Question

Find the sum of
$A)

  (a)\,\,137\,\,and\,\, - 354 \\
  (b)\, - 52\,\,and\,\,52 \\
  (c) - 312,\,39\,\,and\,\,192 \\
  (d) - 50,\, - 200\,\,and\,300\, \\
$
Find the sum of
$
B)

  (a)\,( - 7) + ( - 9) + 4 + 16 \\
  (b)\,(37) + ( - 2) + ( - 65) + ( - 8) \\
$

Answer 1

Hint: Apply the sign multiplication rule and add the given numbers.
First, we are going to add the sums, then if there are multiple signs, then we apply for a sign multiplication rule and then we are going to decide on what operation to happen between the given two numbers from the total equation.
The sign multiplication rule is
$
  ( + ) \times ( + ) = ( + ) \\
  ( + ) \times ( - ) = ( - ) \\
  ( - ) \times ( + ) = ( - ) \\
  ( - ) \times ( - ) = ( + ) \\
$
When doing mathematical operation, based on the symbol of the highest number, the operator is decided and also the sign of the resultant value.

Complete step-by-step solution:
A)
$(a)\,\,137\,\,and\,\, - 354$
We are going to first put them in to apply the sum operator.
$137 + ( - 354)$
Since there are two symbols being multiplied.
We apply sign multiplication rule, we get
$137 - 354 = - 217$
$(b)\, - 52\,\,and\,\,52$
We apply the sum operator, we get
$\, - 52\, + 52$
Then, we get the value
$\, - 52\, + 52 = 0$

$(c) - 312,\,39\,\,and\,\,192$
We apply the sum property for the numbers, we get
$ - 312\, + 39\, + 192$
Here, first we are going perform like operations, we get
$ - 312 + 231$
And further we get
$ - 312 + 231 = - 81$
$(d) - 50,\, - 200\,\,and\,300$
We apply the sum operator to the given numbers
$( - 50) + ( - 200) + 300$
Apply sign multiplication rule, we get $ - 50 - 200 + 300$
Perform like operations. Then we get $ - 250 + 300 = 50$

B)
$(a)\,( - 7) + ( - 9) + 4 + 16$
First, we have to apply the sign multiplication rule, then we get
$ - 7 - 9 + 4 + 16$
Perform Like operations, which we get
$ - 16 + 20 = 4$

$(b)\,(37) + ( - 2) + ( - 65) + ( - 8)$
We apply the sign multiplication rule, then we get
$37 - 2 - 65 - 8$
We perform like operator
$37 - 75 = - 38$

Note: We have to be careful while applying the sign multiplication rule, we have to be careful and also while after we finish the operation, we should take the sign of the largest number amongst the given number for the resultant number.