Find −115+(−35) Write your answer as a fraction in simplest form.

The Correct Answer and Explanation is:

To solve the expression (-115 + (-35)), we can start by understanding how to combine negative numbers.

Step 1: Understanding the Operation

In mathematics, when you add a negative number, it is equivalent to subtracting that number. Therefore, we can rewrite the expression as follows:

[
-115 + (-35) = -115 – 35
]

Step 2: Performing the Calculation

Now, we need to calculate (-115 – 35). When subtracting a positive number from a negative number, we combine the absolute values of the two numbers and then apply the negative sign to the result.

Absolute values:
The absolute value of (-115) is (115).
The absolute value of (-35) is (35).

Adding these absolute values gives us:

[
115 + 35 = 150
]

Step 3: Applying the Negative Sign

Since we are dealing with negative numbers, we must attach a negative sign to the result:

[
-115 – 35 = -150
]

Step 4: Expressing as a Fraction

Now, we need to express (-150) as a fraction in simplest form. Any integer can be expressed as a fraction by putting it over 1. Thus:

[
-150 = \frac{-150}{1}
]

Step 5: Simplifying the Fraction

The fraction (\frac{-150}{1}) is already in its simplest form because there are no common factors between the numerator and the denominator (the denominator is 1, which has no effect on simplification). Therefore, the final answer is:

[
\boxed{\frac{-150}{1}}
]

Conclusion

In summary, we began by interpreting the addition of two negative numbers as subtraction. We then added the absolute values and applied the negative sign to arrive at (-150). Finally, we expressed the answer as a fraction, which is (\frac{-150}{1}). This understanding of operations with negative numbers is crucial in mathematics, especially when dealing with integers and fractions.