Final answer:
The simplified value of 10 + (-3) + (-7) is calculated by understanding that adding negative numbers is akin to subtraction. By subtracting 3 and then 7 from 10 sequentially, we find that the result is 0.
Step-by-step explanation:
To solve the mathematical problem completely and find the simplified value of 10 + (-3) + (-7), follow these steps:
- Start with the original expression: 10 + (-3) + (-7).
- Understand that adding a negative number is the same as subtracting its positive counterpart. Therefore, the expression can be re-written as: 10 - 3 - 7.
- Perform the subtraction from left to right: start with 10 and subtract 3, which gives you 7.
- Then, subtract 7 from the result you got in the previous step: 7 - 7 equals 0.
- The simplified value of the expression is therefore 0.
In algebra, these steps are guided by the rules of adding and subtracting positive and negative numbers. When two negative numbers add, the result is negative, whereas adding a negative number to a positive one reduces the positive number. If the positive number is larger, the result will be positive; if the negative is larger, the result will be negative.
In this case, since the positive number (10) is smaller than the sum of the absolute values of the negative numbers (-3 and -7), the overall result is zero.