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# Free A Game that Can be Used to Learn Algebra Essay Sample

From the basic definition, Algebra may be defined as that part of arithmetic whereby letters among other general signs/symbols are used in place of numbers and quantities in equations and formulas. Algebra concept on the other hand refers to the abstract idea that makes it public and widely recognized.

The drawing below enables one to solve mathematical problems associated with the use of algebraic equations. This is more of a game used to play with arithmetic since majority of students have over past, had mathematical problems brought about by confusion of algebra concepts. An appropriate name for this game is Algebraic Wizard. This is because it eases the calculation of algebra.

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When we add the values clockwise (a + b +c +d) is the same as adding them in an anticlockwise direction (d + c+ b +a). This is known as the associative characteristic used in addition of integers. However this property of distributive is not applicable to binary calculations involving subtraction and division. For example, if the value of a, b, c and d is 4, 5, 6, and 7 respectively, when we compute the sum, we obtain the value of 22. (4+5+6+7). The vice versa is true because of the distributive characteristic i.e. 7+6+5+4=22. However, when it comes to subtraction, the value obtained is totally different. For instance, 4-5-6-7=-14, which is not equal to the value obtained when we subtract the values in anticlockwise direction. For example, 7-6-5-4=-8. When it comes to the case of division, when the value of (a) is divided by the value of (b), the answer obtained will not be equal to the value obtained when the vice versa is done. a/b=4/5 while b/a=5/4. This therefore implies that the distributive property only applies to the addition of values but not subtraction or division.

When it comes to the commutative characteristic of the integers, the order in which the numbers are added does not affect the sum or rather the end result.  When it comes to multiplication, the commutativity is also applicable. This is however not applicable when it comes to multiplication of matrices. In addition, there is a distributive characteristic existing from the above integers. For example, (a+b)*c= (a*c) + (b*c). The multiplication sign is referred to as being distributive over the addition sign.

In the event of solving quadratic equations the above diagram is of great importance since it gives a hint on how to go about it. Quadratic equations are used and are applicable in life. It can be used to determine the population of a given area among other uses. When one is required to find the square of (a+b), the value obtained will be a2+2ab+b2. I.e. a (a+b) +b (a+b). when there is existence of a negative sign, (a-b)2 the value will be equal to a2-2ab+b2 obtained as follows: a(a-b)-b(a-b)

In summary the rules of the game are as follows:

1) When the integers are added either clockwise or anticlockwise, the answer obtained is the same.

2) When the same integers are multiplied as well, the value obtained is also the same, indiscriminate of the order in which the integers are multiplied.

3) When integers are added and then multiplied by another integer, a distributive characteristic is portrayed and the multiplication sign is considered to be distributive over the addition sign.

Usually quadratic concept of linear functions is applicable in three major parts in statistics. These areas are: computation of commission and demand, supply and equilibrium. Below is an illustration under the computation of commissions.

A salesperson daily wages are composed of fixed amount of variable component which is dependent on the number of units sold. He finds that when he sells ten units on a given day, he is paid \$ 600.whereas when he doubles his sales, he is paid an extra of \$ 100. One is therefore required to compute the daily fixed earnings of the salesperson. To solve this algebraic problem, we realize that ten units go for \$600 while twenty units go for \$ 700. We are therefore required to make a linear equation in form of algebra and this will be as follows.

Y=a+bx. Through replacement method, the value of y takes the \$600, while a and b remains unknown variables. The value of x takes the no of units sold. The equations that emerge are as follows.    \$600=a+10b as the first equation and \$ 700=a+20b. When we subtract the first equation from the second, we realize that \$100= 10b. This implies that the value of b will be definitely be 10, whereas through substitution, the value of (a) becomes 500. From this point, one can confidently come up with the daily fixed earnings.

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