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Illustration of Negative Numbers (Integers)

Negative Numbers (Integers)

Negative numbers are real numbers that are less than zero.

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Reads at Grades K-2 Listens at K–3

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The story

The Number Less Than Nothing

Have you ever owed your friend a toy? Or felt the chilly air when the thermometer drops way, way down? That’s where I live. I’m the number you need when you go below the start, like taking an elevator down to a basement garage. I am the backward step in a board game, the money you owe, and the cold on a frosty winter day. For a long time, people weren't sure what to think of me. A number smaller than zero? It sounded a bit silly. But I was just waiting for everyone to see how helpful I could be. I am a Negative Number, and I’m part of a big, important family called the Integers.

My story starts a very long time ago. In ancient China, during the Han Dynasty around the 2nd century BCE, clever people were trying to solve math problems about money. They used red counting rods for the money they had, and black counting rods for the money they owed. Those black rods? That was me. It was the first time anyone wrote me down so clearly. Then, many years later in India, a brilliant mathematician named Brahmagupta wrote a book in the year 628. He gave me a job and rules to follow. He called me a 'debt' and figured out how to add, subtract, multiply, and divide with me. But even with my new rules, some people weren't ready for me. For centuries in Europe, many mathematicians called me 'fictitious' or 'absurd.' They just couldn't wrap their minds around a number that was less than nothing. I had to be patient and wait for the world to catch up.

And they did. Today, you can find me everywhere, and I’m not absurd at all. I help scientists measure freezing temperatures and tiny electrical charges. I help grown-ups with their bank accounts, showing them when money is spent. I even help rockets count down to launch: 3, 2, 1, 0… Blast off. I show that going backward or down is just as important as going forward or up. I help you understand a whole world of opposites. So the next time you see my little minus sign, remember my story. I'm proof that even an idea that seems strange at first can change the world for the better.

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About

Negative numbers are real numbers that are less than zero. They represent opposites, debts, or quantities that are removed or decreased.

First known use 202 BCE - 220 CE (circa)
First formal rules established 628 CE

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Question 1 of 4

Why did some mathematicians in Europe think negative numbers were 'absurd'?

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Negative Numbers (Integers)
The Number Less Than Nothing 0:00 / 0:00