times b)\]. Through the simple application of the BODMAS rule we can also check if the answer is correct or not. Moreover the brackets should be solved first so we know the correct step should be as mentioned in the solution.