Table of Contents

- 1 Why is negative multiply negative equal to positive?
- 2 Why do you flip the sign?
- 3 What does a negative times a negative make?
- 4 Do you flip the inequality sign when multiplying by a negative number?
- 5 How do you reverse the position of negative numbers?
- 6 Why was the inequality sign on the number line reversed?

## Why is negative multiply negative equal to positive?

Each number has an “additive inverse” associated to it (a sort of “opposite” number), which when added to the original number gives zero. The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.

## Why do you flip the sign?

The main situation where you’ll need to flip the inequality sign is when you multiply or divide both sides of an inequality by a negative number. To solve, you need to get all the x-es on the same side of the inequality.

**Why do you reverse the inequality?**

Starts here2:40Why do we flip the inequality sign sometimes? – YouTubeYouTubeStart of suggested clipEnd of suggested clip47 second suggested clipSo in order to keep it true. We have to reverse the inequality. So every time we multiply or divideMoreSo in order to keep it true. We have to reverse the inequality. So every time we multiply or divide both sides by a negative number. We have to reverse the inequality.

**What happens when you multiply a positive to a negative?**

When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive. Now we have two negative numbers, so the result is positive.

### What does a negative times a negative make?

Why a negative times a negative is a positive.

### Do you flip the inequality sign when multiplying by a negative number?

Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa.

**Do you flip the inequality sign when multiplying?**

Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign. This means that if you had a less than sign <, it would become a greater than sign >.

**Does multiplying by a negative change the inequality?**

Multiplying or dividing both sides by a negative number reverses the inequality. This means < changes to >, and vice versa. For example, given that 5 < 8 we can multiply both sides by 6 to obtain 30 < 48 which is still true.

## How do you reverse the position of negative numbers?

But negative numbers should be at the left hand side of so we reverse its position by rotating it 180 degrees from any point of rotation (for example, 0). The resulting figure is shown in Figure 3. Notice that the blue and red points changed order and that the blue point is now at the left of the red point.

## Why was the inequality sign on the number line reversed?

Notice that the blue and red points changed order and that the blue point is now at the left of the red point. Therefore, VALUE OF BLUE POINT< VALUE OF RED POINT. That is, why the inequality sign was reversed. Summarizing, multiplying an inequality by a negative number is the same as reversing their order on the number line.

**How to multiply an inequality by a negative number?**

Summarizing, multiplying an inequality by a negative number is the same as reversing their order on the number line. That is, if and are real numbers, and , then . Our summary above is actually a mathematical theorem. The proof of this is shown below. It is a very easy proof, so, I suppose, that you would be able to understand it.

**What is the geometric consequence of multiplying every number on the line?**

If we multiply every number on the number line by , the geometric consequence would be a number line with negative numbers on the right hand side of , and positive numbers at the left hand side of as shown in Figure 2. Figure 2 – Afer multiplying all numbers on the number line by -1