## Why does the sign change when you divide by a negative?

When you multiply both sides by a negative value you make the side that is greater have a “bigger” negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.

## What happens when you divide a negative by a negative?

Rule 3: a negative number divided by a negative number equals a positive number. Two negatives make a positive, so a negative number divided by a negative number equals a positive number. For example, -8 / -2 = 4.

## How does the inequality sign change?

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.

## What does it mean to divide by a negative number?

arithmetic fractions. I’ve learnt in school that a positive number, when divided by a negative number, and vice-versa, will give us a negative number as a result. On the other hand, a negative number divided by a negative number will give us a positive number. Given the following equations: −182=−9.

## Does the inequality sign change when taking square root?

Taking a square root will not change the inequality (but only when both a and b are greater than or equal to zero).

## Does squaring an inequality flip the sign?

For example, the function y = x2 is decreasing for x < 0. Hence, squaring inequalities involving negative numbers will reverse the inequality.

## Why when you divide a negative by negative it is positive?

When you multiply a negative by a negative you get a positive, because the two negative signs are cancelled out.

## What does a positive times a negative equal?

Rule 2: A negative number times a positive number equals a negative number. When you multiply a negative number to a positive number, your answer is a negative number. It doesn’t matter which order the positive and negative numbers are in that you are multiplying, the answer is always a negative number.

## When you divide a positive by a negative?

When you divide a positive number by a negative number then the quotient is also negative. When you divide two negative numbers then the quotient is positive. The same rules hold true for multiplication.

## What are some real life examples of inequalities?

Situation | Mathematical Inequality |
---|---|

Speed limit | Legal speed on the highway ≤ 65 miles per hour |

Credit card | Monthly payment ≥ 10% of your balance in that billing cycle |

Text messaging | Allowable number of text messages per month ≤ 250 |

Travel time | Time needed to walk from home to school ≥ 18 minutes |

## How do you simplify an inequality?

Summary. Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Multiplying or dividing both sides by a negative number.

## What are the rules for negative and positive numbers?

The Rules:

Rule | Example | |
---|---|---|

+(+) | Two like signs become a positive sign | 3+(+2) = 3 + 2 = 5 |

−(−) | 6−(−3) = 6 + 3 = 9 | |

+(−) | Two unlike signs become a negative sign | 7+(−2) = 7 − 2 = 5 |

−(+) | 8−(+2) = 8 − 2 = 6 |

## What happens when you add two negative numbers?

When you have two negative signs, one turns over, and they add together to make a positive. If you have a positive and a negative, there is one dash left over, and the answer is negative.