Elementary Math Area

Introduction For elementary Math Area:

Elementary math area consist of area for square, rectangle ,triangle it is a menstruation part it is interesting in finding area of shapes and measuring length for given shapes. In menstruation area is an essential part for measuring the shape length. Measurement math consists also volume, surface area such as in higher grade for elementary math we have only fundamental shapes.

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Elementary Math Area For Square:


Area of a Square:
We know  square is a like rectangle in which its Length = Breadth.
The area of the square
= Length `xx ` Length
= (Length)2 = (Side)2
= a × a
= a^2

Example 1:
Find area of a square whose side is 12 cm.

Solution :
Side of the square, a = 12 cm
Area of the square, A = a^2
= a × a
= 12 × 12
= 144 sq.cm (or 144 cm2)
Example 2:
Find area of a square whose side is 14 cm.

Solution :
Side of the square, a = 14 cm
Area of the square, A = a^2
= a × a
= 14 × 14
= 196 sq.cm (or 196 cm2)

Area of Rectangle:
Length `xx` Breadth

Example 1 :
Length and breadth of a rectangle are 15 cms and 13 cms respectively. find its area.

Solution:
= Length `xx` Breadth
= l `xx` b
= 15 cm. `xx` 13 cm.
= 195 Sq. cm.

Example 2:
Find the area  of a rectangle whose length is 2m and breadth is 70 cm.

Solution :
Length of the rectangle, l = 2 m or 200 cm
Breadth of the rectangle, b = 70 cm
Area of the rectangle, A = l × b
= 200 cm × 70 cm
Area = 14000 sq.cm.

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Elementary Math Area For Triangle:


Area of a  triangle:
`1/2` × base × height

Example 1 :
In a triangle the length of sides containing  angles are 20 cm and 21 cm. Find its area.

Solution :
Let b = 20 cm and h = 21 cm
Area of the right triangle, A =1/2 bh
= `1/2` × 20 cm × 21 cm
= 210 sq.cm

Example 2 :
In a right triangle the length of sides containing the right angles are 15 cm and 20 cm. Find its area.

Solution :
Let b = 15 cm and h = 20cm
Area of the right triangle, A = `1/2` bh
=`1/2` × 15 cm × 20 cm
= 150 sq.cm

Rules for Elementary Algebra

Introduction to rules for elementary algebra:

Algebra is a system of written calculations that help us reason about numbers. At the very first, we should realize that algebra is a skill. The initial thing to note is that, in algebra, we use letters as well as numbers.  But the letters represent numbers.  And the rules of algebra match to the rules of arithmetic, but we write those rules using letters. Rules for elementary algebra is very basic in algebra, Now we are going to see about the rules for elementary algebra.

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Rules for elementary algebra part - I:


Property of zero

0 · x = 0
0 + x = x

Property of One

1 + x = 1
1. x = x

Identity Property

x · x = x
x + x = x

Redundancy Property

x · ( x + y ) = x
x + ( x · y ) = x

Commutative property

x · y = y · x
x + y = y + x

Associate Property

x · ( y · z ) = ( x · y ) · z
x + ( y + z ) = ( x + y ) + z

Distributive Property

x · ( y + z ) = ( x · y ) + ( x · z )
x + ( y · z ) = ( x + y ) · ( x + z )


Rules for elementary algebra part - II:


Properties of negation

a ( -1 ) = -a

-( -a ) = a

( -a ) b = - ( ab ) = a ( -b )

( -a ) ( -b ) = ab

-( a + b ) = ( -a ) + ( -b )

Properties of equality

If a + c = b + c, then a = b

Word Problems Elementary Level

Introduction:

The term word problem refers to the math exercise which has information about the problem in words rather than text. It is hard to translate the words into mathematical expression or equations. When it is done, then it is easy to solve those problems. But translation of those words to mathematical symbols or equation is hard. Understanding the given condition or situation in the word problem is more important than solving it. Without understanding the math word problems the solving work can’t be done. Elementary level word problems are easy to solve. The elementary level word problems involve basic arithmetic operations only. Those elementary level problems are not much complicated.

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Elementary level Word problems:


Example 1:

A fish tank contains 30 fish of which 5 are stationary. How many fish in the tank are moving?

Solution:

Here the total number of fish = 30

Number of stationary fish = 5

Numbers of moving fish = 30 – 5

= 25 fish

The answer is 25 fish.



Example 2:

A zoo has 18 Thailand elephants and 6 Indian elephants. How many elephants are there in the zoo?

Solution:

Number of Thailand elephants = 18

Number of Indian elephants = 6

Total number of elephants = 18 + 6

= 24 elephants.

The answer is 24 elephants.



Example 3:

Raja sent invitations to 60 relatives for a family get-together. Only 35 relatives came to the function. How many relatives did not come?

Solution:

Total number of invitations send = 60

Number of relatives came to function = 35

Number of relatives did not come = 60 – 35

= 25

The answer is 25.

More elementary level word problems:


Example 4:

Lokesh had brought 17 flowers from a Park last time. His mom wants Lokesh to bring 4 times as many this time. How many flowers will Lokesh bring this time?

Solution:

Number of flowers Lokesh bought last time = 17

He bought 4 times as many flowers this time,

Hence,

Number of flowers Lokesh bought this time = 17*4

= 68

The answer is 68 flowers.



Example 5:

There are 60 apple trees planted in 5 rows. How many apple trees are there in each row?

Solution:

Total number of trees planted = 60

Total number of rows = 5

Number of apple trees peer row = 60/5

= 12 trees

The answer is 12 trees.

5th Grade Math Variables

Introduction to 5th grade math variables:

In mathematics, 5th grade math variables are using addition and subtraction operation with variables. Single-symbol are called for variables are the normal, with x, y, and z being most common using in variables problem. Constants are generally denoted as a, b, c. In mathematics, constants and variables are usually set in an italic typeface.

Specific branches and applications of mathematics regularly have specific naming conventions for variables.

Meanings or variables with similar roles are regularly assigned consecutive letters. For example, x, y, and z is the three axes in 3D coordinates space are conventionally.

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Examples problems for 5th grade math variables:


1. Find the x value, for the given for single variable expressions.

18x + 2 = 38

Solution:

18x + 2 = 38

Subtract (2) with both sides,

18x + 2 – 2 = 38 – 2

18x = 36

Divide (18) with both sides,

18x / 18 = 36 / 18

x = 2.

The solution to the given expression in single variable x = 2.

2. Find the y value, for the given for single variable expressions.

4y + 4 = 20

Solution:

4y + 4 = 20

Subtract (4) with both sides,

4y + 4 – 4 = 20 – 4

4y = 16

Divide (4) with both sides,

4y / 4 = 16 / 4

y = 4.

The solution to the given expression in single variable y = 4.


More examples problems for 5th grade math variables:


3. Find the z value, for the given for single variable expressions.

5z + 5 = 30

Solution:

5z + 5 = 30

Subtract (5) with both sides,

5z + 5 – 5 = 30 – 5

5z = 25

Divide (5) with both sides,

5z / 5 = 25 / 5

z = 5.

The solution to the given expression in single variable z = 5.

More examples problems for 5th grade math variables:


4. Find the x value, for the given for single variable expressions.

6x - 2 = -38

Solution:

6x - 2 = -38

Add (2) with both sides,

6x - 2 + 2 = -38 + 2

6x = -36

Divide (6) with both sides,

6x / 6 = -36 / 6

x = -6.

The solution to the given expression in single variable x = -6.

Elementary Set Theory

Introduction to elementary set theory:

A set theory is a collection of elements or the items can be considered as a whole. If the set contains only a few items or elements, then the set can be defined by listing them in braces. For example: A = {1,2,3}. Now we are going to see about the elementary set theory.

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Elementary set theory:


Now we are going to see about the elementary set theory as follows,

Set and Sample Space:

The sets are the important part and the basic concepts in mathematics and probability. Sets are usually consists of collection of some elements.

Example of sample spaces:

Pick a card from a pack of 52 cards:

Sample space = {1, 2 ...52}, which is a infinite sample space.

Subset:

A subset is can be defined by some property of its elements.

For example, let P = {1,2,3,4}, and let Q = {2,}. Then Q can be defined as the set of all elements of P which are even, or in symbols:

Q ={x  `in` A |  x is even}.

The operation properties are given as follows,

The intersection operation has the properties are given as,

Commutative: A `nn` B = B `nn` A.

Associative: (A `nn` B) `nn` C = A `nn` (B `nn` C).

The union operation has several properties

Commutative: A `uu` B = B `uu` A.

Associative: (A `uu` B) `uu` C = A `uu` (B `uu`C).

Ordered pairs:

An ordered pair contains set of two elements that are arranged in a specified order. An ordered pair is usually written as (x, y).

Relations:

A relation R is on a set A, where A is simply a set of ordered pair of element of A.

Functions:

A function ‘f’ from the set X to the set Y is a rule given any element x of A, This concept is often expressed symbolically as f: X--->Y

Problems for elementary set theory:


Example 1:

A = {1, 2, 3, 4, 5, 6, 7, 8, 11, 12} B = {9, 10, 11, 12, 13). Determine the union and intersection of set A and B.

Solution:

The union of set is nothing but including both the set elements in a single set

(B `uu` C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, (B ∩ C) = {11, 12}.

Example 2:

P = {f, g, h, i, j, k, l} Q = {g, j, l, m, n}. Determine (P – Q) and compliment of C related to Q.

Solution:

The difference of the two sets P and Q are given as,

(P – Q) = {f, h, I, k}, Cc = {m, n}

Study Elementary Probability

Introduction to study elementary probability:

The elementary probability theory condition for all probability mass function (pmf) there is functions which give the probability in a divide random variable which is accurately corresponding to some of the value recognized. A pmf differs as of a common probability density function (pdf) in the values of a pdf, defined for the permanent random variables and not the probabilities as such desired.


How to study elementary probability:


The study of elementary probability function always defines as known in the relationship among the two such variables in a probability distribution function which is named as the "Probability Function". An elementary probability function assumes that the "variable" which indicates the values within the given range of such a random variable at its independent variable and "probability" defined as the dependent variable.

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Study the representation of probability function for elementary type:


An elementary probability function which relates the break up random variable is recognized as the "Probability Mass Function". In the sequence of a random variable the value of "X" assumes that the distinct set of values `x_1, x_2, x_3, ... x_n,` then the function "f" is defined by the f(xi) = P(X = xi) and that is called as the "Probability Function" or "Probability Mass Function". The pmf assigns a value for the required probability [P(X = xi)] in each of the possible values [xi] of the variable.

That gives the study of elementary probability value and the variable which represents the sequence of the distinct random variable which equals to some value. A study of discrete probability function f(x) defines the following properties.

f (xi) ≥ 0 is given by the probability for the variable to carryover a particular value which is always a positive real number.

Σ f (xi) = 1 [i = 1, 2, 3, ... ∞] The sum of the corresponding probabilities of all the given possible values and that suits the variable which represents the range of all the discrete random variable which may carry the value equal to One.

Solve Elementary Statistics Problems

Introduction of elementary statistics problem:

Data is a word in a plural form of the Latin word datum. Every part of our lives utilizes data in one form or the other. This extraction of significant information is study in a branch of mathematics called statistics. A step additionally by studying certain numerical representatives of the ungrouped data, also called measures of central tendency, namely, mean, median, mode and also range are under the elementary statistics only.

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About Elementary statistics


Elementary statistics is deals with the basic static calculations of data’s for finding the mean values etc... The word ‘statistics’ appears to have been taken from the Latin word ‘status’ meaning ‘a state (related to a political)’... Statistics deals with collection, organization, analysis, and Interpretation of data. ‘Statistics’ has held different meanings in different contexts, so that the calculation process is based on the meaning and data. Elementary statistics problems are mainly deals with the mean, median, mode, and range.

Example for elementary statistics problems


Let us see about the basic elementary stastistics problem below,
Example for Mean: what is the mean of 3, 8 and 5?
Add the numbers: 6 + 8 + 4 = 16
divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
so the Mean is 6
Example for Median: Find the Median of {12, 3 and 5}. Put them in order: {3, 5, 12}, the middle number is 5, so the median is 5.
Special Case: If there are two middle numbers (as happens when there are an even amount of numbers) then average those two numbers.
Find the Median of {12, 3, 5 and 2}. Put them in order: {2, 3, 5, 12}, the middle numbers are 3 and 5, the average of 3 and 5 is 4, so the median is 4.
Example for Mode: The number, which appears mostly, repeated in a set of numbers. In Set {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6.
Example for Range: is nothing but the difference between the lower and higher values.
In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9-3 equals 6.
Range can also mean all the output values of a function.