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When you multiply two negative numbers, the result is always a positive number. This might seem counterintuitive at first, but it becomes clearer with some basic rules of arithmetic. Imagine you have the multiplication problem

• \(-2 \times -3\)

The result is \(+6\). Why is that? Think of it this way: multiplying by a negative number is like reversing direction. So, if you're heading in the negative direction and you "reverse" it twice (because there are two negatives), you're now heading in the positive direction.

Similarly, you can think of it as first considering what

• \(2 \times 3\)

would be, which is \(6\). Then, applying the two negatives changes the direction twice, bringing you back to positive \(6\).

Multiplication of negative numbers is consistent and is part of the foundational rules of arithmetic that apply to all numbers.

Adding negative numbers might feel tricky, but it's simple with some practice. Let’s consider adding two negative numbers:

• \(-2 + (-3)\)

When you add these, think of starting at zero on a number line and moving left two spaces to \(-2\). Then, from \(-2\), you move left three more spaces, ending at \(-5\). The movement to the left signifies the negative direction.

So, adding two negative numbers results in a more negative number. It's helpful to remember that:

• Adding a negative number is like subtracting a positive number.

Visualizing addition on a number line often helps practice understanding addition of negative numbers better.

Subtraction of negative numbers can sometimes be confusing, but a helpful way to think about it is by "taking away a negative," which is similar to "adding a positive." For instance, when you encounter an expression like:

• \(-5 - (-3)\)

you can interpret it as: starting at \(-5\) and removing \(-3\) moves you in the positive direction.

So the solution becomes:

• \(-5 + 3 = -2\)

Think of it like removing a negative burden; you’re merely advancing forward on the number line. The rule of thumb is "minus a negative equals a plus."

If we visually reflect on how subtraction of negative numbers is often the same as adding their positive counterparts, this understanding becomes intuitive and easy to apply.