Question

Find the sum. $$2+(-6)$$

Short answer

-4

Step-by-step solution

Identify the numbers

First, identify the two numbers which are 2 and -6. Here, -6 is a negative number.

Substitute the negative sign

The operation here is '2 + (-6)'. The '+' and '–' are essentially making a subtraction operation, so it can be rewritten as '2 - 6'.

Perform the subtraction

Subtract 6 from 2. As 6 is greater than 2, the result will be a negative number, -4.

Key concepts

Understanding Negative Numbers

When dealing with negative numbers, it's important to remember that they represent values less than zero. Think of them in terms of 'owing' rather than 'having'. For instance, if you have \( -6 \) it’s as if you owe 6 units, while \( 2 \) implies you possess 2 units. This becomes particularly relevant when performing arithmetic operations, such as addition and subtraction.

In the exercise \( 2 + (-6) \), you combine a positive number (2) with a negative number (-6). Visualizing this can be helpful: if you have 2 apples and owe 6, you are actually short of 4 apples, illustrating why the sum is negative. Always keep in mind that negative numbers represent a deficit or reduction, which affects the outcome of arithmetic operations.

Navigating Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These are the building blocks of mathematics and understanding them is crucial to solving more complex problems. Addition and subtraction are inverses of each other; one adds value while the other removes it.

For the operation \( 2 + (-6) \) we are adding a negative number, which is equivalent to subtraction. When adding a negative number, think of it as moving backwards on a number line. Starting from 2 and moving 6 steps back lands you at -4. This concept can be applied universally when mixing positive and negative numbers in addition or subtraction, making it easier to comprehend and solve the exercises accurately.

Mastering Subtraction

Tips for Subtracting Integers

Subtraction often trips up students when negative numbers enter the mix. The key is to recognize that subtraction is about finding the difference between values. When you subtract a larger number from a smaller one, as in \( 2 - 6 \), the result is negative because you're moving left on the number line, signifying loss or decrease.

In our exercise, converting \( 2 + (-6) \) into a subtraction problem simplifies it to \( 2 - 6 \). This demonstrates that adding a negative is the same as subtracting its absolute value. Always take a moment to establish which number is larger and whether your answer will be positive or negative based on this assessment. Remember, subtracting a negative is the same as adding the positive counterpart, so in cases with two negative signs, they cancel out to become a positive addition.