Life and society as it is known today would not be the same if it were not for Mathematics and Calculation, absolutely everything we do today has already been calculated, quantified, analyzed and understood after equations, functions, limits, integral derivatives and other algebraic procedures, which have been developed by the different technologies available in any area.
Theories, hypotheses, laws, theorems, rules, have always implied calculations and accounts that have gone from the simplest to the most complex, and in mathematics and calculation we have something fundamental such as “The Rule of Signs“.
What do you need:
For this topic you will need:
- Blank paper.
- Pencil.
- Draft.
- Sharpener.
- A calculator.
- Dictionary (to support you in the definitions).
- Eager to learn from the most basic to the most intricate.
- Good memory.
Instructions
- All mathematical operations have certain symbols that indicate the procedure to perform, elements or factors to consider, as well as strict conditions that cannot be ignored. We will begin by defining the main mathematical symbols and in turn the concept of the fundamental operations of mathematics.
- First of all, let’s be aware that a sign is a visual representation of a meaning that may or may not imply an action to follow and that it can have many interpretations depending on the linguistic environment in which it is applied.
- THE SIGN (+): the symbol “+” from the Latin “magis” in the strict mathematical concept represents the action of adding, adding, adding, including or annexing. It is also used to define the nature of a number or quantity that can be presented in the following way: –9, –8, –7, –6, –5, –4, –3, –2, –1, 0 1 , 2, 3, 4, 5, 6, 7, 8, 9 Here we can notice how the correlation of the numeral sequence takes us from negative quantities (–) to positive quantities (+) passing through the number 0, in what is known as negative limits and positive limits when they tend to zero (0). Another very representative use of the plus sign “+” and the minus sign “–” (which we will define later) is in the construction of a Cartesian Plane or Coordinate Axis, in which the symbology will define the location of a point on the y-axis is what is known as Cartesian Coordinates, which for positive units “+” will have location above the “X” axis (abscissa) or to the right of the axis of the “Y”. And we cannot forget the perhaps most basic and fundamental reference that indicates the sign “+” which is the addition (sum) of elements in which one quantity is added to another increases its size, example: 2 + 2 = 4; 210 + 100 + 50 = 360
- THE SIGN (–): from the Latin “minus” represents the opposite of the meaning of the sign (+), implies the subtraction, subtraction or decrease of a quantity when affected by another under this sign. Subtraction is the second basic operation of mathematics. 10 – 5 – 3 = 2; 15 – 17 = – 2 In the graphic location within a Cartesian axis, the coordinate points with negative values (–) will be located to the left of the “X” axis (abscissa) and in the lower part of the axis. “Y”. Special care must be taken with the visual representation of this sign, for a symbol (–) the length is greater than for a dash sign (-), an error that is usually made when writing quantities on computers and transcriptions on paper and pencil. The symbol (–) is often related to losses, reductions, magnitude decreases, and to some extent it is very common to see that it is interpreted as a negative and counterproductive action, it is like the bad guy in the movie that everyone fears or the negative energy that everyone rejects. These interpretations or appeals that can be generated with the use of positive (+) and negative (–) quantities lead us to a very necessary point to understand many mathematical and physical phenomena such as the use of the equation of the line: Y = mx + b X = variable; y = variable; m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of It’s like the bad guy everyone fears or the negative energy everyone rejects. These interpretations or appeals that can be generated with the use of positive (+) and negative (–) quantities lead us to a very necessary point to understand many mathematical and physical phenomena such as the use of the equation of the line: Y = mx + b X = variable; y = variable; m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of It’s like the bad guy everyone fears or the negative energy everyone rejects. These interpretations or appeals that can be generated with the use of positive (+) and negative (–) quantities lead us to a very necessary point to understand many mathematical and physical phenomena such as the use of the equation of the line: Y = mx + b X = variable; y = variable; m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of These interpretations or appeals that can be generated with the use of positive (+) and negative (–) quantities lead us to a very necessary point to understand many mathematical and physical phenomena such as the use of the equation of the line: Y = mx + b X = variable; y = variable; m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of These interpretations or appeals that can be generated with the use of positive (+) and negative (–) quantities lead us to a very necessary point to understand many mathematical and physical phenomena such as the use of the equation of the line: Y = mx + b X = variable; y = variable; m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of m = slope of the line; b = independent term. Where when the slope (m) has signed values (–), negative slope, it is inclined downwards and when it has signed values (+), positive slope, it is inclined upwards, being located on a coordinate axis. This equation is a very important example of how they can influence the positive or negative assessment of the magnitude of a quantity or value, and it is the foundation for the realization of graphs (bar, linear, histograms, etc.) used in different areas of the industry as a tool for interpretation of phenomena.
- The Sign (=): in 1557 Robert Recorde (1510 – 1558) Welsh mathematician implemented for the first time the use of the symbol “equals” (=), defining it with the following expression: “Two things cannot be more equal than two parallel lines ”. The “equals” sign (=) in mathematics fulfills the function of indicating the final result or completion of an operation or procedure, it also serves as a reference point in operations to clear up unknowns and change signs. The following addition shows how adding two values after the “=” sign shows the end of the operation and the result obtained. 1600 + 2400 = 4000 After having clarified these fundamental basic terms in our topic, we will proceed to explain The Rule of Signs.
The Rule of Signs
When adding values with a positive sign, logic tells us that the result to be obtained will always be a higher value resulting from the union of the quantities in question, here there is no problem, a consensus was reached that for the quantities with a positive sign it would not be necessary to indicate its value with the use of the sign (+), this with the aim of simplifying the writing in mathematical operations and especially in large and complicated advanced calculation procedures.
In the following procedure we can understand the above: Positive quantity + positive quantity = largest positive number (+5500) + (+2500) = (+8000) Regardless of the quantities to be added, the same situation is maintained: (+1000) + ( +2500) + (+2500) = (+ 6000). Due to the agreement reached on the need not to indicate the sign (+) in positive quantities, it is possible to simplify the writing of the operation: 5500 + 2500 = 8000; 1000 + 2500 + 2500 = 6000. And in the case of subtraction or subtraction: (+ 250) – (+ 50) = 200; 250 – 50 = 200.
But the “logic” perhaps no longer seems so obvious when we have negative values (-) within the same addition or subtraction operation, such as: Negative value + negative value = negative number (- 100) + (- 50) =(-150). And It may look more abstract in subtraction operations: Negative value – negative value = negative number (-100) – (-50) = (-50).
Remember that the numbers that are added are known as addends and the result of the operation is called the sum.
From this remains the following rule and which defines our concept of the rule of Signs:
For The sum: The sum of two positive numbers gives a positive result to we can also see it like this, “my friend’s friend is my friend”. (+) + (+) = (+). Adding a positive and a negative value generates an unknown result. (+) + (-) = ? Adding a negative value with a positive one results in an unknown value. (-) + (+) = ? The sum of two negative values gives a negative result: (-) + (-) = (-).
In the case of multiplications and divisions, the rule is fixed and applies in the following strict manner, but it is easy to memorize: “My friend’s friend is my friend” + by + = + “My enemy’s enemy is my friend”- by – = + “The friend of my enemy is my enemy” + by – = -. “My friend’s enemy is my enemy.” – by + = -.
In the same way we can express it in the following way having the same meaning but it gives us another possibility to understand the subject: More for more, more; More for less, less; Less for more, less; less for less more
For quantities raised to a power there are also certain considerations that we must take into account to analyze how to easily learn the rule of signs: All powers raised to an exponent with an even number give us a value with a positive sign as a result of the operation. (+)(PAR) = positive value (4)(4) = 32 (-)(PAR) = positive value. (- 4)(4) = 32. In powers raised to an odd exponent, the resulting sign at the end of the operation is equal to the sign of the value of the base of the power. (+)(ODD) = +. 23 = 8. (-)(ODD) = (-2)3 = -8.
Regarding the Rule of Signs in the filing, the following is expressed:
- For a root with an odd index, the sign of the radicand is preserved.
- For a root with an even index and a positive radicand, two opposite numbers will result.
- In a root of even index and negative radicand it is not possible to have a resolution in the set of integers.
Tips
- Mathematics and calculus in general are subjects that generally create a lot of concern and generate great difficulty for the majority of students or interested parties who for one reason or another find themselves in need of applying it, without forgetting, of course, other subjects such as Physics, Chemistry among others.
- All these subjects have in common that most of their procedures, if not all, include some simple mathematical processes and others perhaps not so much that for their understanding it is necessary to understand basic concepts and tools such as the Chain Rule.
- A key to succeed in mathematics is the combination of perseverance, discipline and practice, a lot of practice, relying on some mathematical texts, and it is not a bad idea to go from the simplest to the most complicated and have a lot of patience.
- The signs (+) and (-) apart from what they refer to mathematics, have been related to many other fields, in the scientific, religious and even cultural fields, even thoughts have been classified as positive or negative.