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NEGATIVE NUMBERS - HISTORY

Negative numbers were not widely accepted throughout history; it was rejected by some cultures.

China and India were the first to extend their understanding of numbers to Zero and negative numbers.

Negative numbers are typically challenging for many students to conceptualise. So having some knowledge into the history of negative numbers will help students to develop a positive approach to this area of mathematics.

Furthermore, by using the manipulative that the ancient Chinese used, learners can conceptualise the operation of negative numbers more deeply.

We can state at this stage, that negative numbers had a troubled past dating back to mid 1700. There were obstacles faced in trying to accept negative numbers:

People had difficulties understanding the fact that zero is not the smallest number and that there are numbers less than zero.

In Greece and other western nations for instance, mathematics needed to make geographical sense. Numbers were used as a way to measure space, and in these historical societies, people were very practical in their use of mathematics.

Trying to differentiate between an abstract number and the actual concrete number was quite challenging, and as such negative numbers in geometry could not work for them. They were right in the sense that you could not have a negative length and a negative area.

China, in 200 BC, revived the concept of negative numbers. Theirs was practical; they conceived it as a quantity to be subtracted from another quantity or as an amount yet to be paid.

They used red rods to show positive quantities or money received and black rods to show negative quantities or money taken away. Red and black rods ‘merge’ to show ‘mutual elimination’.

Lui Hui, a chinese mathematician, explained that in order to reckon with his rods, you would merge and mutually eliminate opposing colours. So a red and a black would mutually eliminate together and with that same notion you could mutually add when computing with them.

In computing with the chinese rods, two sign rules were used and they included working with negative numbers. They are:

‘‘When (in) adding, like signs add and opposite signs subtract.’’

E.g (4) + (5) like signs add

(4) + (-5) opposite signs subtract;

‘’When (in) subtracting, like signs subtract and opposite signs add.’’

E.g (4) - (5) like signs subtract

(4) - (-5) opposite signs add.

This ultimately brings out the negative number concept.

We will use the rules to create and calculate quantities with the red and black rods in our next article on calculating with negative numbers.

India, later on, also very readily accepted negative numbers. In the 7th century, Brahmagupta, an Indian mathematician, started using numbers outside of counting and measuring. He got into the abstract of maths and realised that an equation such as 3 minus 4 is solvable, and there could be a number as negative.

Brahmagupta, like the chinese, had his experimentation with negative numbers economically driven and can be applied to everyday life. So he referred positive quantities as a property or fortune and negative quantities as debt or loss.

He then came out with eleven statements or for rules about how you will compute with given quantities. He included rules with multiplication and division.Brahmagupta stated the rules for dealing with positive and negative quantities as follows:

A debt minus zero is a debt. A fortune minus zero is a fortune. Zero minus zero is a zero. A debt subtracted from zero is a fortune. A fortune subtracted from zero is a debt. The product of zero multiplied by a debt or fortune is zero. The product of zero multiplied by zero is zero. The product or quotient of two fortunes is one fortune. The product or quotient of two debts is one fortune. The product or quotient of a debt and a fortune is a debt. The product or quotient of a fortune and a debt is a debt.

We will explain further the statements in our next article on Negative Numbers.

Related sites:

https://gupea.ub.gu.se/bitstream/2077/24151/1/gupea_2077_24151_1.pdf

http://www.storyofmathematics.com/indian_brahmagupta.html

https://www.basic-mathematics.com/history-of-negative-numbers.html

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