Question

A number 5 times \[\left( { - 6} \right) + \left( { - 15} \right)\] is ….
A.-54
B.-45
C.54
D.-105

Answer 1

Hint: 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. Using this definition, we can find out the correct answer.

Complete step-by-step answer:
We have to find 5 times of \[\left( { - 6} \right) + \left( { - 15} \right)\] , so we have to first simplify the equation \[\left( { - 6} \right) + \left( { - 15} \right)\] .
 \[
  \left( { - 6} \right) + \left( { - 15} \right) = - 6 - 15 \\
   \Rightarrow ( - 6) + ( - 15) = - 21 \;
 \]
Now, 5 times of \[\left( { - 6} \right) + \left( { - 15} \right)\] can also be written as 5 times of -21.
5 times of -21 is $( - 21) + ( - 21) + ( - 21) + ( - 21) + ( - 21) = 5( - 21) = - 105$
Thus 5 times of \[\left( { - 6} \right) + \left( { - 15} \right)\] is $ - 105$
So, the correct answer is “Option D”.

Note: We put parentheses to avoid confusion, as $2 \times ( - 5)$ is easier to understand than $2 \times - 5$ .
We know that two types of numbers are positive and negative numbers, the positive numbers are denoted by sign before the number and the negative numbers are denoted by sign before the number. The numbers without any sign before them are usually positive. So, now the question arises that how can we multiply a positive number with a negative number. The simple answer is the rules which tell us how to multiply two signs. When we multiply two like signs, the resultant sign is positive that is $( + ) \times ( + ) = ( + )\,or\,( - ) \times ( - ) = ( + )$ and when two unlike signs are multiplied, the resultant sign is negative that is $( + ) \times ( - ) = ( - )\,or\,( - ) \times ( + ) = ( - )$ .