## Concept of math

**Introduction :**

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".

Source – Wikipedia.

Concept of math Covers:

Concept of math contains the following these fundamental operations,

1) Algebra

2) Fractions

3) Factoring

4) Arithmetic

**Algebra:**

Algebra is the partition of mathematics involving to the study of the policy of operations and relations, and the group and ideas happening from them, in cooperation with provisions, polynomials, equations and algebraic structures.

**Fractions:**

Fraction is described as the same amount of one complete thing. It can be symbolized as “x / y " where 'x' signifies the value known as numerator and 'y' signifies the value known as denominator and q not identical to zero. We can simply achieve these operations.

**Factoring:**

In common, the calculation of a countable value of monomials is represented as polynomials. The method of writing polynomials as an invention of two or more easier polynomials is symbolized as factorization.

**Arithmetic:**

Arithmetic is the oldest and generally fundamental division of mathematics, used by around everybody, for everyday jobs collection from easy day-to-day counting to higher science and business computation.

Example problems for concept of math:

**Example 1 for concept of math algebra:**

1) (j + 5) (j – 7)

**Solution:**

= (j + 5) (j – 7)

= j2 -7j + 5j– 35

**= j2 – 2j- 35**

**Example 2 for concept of math algebra:**

2) simplify algebraic expression: 6(a -2) + 5b - 2(a -b -4) + 6

**Solution:-**

Given 6(a -2) + 5b - 6(a -b -4) + 6

= 6a - 12 + 5b -6a + 6b +48 + 6

Groups like terms

**= 11b + 42**

**Example 3 for concept of math fraction:**

3) `1 / 3` + `1 / 5`

**Solution:**

Given `1 / 3` + `1 / 5`

= (1+1) / (3+5) [simplify fractions]

= `2 / 8`

= `1 / 4`

**Example 4 for concept of math algebra:**

**4) Factoring the certain polynomial by grouping: 3x3+6x2−3x−6**

**Solution:**

Given 3x3+6x2−3x−6

(3x3+6x2) and (−3x−6) both terms have a GCF

Taking out the GCF outside, we obtain

(3x3+6x2) + (−3x−6) = 3x2(x+2)-3(x+2)

Note that there is a common factor, x+2. So, Factor out (x+2).

By distributive law, we get

**3x3+6x2−3x−6=(x +2) (3x2-3).**

**Example 5 for concept of math algebra:**

4) Calculate 5 times 4.

**Solution:**

5 times 4 mean 5 multiplying with 4.

5 * 4 = 20

The other method of multiplication returning addition,

5 times 4 = 20

**5 + 5 + 5 + 5 + 5 = 20.**