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Adding zero to any number is a fundamental concept in arithmetic. When you add zero to any number, the number remains the same. Here’s how it works:

- When you see a problem like 0 + (-35), remember that adding zero does not change the value of the other number.
- It applies to all numbers, whether they are positive, negative, whole numbers, or even fractions.

For example:
- 5 + 0 = 5
- 0 + (-7) = -7
- 3/2 + 0 = 3/2

This property of zero can make addition problems easier to solve as you essentially don't have to do any adding; you retain the same number you started with.

Negative numbers represent values less than zero. They are indicated by a minus sign (-) in front of the number.

Here are some key points to better understand negative numbers:
- When you move left on the number line, numbers get smaller and thus more negative the further you go.
- A negative number added to zero gives you the negative number itself (as shown in 0 + (-35) = -35).
- When adding a negative number to a positive number, imagine combining debts and credits. For example, 3 + (-5) means you start with 3 and reduce it by 5, resulting in -2.

Negative numbers are integral in math, often used in temperature readings, financial calculations like debts, and various other real-world applications.

A number line is a visual representation of numbers placed along a straight line. It is a useful tool for understanding addition, subtraction, and the relationship between numbers.

Basic features of a number line:
- It has a point called zero which is the starting point.
- Positive numbers are located to the right of zero.
- Negative numbers are located to the left of zero.

For the example presented in the exercise (0 + (-35)), using a number line can help:
1. Start at zero.
2. Since you are adding -35, move 35 steps to the left.
3. You will end at -35.

This simple visualization confirms that 0 + (-35) indeed equals -35. Number lines are especially helpful for visual learners and for checking your work.