Let's break down the solution to the given equations step-by-step.
### For the First Equation: [tex]\( (+456) + (-983) \)[/tex]
1. Start with the first number which is [tex]\( +456 \)[/tex].
2. The problem requires adding a negative number, [tex]\(-983\)[/tex], to it.
3. Adding a negative number is the same as subtracting the positive of that number. So, this can be rewritten as:
[tex]\[
+456 - 983
\][/tex]
4. Perform the subtraction [tex]\( 456 - 983 \)[/tex]:
- Subtracting a larger absolute value from a smaller one results in a negative value.
- The absolute difference between 456 and 983 is:
[tex]\[
983 - 456 = 527
\][/tex]
- Since 983 is larger, the result is negative:
[tex]\[
456 - 983 = -527
\][/tex]
Thus, the result of the first equation is:
[tex]\[
(+456) + (-983) = -527
\][/tex]
### For the Second Equation: [tex]\( (-789) + (-8346) \)[/tex]
1. Start with the first number which is [tex]\( -789 \)[/tex].
2. The problem requires adding another negative number, [tex]\(-8346\)[/tex], to it.
3. Adding two negative numbers results in adding their absolute values together, then applying a negative sign:
[tex]\[
- (789 + 8346)
\][/tex]
4. Perform the addition:
[tex]\[
789 + 8346 = 9135
\][/tex]
5. Applying the negative sign to the sum:
[tex]\[
- (789 + 8346) = -9135
\][/tex]
Thus, the result of the second equation is:
[tex]\[
(-789) + (-8346) = -9135
\][/tex]
### Final Answer
The final results for each equation are:
1. [tex]\( (+456) + (-983) = -527 \)[/tex]
2. [tex]\( (-789) + (-8346) = -9135 \)[/tex]
Therefore, the solutions are:
[tex]\[
(-527, -9135)
\][/tex]
