As you might have noticed, you write negative numbers with the same symbol you use in subtraction: the minus sign -. The minus sign doesn't mean you should think of a number like -4 as subtract four. After all, how would you subtract this? You couldn't—because there's nothing to subtract it from. We can write -4 on its own precisely because it doesn't mean subtract 4. It means the opposite of four.
Take a look at 4 and -4 on the number line:. You can think of a number line as having three parts: a positive direction, a negative direction, and zero. Everything to the right of zero is positive and everything to the left of zero is negative. We think of positive and negative numbers as being opposites because they are on opposite sides of the number line. Another important thing to know about negative numbers is that they get smaller the farther they get from 0.
On this number line, the farther left a number is, the smaller it is. So 1 is smaller than 3. When we talk about the absolute value of a number, we are talking about that number's distance from 0 on the number line.
Remember how we said 4 and -4 were the same distance from 0? That means 4 and -4 have the same absolute value. We represent taking the absolute value of a number with two straight vertical lines. This is read "the absolute value of negative three is three. Something important to remember: even though negative numbers get smaller as they get further from 0, their absolute value gets bigger. For example, is smaller than However, is bigger than -6 because has a greater distance from 0 than Using negative numbers in arithmetic is fairly simple.
There are just a few special rules to keep in mind. When you're adding and subtracting negative numbers, it helps to think about a number line, at least at first. Let's take a look at this problem: 6 - 7. Even though 7 is larger than 6, you can subtract it in the exact same way as any other number, as long as you understand there are numbers smaller than 0.
While the number line makes it easy to picture this problem, there's also a trick you could have used to solve it. First, ignore the negative signs for a moment. Just find the difference between the two numbers. In this case, it means solving for 7 - 6 , which is 1. Next, look at your original problem. Which number has the highest absolute value? In this case, it's Because -7 is a negative number, our answer will be one too: Because the absolute value of -7 is greater than the distance between 6 and 0 , our answer ends up being less than 0.
This is because the plus sign simply lets you know you're combining two numbers. When you combine a negative number with a positive one, the sum will be less than the original number—so you might as well be subtracting.
Whenever you see a positive and negative sign next to each other, you should read it as a negative. This is true whenever you're adding a negative number. Adding a negative number is always the same as subtracting that number's absolute value. Their proofs consisted of logical arguments based on the idea of magnitude. Magnitudes were represented by a line or an area, and not by a number like 4.
In this way they could deal with 'awkward' numbers like square roots by representing them as a line. For example, you can draw the diagonal of a square without having to measure it see note 2 below. Negative numbers did not begin to appear in Europe until the 15th century when scholars began to study and translate the ancient texts that had been recovered from Islamic and Byzantine sources.
This began a process of building on ideas that had gone before, and the major spur to the development in mathematics was the problem of solving quadratic and cubic equations. As we have seen, practical applications of mathematics often motivate new ideas and the negative number concept was kept alive as a useful device by the Franciscan friar Luca Pacioli - in his Summa published in , where he is credited with inventing double entry book-keeping.
In the 17th and 18th century, while they might not have been comfortable with their 'meaning' many mathematicians were routinely working with negative and imaginary numbers in the theory of equations and in the development of the calculus. Negative numbers and imaginaries are now built into the mathematical models of the physical world of science, engineering and the commercial world.
There are many applications of negative numbers today in banking, commodity markets, electrical engineering, and anywhere we use a frame of reference as in coordinate geometry, or relativity theory. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Register for our mailing list. University of Cambridge. All rights reserved. Although the first set of rules for dealing with negative numbers was stated in the 7th century by the Indian mathematician Brahmagupta, it is surprising that in the British mathematician Francis Maseres was claiming that negative numbers " In BCE the Chinese number rod system see note1 below represented positive numbers in Red and Negative numbers in black. An article describing this system can be found here. These were used for commercial and tax calculations where the black cancelled out the red.
The amount sold was positive because of receiving money and the amount spent in purchasing something was negative because of paying out ; so a money balance was positive, and a deficit negative. A debt minus zero is a debt.
0コメント