Question

Find the product using suitable properties:
(a) $ 26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right) $

Answer 1

Hint:First, we will use the DMAS rule i.e. if there is division in the equation then we will first solve that term, then we will solve multiplication, then addition and at last we will do subtraction. So, here we will first do multiplication of first 2 and last 2 terms and then we will add both the values. We will also use the sing rule in multiplication i.e. $ \left( - \right)\times \left( + \right)=\left( - \right) $ and $ \left( - \right)\times \left( - \right)=\left( + \right) $ . Thus, we will get the answer.

Complete step-by-step answer:
Here, we will apply DMAS rule i.e. Division, Multiplication, Addition and Subtraction. This means that first we have to do division, then multiplication, then addition and at last subtraction. This is the sequence which we will follow here.
We are given $ 26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right) $ .
So, first we will multiply the first 2 terms and last two terms as they are in multiplication. So, on multiplication, we get as
 $ -1248+1728 $
We have used the rule that $ \left( - \right)\times \left( + \right)=\left( - \right) $ and $ \left( - \right)\times \left( - \right)=\left( + \right) $ .
On further solving, we get as
 $ -1248+1728=480 $
Thus, the answer of $ 26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right) $ is 480.

Note: Instead of using DMAS rule, if we directly solve them from left to right, we get $ -1248+\left( -48 \right)\times \left( -36 \right) $ . On further solving, we get as $ -1296\times \left( -36 \right) $ . Thus, we get an answer as 46656. Thus, we can see that the answer is totally changed from what we got in solution and this is wrong. So, always in this type of question DMAS rule should be used to get the correct answer.