Question

Find the value of the following:
A. $ 297 \times 17 + 297 \times 3 $
B. $ 54279 \times 92 + 8 \times 54279 $
C. $ 81265 \times 169 - 81265 \times 69 $
D. $ 3845 \times 5 \times 782 + 769 \times 25 \times 218 $

Answer 1

Hint: When the two numbers are multiplied, the resultant number is quite greater than both the numbers. In the given question, we have to find out the sum of the product of very big numbers, so multiplying them is a difficult task, that’s why we have to find out a quick way to multiply such big numbers. When one of the terms is the same in both the products that are in multiplication, we can take that term common and write the rest of the expression in the parenthesis. For example, $ a \times b + a \times c = a \times (b + c) $ . We apply the given mathematical operation within the parenthesis and then multiply the resultant numbers.

Complete step-by-step answer:
A. $ 297 \times 17 + 297 \times 3 $
Taking 297 as common, we get –
 $
  297 \times (17 + 3) \\
   \Rightarrow 297 \times 20 \\
   \Rightarrow 5940 \;
  $
So, the correct answer is “5940”.

B. $ 54279 \times 92 + 8 \times 54279 $
Taking 54279 as common, we get –
 $
  54279 \times (92 + 8) \\
   \Rightarrow 54279 \times 100 \\
   \Rightarrow 5427900 \;
  $
So, the correct answer is “5427900”.

C. $ 81265 \times 169 - 81265 \times 69 $
Taking 81265 as common, we get –
 $
  81265 \times (169 - 69) \\
   \Rightarrow 81265 \times 100 \\
   \Rightarrow 8126500 \;
  $
So, the correct answer is “8126500”.

D. $ 3845 \times 5 \times 782 + 769 \times 25 \times 218 $
In the given question, 25 can be written as a product of two fives,
 $ 3845 \times 5 \times 782 + 769 \times 5 \times 5 \times 218 $
Now, we see that product of 769 and 5 is 3845,
 $
  3845 \times 5 \times 782 + 3845 \times 5 \times 218 \\
   \Rightarrow 19225 \times 782 + 19225 \times 218 \;
  $
Taking 19225 as common, we get –
 $
  19225 \times (782 + 218) \\
   \Rightarrow 19225 \times 1000 \\
   \Rightarrow 19225000 \;
  $
So, the correct answer is “19225000”.

Note: Multiplication is one of the most basic operations in mathematics. It can be defined as the repeated addition of one number to itself. For example, \[2 \times 3 = 2 + 2 + 2\] , this example can be written in statement form as “2 times 3 or 3 times to” that is 3 added to itself two times or two added to itself 3 times. When we can’t find any number common in the sum of the two products, then we have to try to write the expression to get a common term, as we did in the (d) part.