Elementary Math Estimation

Introduction to elementary math estimation:

In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruence’s belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. (Source: Wikipedia)

Types of Elementary Math Estimation:

There are four types of basic theory are mainly used in the elementary number theory; these types are classified according to the representation of the number. It will be shown as below,

Addition
Subtraction
Multiplying
Division
In elementary math to estimation it very easy to learning to study. And solve it easy. There are four steps are used in the elementary estimation of the math problems they are solved in the example problems in given below.

Example Problem for Elementary Math

Example 1:

Estimation the example of adding two numbers 163 and 13

Solution:

Let us write the given problem as 163 + 13.

Add the number 163 and 13 we get the sum as,

163 + 13 =176

Therefore, the solution for adding 163 + 13 is 176.

Example 2:

There are 56 peoples travelling in a bus. 17 of them left from the bus in one stopping. Estimation how many people will be left in the bus?

Solution:

Total number of peoples = 56

Number of peoples left from the bus in one stopping = 17

Number of peoples left in the bus = 56 - 17

= 39

Example 3

Estimation the multiplying two numbers 31 and 27

Solution:

The given two numbers 31 and 27

We need to find the product of two numbers

By multiplying 31 and 27

We get 837

So the answer is 837

Problem 4:

Estimation to divide 400 / 4

Solution:

100(quotient)

----

4)  400

400 -

---------

0(remainder)

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Practice Example Problem for Elementary Math

1. Estimation of adding 33 and 70

Key: 103

2. Estimation of Subtract 119 and 9

Key: 110

3. Estimation of Multiplying 29 by 20

Key: 580

4. Estimation of Divided 68 by 7

Key: 9.71

Number Theory and Inequalities

Introduction for inequalities and number theory:

           Number theory is the branch of the pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. Number theory may be subdivided into the several fields, according to the methods used and the type of questions investigated. These are the somewhat older terms, which are no longer as popular as they once were. Inequalities are the statement about the relative size or order of two objects or about whether they are the same or not.


Number Theory and Inequalities:-examples for Number Theory:

Ex 1:

Let a sequence can be defined by a1 = 1, a2 = 1, an = an–1 + an–2 for n > 2. Find the sequence.

Sol:

a1 = 1, a2 = 1an = an–1 + an–2 for n > 2

a3 = a2 + a1 = 1 + 1 = 2

a4 = a3 + a2 = 2 + 1 = 3

a5 = a4 + a3 = 3 + 2 = 5

? The sequence is: 1, 1, 2, 3, 5,...

Ex 2:

 Find the common difference and the next three terms of the A.P. 1, 4, 7, ...

Sol:

The common difference = 4 – 1 = 3

The next three terms are 7 + 3 = 10, 10 + 3 = 13

13 + 3 = 16

Integers:

Ex1:

The numbers 0, 1, -1, 2, -2 … are called integers

 1, 2, 3 … are called positive integers

 -1, -2, -3… are called negative integers. The collection of all integers is denoted by the letter Z. Thus Z = {…, -3, -2, -1, 0, 1, 2, 3…}.

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Number Theory and Inequalities:-examples for Inequalities:

 Solve the inequalities - x2 + 3x - 2 > 0

Sol:

- x2 + 3x - 2 > 0 ? - (x2 - 3x + 2) > 0

? x2 - 3x + 2 < 0

? (x - 1) (x - 2) < 0

On equating the factors to zero, we get x = 1, x = 2 are the roots of the quadratic equation. Plotting these roots on number line and making positive and negative alternatively from the right most part we get the corresponding number line as given below.

The three intervals are (- 8, 1), (1, 2) and (2, 8). Since the sign of (x - 1) (x - 2) is negative, select the interval in which (x - 1) (x - 2) is negative. ? x ? (1, 2)

Practice Problem for Inequalities Theory:

Solve : 4x2 - 25 = 0

Answer: Thus the solution set is (- 8,- 5/2 ] ? [5/2 , 8)