- Comparing absolute values on the number line
- Compare and order absolute values
- Placing absolute values on the number line
- Comparing absolute values
- Testing solutions to absolute value inequalities
- Comparing absolute values challenge
- Interpreting absolute value
- Interpreting absolute value
- Negative numbers FAQ
Frequently asked questions about negative numbers
What are negative numbers?
Negative numbers are numbers that are less than zero. They have a negative sign () in front of them, like or . Negative numbers can represent things that are opposite, missing, or below something else.
For example, if we own apples and we eat of them, we can say that we have apples left. But if we own apples and we eat apples, we can say that we have apples left. That means we ate more apples than we had, or we owe apples to someone.
Negative numbers can also represent temperatures that are below freezing, heights that are below sea level, or debts that we owe.
How do we compare negative numbers?
Comparing negative numbers means finding out which one is smaller or larger than another one. It works the same as comparing positive numbers. Numbers farther to the right (or farther up, on a vertical number line) are greater than numbers that are farther left (or down) on the same line.
To compare negative numbers, we need to remember that the farther left a number is relative to on the number line, the smaller it is. For example, is smaller than 1, because is farther left of than is. We can write this as or as .
We can also use the opposite numbers to compare two negative numbers. For example, the opposite of is , and the opposite of is . Since positive is farther right of than positive is, . The negative numbers will have the opposite relationships, since they move left of instead. So is less than , which we write as .
A positive number is always greater than a negative number.
What is absolute value?
Absolute value is the distance of a number from zero on the number line. It is always a positive number or zero. We write it with two vertical bars around the number. For example, the absolute value of is , and the absolute value of is also . We can write this as and . The absolute value of is , since there is no distance between and itself.
The absolute value of a rational number is the same as the value of the number without the sign. For example, the absolute value of is , and the absolute value of is . We can write this as and .
Where do we use negative numbers in the real world?
Negative numbers and absolute value can help us describe and measure many things that we encounter every day. Here are some examples of where we use negative numbers and absolute value in the real world:
- We use negative numbers to show temperatures that are below freezing, like Celsius or Fahrenheit. We can also use negative numbers to show how much colder or warmer a place is than another place, like degrees difference or degrees difference.
- We use negative numbers to show heights that are below sea level, like meters or feet. We can also use negative numbers to show how much deeper or higher a place is than another place, like meters difference or feet difference.
- We use negative numbers to show debts that we owe, like or .
- We use negative and positive numbers to show movement in specific directions, like saying that we moved seconds in a video to mean that we went seconds backwards in the video. If moved seconds forward in the video, we could use positive .
The absolute value tells us the amount of the change in each case, but removes the information about the direction of the change. For example, the absolute value of a height could tell us its distance from sea level, but would not tell us whether the object was above or below sea level.
Want to join the conversation?
- I wonder why they didn't put practice questions?(9 votes)
- who invented negative numbers? are those the only times we use them?(3 votes)
- *In the seventh century, an Indian mathematician named Brahmagupta is said to be the first to write rules for negative numbers. He wrote about negative numbers in addition, subtraction, multiplication, and division!*(8 votes)
I’m wondering if negative numbers become “more negative” the further to the left of zero you go? Or are all negative numbers equal in “negativity” by virtue of being left of zero? My hunch is the latter, but some wording on an assessment I’m giving has me questioning this concept. Thanks for your help!(4 votes)
- Your first statement is correct, they get "more negative." Think about owing money, is owing 5 dollars the same as owing 10 dollars? No, most people would rather only owe 5 dollars than 10 dollars. With the logic of the second statement, how would that be different than positive numbers? You would not say all positive numbers are equal in "positivity" by virtue of being right of zero.(2 votes)
- I don’t know why they don’t put practice questions when its explaining a strategy or “explanation”(3 votes)
- I don't have a question about anything!(0 votes)