Exhaustive Events

Introduction to exhaustive events:

Random Experiment:

Random experiment is an experiment in which outcome is not known in advance. For example, if a uniform unbiased coin is tossed, then the outcome may be tail or head.

Exhaustive Events:

All possible outcome of an experiment is called exhaustive events or exhaustive cases. In tossing a coin, either the head or tail turns up. There is no other possibility and therefore these are the exhaustive events.Let us see concepts and sample problems for exhaustive events. Two or more events that have the property that their union equals the sample space is called exhaustive event.

Exhaustive events covers all the possible outcomes that is sample space of the problem.


Exhaustive events:


Exhaustive events:

If two or more events together form sample space S then these events are said to be exhaustive events. I

Example 1:

In an experiment of throwing the die find the chance of exhaustive events.

Solution:

" n " throwing a die,

The events of getting an odd number and the event of getting an even number together form the sample space.

A = {The events of getting an odd number} = {1,3,5}


B = {The events of getting an even number} = {2,4,6}

A ? B = {1,2,3,4,5,6} = {S}

So, they are exhaustive events.

Example 2:

In an experiment of tossing three coins, consider the following events.

A : exactly one head appears,

B : exactly two heads appear

C : exactly three heads appear

D : atleast two tails appear

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

A = {HTT, THT, TTH}

B = {HHT, HTH, THH}

C = {HHH}

D = { TTH, THT, HTT, TTT}

The events A, B, C and D together form the sample space S.

That is, S = A ? B ? C ? D. Therefore A, B, C and D are called exhaustive events.


Exhaustive events:


Example 3:

In an experiment of tossing two coins, consider the following events.

A : exactly one head appears,

B : exactly two heads appear

C : exactly two tails appear

S = {HH, HT, TH, TT}

A = {HT, TH}

B = {HH}

C = {TT}

The events A, B and C together form the sample space S.

That is, S = A ? B ? C. Therefore A, B and C are called exhaustive events.

Example 4:

In an experiment of card game find the chance of exhaustive events.

Solution:

" n " getting a card,

The events of getting an diamond card,event of getting an heartine card,event of getting an spade,event of getting an club card together form the sample space (S).

Sample space(S) = 54.

A = {The events of getting an diamond card } = {13}

B = {The events of getting an heartine card }  = {13}

C = {The events of getting an club card }        = {13}

D = {The events of getting an spade card }     = {13}

A ? B ? C ? D = {54} = {S}

So, they are exhaustive events.

Function Substitution

Introduction to function substitution:

In mathematics, function substitution system is a method used to solve system of linear equations. A system of linear equation is a position of two or three linear equations by means of two or three variables in that order.

In the direction of answer system of linear equations, we contain to solve one of those equations for an exacting variable. The explain equation is now substituted in the other equation, and the value of the other variable is obtained. In this article we are going to study how to do function substitution to solve system of linear equations.

Substitution method:

For answer the systems of equations, function Substitution is used.

In the function substitution method of solving equations, from side to side a exacting variable, another variable can be solved if any one of the equations is solved.


Steps involved in solving function Substitution method:


For answer the system of linear equations using the method of function substitution, the subsequent steps are to be followed:

Step 1: Answer anyone of the equation to write one variable in terms of other variable.

Step 2: After that Substitute this in the second equation to obtain a single variable equation.

Step 3: The after that step is to answer the single variable equation to locate the value of that variable.

Step 4: Once we obtain the value of one variable, substitute the value in some of the equation to obtain the value of the second variable.

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Solving Problems based on function Substitution:


Example 1:

Answer the subsequent system of linear equations using the method of function substitution.

x - y = -5

3x+8y = -48.
Solution:

Step 1: Rearrange the first equation,
x - y = -5
y = x + 5

Step 2:Substitute this value for y into the second equation;
3x + 8(x + 5) = -48

Step 3:Expand and simplify the equation:
3x + 8x + 40 = -48
11x = -88
x = -8

Step 4:Substitute x back into one of the original equations;
-8 - y = -5
y = -3

Solution:  x = -8, y = -3

Example 2:

Answer the subsequent system of linear equations using function Substitution method:

x + y = 25

-4x + y = 10.
Solution:

Step 1: Rearrange the first equation,
x + y = 25
y = 25 - x

Step 2:Substitute this value for y into the second equation;
- 4x + (25 - x) = 10

Step 3:Expand and simplify the equation:
-4x + 25 - x  = 10
-5x = 10 - 25
-5x = -15

x = 3

Step 4: Substitute x back into one of the original equations;
3 + y = 25
y = 22

Solution: x = 3, y = 22

These are the examples for solving substitution method.

Geometric Introduction

Introduction to geometry:
Geometry is one of the main branch of mathematics it deals with the pre algebra concepts.Geometry is the study of object; It contains the 2 dimensional objects and three dimensional objects. Geometry is the study of these objects size and shapes .Each object have different sizes and different shapes. Without geometry we cannot easily find the object shapes and size of an object. Main concept of geometry is line, angles, Line segment.

Basic concepts of geometry introduction:

Line
Line segment
Angles
Rays
Introducing geometric two dimensional objects:

Square
Rectangle
Triangle
Circle
Three dimensional objects:

Cube
Cylinder
Prism
Sphere

Basic terms of geometry Introduction:


Basic terms in geometry:

Introduction for line:

Line is nothing but straight line curve; It is a infinite length of one dimensional object. It plot the doubled direction, that Mean we can draw the line both direct and inverse direction

Introduction for line segment:

Line segment mean nothing but a one-dimensional, curved finite length  of the single direction line is called line segment.

Two types of lines:

Horizontal line
Straight line is called horizontal line

Vertical line
When the lines are stand at 90 degree called as vertical line

Comparison of two lines also classified into many types:

Parallel line
When the two lines stands opposites to each other called parallel line example Ladder)

Perpendicular lines
When one vertical line stands on horizontal line that is called as Perpendicular line.(example alphabet letter “T”)

Intersection line:
When two lines are intersected each other (Example: Alphabet x)


Basic terms of angles in geometry Introduction:


Angles:

Angle mean nothing but a Inclination of two line is called angles

Angles are classified in different ways:

Right angle
Right angle mean nothing nut a angle between two lines is 90 degree

Acute angle
Acute angle mean nothing but angle between two line s is < 90 degree

Abtuse angle
Abtuse angle mean only one angle should be > the 90 degree

Straight angle:
It is nothing but Horizontal line. Angle between the line is 180 degree

Other angles using in geopmety:

Supplementary angle
Complementary angle
Vertical angle
Reflex angle

Math Mid Term Help

Introduction to math mid term help:

Math mid term help is the practice problems for math mid term exam. Mid term exam is conducted to check the performance of  students. Math mid term help covers many topics under mathematics. Below given some of examples and practice problems to math mid term help. Math lessons are used in real life situations such as counting the money, calculating time, measuring weight, measuring distance, etc. In this article math mid term help let us see practice problems and practice exam with solutions.


Example Problems - Math mid term help:


Example 1:

Calculate median of the values

55, 65, 23, 11, 77

Solution:

Arrange in ascending order

11, 23, 55, 65, 77

Median = 55

Example 2:

Find the factor of 17

Solution

We know that 17 is a prime number

All the prime numbers have only two factors

The two factors are 1 and the numbers itself

So the factor of the number 17 is 1 , 17 alone.

Example 3:

Find the area of triangle if its base is 20cm and height is 9 cm.

Solution:

The formula for area of triangle = ` (1 /2 xx base xxheight)`

Here, base = 20 cm

height = 9 cm

Therefore, area of triangle = `(1/2)xx20xx9 `

= `(1/2)xx 180`

= 90 cm^2.


Few More Example Problems - Math mid term help:

Example 4:

Evaluate  25 – 6 × 2 +6

Solution:

Here we use PEMDAS rule for solving the problem since it has various operations to perform

From this question there is no parenthesis exponents and division.

So we perform multiplication first.

6 × 2 = 12

25 -12 + 6

13 + 6

The answer is 19.

Example 5:

Find the value of a in the given

4a + 40 = 0

Solution:

Subtract 40 on both side

5a + 40 -40 = -40

5a = -40

a =-`40/5`

a = -8

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Practice problems - Math mid term help:


Below are some of the problems for practice with answers. You can work out and check with this answer

Practice midterm exam:

1. Add 256.234 + 210.325

2. Subtract 64.23 - 23.65

3. Find the median of the given term 101, 112, 108, 105, 123

4. Solve using PEMDAS rule. 12 +14 x2 - 22

Answer:

1. 466.559

2. 40.58

3. 108

4. 36

Pattern Math Terms

Introduction-pattern math terms:

A pattern, from the French patron, is a type of theme of recurring events or objects, sometimes referred to as elements of a set. These elements repeat in a predictable manner. It can be a template or model which can be used to generate things or parts of a thing, especially if the things that are created have enough in common for the underlying pattern to be inferred, in which case the things are said to exhibit the unique pattern.

Source: Wikipedia


Concept-pattern math terms:


In math, numeric patterns in algebra are pattern ready from numbers.

The numbers can be in a listing. Any math process likes addition, subtraction, multiplication, or division, you create the pattern.

Many of the patterns in math you observe will use addition. The same number will be additional to each number in the list to create the next number in the pattern math.

Example for pattern math terms:

2, 4, 6, 8, 10, 12, 14…

The pattern in math is to adding 2 always. The subsequently number is 16, then 18.


Example- pattern math terms:


Blue, black, orange and brown counters are arranged in a row. The brown counter is to the left of the orange counter and to the right of the blue counter. The black counter is to the left of the orange counter and not next to the blue one. What are the colors of the counters in the row from left to right?

Solution:

Given:

The brown counter is to the left of the orange counter and to the right of the blue counter.

Blue counter is to the left of brown counter

Brown counter is to the left of the orange counter

Given:

The black counter is to the left of the orange counter and not next to the blue one

Black counter is to the left of the orange counter

Black counter is not next to the blue counter

Black counter is between brown counter and orange counter.

So the order is: Blue, Brown, Black and Orange.

Equalities in Math

Introduction to equalities in math:

A state of two values in equal position is termed as equalities in math. The symbol ‘=’ is used for representing a equalities of values. On the other hand we can say that the ‘=’ symbol should match the right hand side to the left hand side.

Example, p=q. Here p, q are termed as equalities in math.


Equalities in math:


Equalities allow some basic operation of math.

Addition:

By adding a number on both sides of equality results another equality.

Example:

Consider an equality p+q. In this if we add the value x, then the equality becomes p+x=q+x.

Subtraction:

By subtracting a common value on both sides of equality results another equality.

Example:

Consider an equality p+q. In this if we subtract the value x, then the equality becomes p-x=q-x.

Multiplication:

If we multiply a number on both sides of equalities, then the result is same.

Example:

p.c = q.c

Division:

If we divide a number on both sides of equalities, then the result is same.

Example:

p `-:` c = q `-:` c


Example problems for equalities in math:


Example: 1

Which of the following is equal 6+10

a. 10+6

b .8+8

c. 2+10

d. 3+7

Solution:

Given equality is 6+10

6+10 = 16

The first choice 10+6 gives =16

Hence 6+10 = 10+6

Answer: 10+6

Example: 2

Which of the following is equal to 9 . 12 =

a) 15 . 2

b) 27 . 4

c) 10 . 12

d) 5.15

Solution:

Given 9 .12 = 108

First choice gives 15 . 2 =30

Second choice gives 27 . 4 =108

Answer: 27 . 4


Practice problems for equalities in math:


Problem: 1

Which of the following is equal to 144 `-:` 2

a) 158 `-:` 9

b) 162`-:` 4

c) 216 `-:` 3

d) 404 `-:` 10

Answer: 216 `-:` 3

Problem: 2

Which of the following is equal to 12 - 5

a) 5-2

b) 17-10

c) 10-8

d) 76-66

Answer: 17-10

Monomial Math Term

Introduction of monomial math term:

Polynomial:

In mathematics, an expression which contains variables and constants is known as polynomial. Based on the number of terms in the polynomial it is divided into three types. They are monomials, binomial and trinomials. In this article we will see the binomials and monomials.

Monomials: A monomial expression contains one term in it.

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monomial math term


Monomial:

In mathematics, a term monomial is an algebraic expression which has a single term as an expression. The word ‘mono’ gives the meaning of only one.

For example, 888y is considered as a monomial term. A single integer digit is also considered as a monomial. Here the monomial term is derived as a variable along with constant number.

For example,12000

Limitation in the term monomial:

A monomial expression does not contain a negative sign and fractions in it.
Possible chances in monomials:

If the  monomial multiplied with other monomial and the result is also monomial.
If the monomial  multiplied with constant and the result is also monomial.
We can multiply the  monomial  with other types of polynomial such as binomials, trinomials.

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Examples for monomial math term:


Example:1

What is the monomial term among the following.

a ) 12-9

b ) z1/4

c ) 56x + 1

d ) 13 y

Solution:

Step 1: The first choice has a negative term in it, so it is also not a monomial term.

Step 2: The second choice has a fraction in it, so it is also not a monomial term.

Step 3: The third choice has two terms in it, so it is also not a monomial term.

Step 4: The fourth choice has variable with constant, so it is called as the monomial term.

Ans: 13y

Example 2:

What is the monomial term among the following.

a ) z +x

b ) 58y

c ) 56 - y

d ) 4 x + 3y + 2

Solution:

Step 1: The first choice has two terms in it, so it is also not a monomial term.

Step 2: The second choice has a one term in it, so it is a monomial term.

Step 3: The third choice has two terms in it, so it is also not a monomial term.

Step 4: The fourth choice has three terms in it, so it is also not a monomial term.

Ans: 58y

Math 4th Grade Probability

Introduction to math 4th grade probability:

Generally probability is defined as the ratio of  the number do ways of an event occur to the total number of possible outcomes ,probability is used in the area of statistics ,finance ,gambling  and science .we are using some terms in probability now we are going to  discus about that terms and example problem on probability.

Terms- math 4th grade probability:

Probability
Event
Outcome
Experiment

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Probability:


It is used to measure how likely an event is.

Event:

It is defined as one or more outcomes

Outcome:

It is the result.

Experiment:

It is the situation we called as chance

Example - math 4th grade probability:

Suppose the rectangle is divided into 6 equal parts and those parts are colored using different colors, 3 pink, one yellow, 2 blue?

Solution:

Here the given problem is called as experiment, and outcome of those experiment are pink, yellow and blue

Now we can find the probabilities of each color

P (pink) =3/6

P (yellow) =1/6

P (blue) =1/6

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Example - math 4th grade probability:


A jar contains 45 marbles of different colors like magenta, yellow, white, it has 12 magenta, 19 yellow and reaming white, suppose you can choose the single marbles from the jar what is the probability for choosing magenta? A yellow marble? a White marble?

Solution:

Here the given problem is called as experiments and outcomes are red, yellow and white

Probabilities;

P (yellow) =19/45

P (red) =12/45

In these problem only the yellow and red and total count is given, there is no count for white so we can find the number of marbles in white color

Total number of marbles =yellow white + red

45=19+x+12

45=31+x

Subtract 31 on both sides we get the count of white marbles

45-31=x

So white marble =14

P (white) =14/45

Example - math 4th grade probability:

The below diagram is colored using different color find the probability of the green shaded portion?

Solution:

Here the rectangle is divided into 12 equal parts; here 5 equal parts are colored as green so the probability of the green color is 5/12

Help on 7th Grade Math

Introduction :

Mathematics is not something that we normally associate with sublime. The way mathematics is taught, it is a subject that many if not most people would prefer to avoid. The ability to state mathematical relationships as formulas greatly improves the ability to introduce abstractions. 7th grade math includes simple arithmetic operations, basic algebra and geometry. Let us see about help on 7th grade math. (Source: Wikipedia)


Example problems for help on 7th grade math:


Example 1: `2/8` of the birthday cake was eaten on john’s birthday day. The next day his sister ate `1/4 ` of what was left. John has to finish the cake, find the remaining cake.

Solution:

Given 2/8 is eaten by john and his sister ate `1/4`

The total amount of cake consider as 1.

` 2/8 + 1/4 = 4/8 = 1/2`

`1 - 1/2 = 1/2`

Therefore, the remaining cake is `1/2`

Answer: The remaining cake is `1/2`

Example 2: Find the coefficients of k in the following algebraic expressions: 4k2 – 2k +1

Solution:

Given 4k2 – 2k +1

The coefficient of k2 is 4

The coefficient of k is -2

Answer: The coefficient of k is -2

Example 3: Find the exponent of following the number: 64

Solution:

Given 64

64 = 6 * 6 * 6 * 6 = 36 * 36

= 1296

Therefore, the exponent of 64 is 1296

Answer: the exponent of 64 is 1296


Practice problems for help on 7th grade math:


Problem 1: Susan reduced her weight 0.45% when she exercised. Write the fraction for the given.

Problem 2: James, Scott and Peter are friends studying in 6th standard. In their class exam in algebra, James scored 10 out of 15. Scott scored 12 out of 15. Their average mark was 11. Find that how much Peter got.

Problem 3: Find the other angle. Given 45° and 75°


Solutions for help on 7th grade math:


Solution 1: `45/100` (or) `9/20`

Solution 2: Peter scored 33.

Solution 3: 60°

A Simple Expression for Math

Introduction to a simple expression for math:

A simple expression for math involves the process of solving simple algebraic expression. The simple algebraic expression in math is mainly used to calculate the unknown variable value with the basis of known values. Generally the variables represented in the simple math expression are nothing but an alphabetic letters. The following are the example problems for simple math expression with detailed solution.


Simple math expression example problems:


Example 1:

Solve the simple math expression.

-5(n + 2) = n + 9

Solution:

Given expression is
-5(n + 2) = n + 9

Multiplying the factors in left term
-5n - 10 = n + 9

Add 10 on both sides
-5n - 10 + 10 = n + 9 + 10

Grouping the above terms
-5n = n + 19

Subtract n on both sides
-5n - n = n + 19 -n

Grouping the above terms
-6n = 19

Multiply -1/6 on both sides
n = -`19/6 `

n = -`19/6` is the solution for the given expression

Example 2:

Solve the simple math expression.

-2(n - 3) - 4n - 1 = 3(n + 4) - n

Solution:

Given expression is
-2(n - 3) - 4n - 1 = 3(n + 4) - n

Multiplying the integer terms
-2n + 6 - 4n - 1 = 3n + 12 - n

Grouping the above terms
-6n + 5 = 2n + 12

Subtract 5 on both sides
-6n + 5 - 5 = 2n + 12 -5

Grouping the above terms
-6n = 2n + 7

Subtract 2n on both sides
-7n - 2n = 2n + 7 -2n

Grouping the above terms
-9n = 7

Multiply -1/9 on both sides
n = - `7/9`

n = - `7/9` is the solution for the given expression


Simple math expression practice problems:


1) Solve the simple math expression.

-7(n - 2) - 2n - 2 = 5(n + 2) - 5n

Answer: N = 0 is the solution for the given expression.

2) Solve the simple math expression.

-5(n - 3) - 2n - 3 = 2(n + 1) - 3n

Answer: n = `13/4` is the solution for the above given expression.

Math Probability for Grade 4

Math probability for grade 4 Introduction:

The grade 4 math probability is number of possible events are divided into total number of possible events this is called the math probability for grade 4. This grade 4 math probability is contains two types of distributions. That is the discrete and continuous distribution.  The general formation of the math probability for grade 4.

The probability of Event P (A) =` ("No. of possible events n(a)")/("Total no. of events n(s)")`

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Math probability for grade 4 Examples:


Dice Problems:

Math probability for grade 4 Example 1:

Throw a single dice; what is the probability of getting number 1?

Solution:

Total Number of possible = n (s) = {1, 2, 3, 4, 5, 6}

Total Number of possibles = n (s) = 6

The number of outcomes = n (a) = {6}

The possible outcomes = n (a) = 1

The probability of getting value = `1/6.`

Math probability for grade 4 Example 2:

Throw a single dice; what is the probability of getting number 4?

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

Total Number of possibles = n (s) = 6

The number of outcomes n (a) = {4}

The Number of possible outcomes = n (a) = 1

The probability of getting value =` 1/6.`

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Coins probability problems for grade 4:


Math probability for grade 4 Example 3:

Flip a coin and what is the probability of getting chance of one tail?

Solution:

Step 1:

Total number of outcomes = n (s) = {H, T} = 2

Step 2:

Tossing a coin with only one tail:

Number of possible event = n (a) = {T} = 1

Step 3:

Formula:

P (A) = n (a)/n (s)

Answer:

P (A) = `1/2.`

Convert into a decimal 0.5

The probability of one tail is 0.5 or Rounded 50%.

Math probability for grade 4 Example 4:

If throw a coin what is the probability of getting one head? The possible outcomes are:

Solution:

Step 1:

Total Number of Possible Events = n (s) = {T, H} = 2

Step 2:

Tossing a coin with only one head:

Number of possible events = n (a) = {H} = 1

Step 3:

Formula:

P (A) = n (a) / n (s)

Answer:

P (A) = `1/2` .

Convert into a decimal 0.5

The probability of one head is 0.5 or Rounded 50%.

Do My Math For Me

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. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. In this article we shall discuss about math problem with detailed solution.


Example problems:


Example 1: Isolate the variable x:

8x + 2y = 12.

Solution:

To isolate x in the given equation the following steps must be followed:

Step 1: Subtract the equation on both sides by 2y

8x + 2y - 2y = 12 - 2y

Step 2: Simplify the above equation it give the equation as:

8x = 12 - 2y

Step 3: Divide the equation both side by the value 8

8x / 8 = (12 - 2y) / 8

Now we get the isolated x value
x = (12 - 2y) / 8

Example 2: A car travels at the rate of 70 miles per hour for 3 hours and for next 3 hours at 80 miles per hour. Calculate the average speed of the whole journey?

Solution:

Step 1: To find the distance travel by the car use the formula

Distance of travel = Rate × Time
Total distance of travel = 70 × 3 + 80 × 3 = 210 + 240 = 450

Step 2:

Total hours of travel = 3+3= 6

Step 3: Using the formula for average speed find the average speed

Average speed of the car = Total distance travelled / Total time taken

=450/6

The average speed of the car journey was 75 miles per hour.


Practice problems:


Problem 1: Isolate the variable x in the equation

6x + 3y = 18.

Answer: x = (18 - 3y) / 6

Problem 2: A car travels at the rate of speed 60 miles per hour for 2 hours and for 3 hours at 70 miles per hour. Calculate the average speed of the whole journey?

Answer: The average speed of the journey was 66 miles per hour.

Geometric Math Templates

Introduction to geometric math templates:

In math, template defines model, shapes etc. In math, geometry is described as about the shapes and their properties. The geometry has a lengthy and legendary history and it is one of the fundamentals of the math. In mathematics, it plays a major role. In math, the geometry contains many templates. The geometric includes the shapes circle, triangle, sphere, cylinder, etc.. Now we are going to solve the problems for geometric math templates.


Examples – Geometric math templates:


Let see solve the problem using triangle shape in geometric math templates.

Example 1:

Work out the area of a triangle with height 8.8 cm and base of 17 cm.

Solution:

The formula for area of the triangle is  `1/2` (bxh)

= `1/2` (8.8 x 17)

= `1/2`(149.6)

=74.8

Hence the area of the triangle is 74.8 cm2.

Example 2:

Work out the volume of the sphere with the radius having 20.89 meter.

Solution:

We know the formula for finding volume of the sphere =` 4/3` П r3

Here П = 3.14, r = 20.89 meter and insert the value into formula we get

Volume =` 4/3` x 3.14 (20.89)3

Simplify the above we get

= ` 4/3`x 3.14 x 20.89 x 20.89 x 20.89

Simplify the above we get

=` 4/3` x28624.97

= 38166.20m3

These are examples in triangles and sphere for geometric math templates.


More examples – Geometric Math Templates:


Now we will solve the line shape problem in geometric math templates.

Work out is the slope of the geometric line which passes through (12.5, 10.2) and (15.6, 13.6)

Solution:

We know that the slope of a given line can be found as m =`(Y2-Y1)/(X2-X1)`

Here, x1 = 12.5 x2 = 15.6 y1= 10.2 y2 =13.6

m = `(13.6-10.2)/(15.6-12.5)`

= `3.4/3.1`

m =1.09

So the slope of the line is found to be 1.09.

Example 4:

The radius of a circle is 5.1cm2 inches.

Calculate is the area of the circle.

Formula= `Pi` r2

= 3.14*5.1*5.1

=81.67cm2

These are examples in line and circle for geometric math templates.

These are examples for geometric math templates.

That’s all about geometric math templates.

Free 4th Grade Math

Introduction about 4th grade math:

Study of basic math operations and math functions is called mathematics. In 4th grade math we can learn some basic math operation.

The basic arithmetic operations of mathematics are addition, subtraction, division, multiplication and placing values. The 4th grade math is deals with basic algebra.In this article we are discussing about 4th grade math with some example problems.

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Free examples problem for 4th grade math:

Free addition problems for 4th grade math:

1. Find the add value of the given numbers, using addition operation, 5 + 2 + 6

Solution:

Given numbers, 5 + 2 + 6

First step, we are going to add the first two numbers,

5 + 2 = 7

Then add third number with first two numbers of sum values,

7 + 6 = 13

Finally we get the answer for given numbers are 13.

2. Find the add value of the given numbers, using addition operation, 8 + 9 + 7

Solution:

Given numbers, 8 + 9 + 7

First step, we are going to add the first two numbers,

8 + 9 = 17

Then add third number with first two numbers of sum values,

17 + 7 = 24

Finally we get the answer for given numbers are 24.


Free subtraction problems for 4th grade math:


3. Find the subtract value of the given numbers, using subtraction operation, 5 - 2 - 6

Solution:

Given numbers, 5 - 2 - 6

First step, we are going to subtract the first two numbers,

5 - 2 = 3

Then subtract third number with first two numbers of subtracted values,

3 - 6 = -3

Finally we get the answer for given numbers are -3.

4. Find the subtract value of the given numbers, using subtraction operation, 2 - 8 - 8

Solution:

Given numbers, 2 - 8 - 8

First step, we are going to subtract the first two numbers,

2 - 8 = -5

Then subtract third number with first two numbers of subtracted values,

-5 - 8 = -13

Finally we get the answer for given numbers are -13.

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Free multiplication problems for 4th grade math:


5. Find the multiply value of the given numbers, using multiplication operation, 6 * 4 * 5

Solution:

Given numbers, 6 * 4 * 5

First step, we are going to multiply the first two numbers,

6 * 4 = 24

Then multiply the third number with first two numbers of multiplied values,

24 * 5 = 120

Finally we get the answer for given numbers are 120.

6. Find the multiply value of the given numbers, using multiplication operation, 2 * 8 * 3

Solution:

Given numbers, 2 * 8 * 3

First step, we are going to multiply the first two numbers,

2 * 8 = 16

Then multiply the third number with first two numbers of multiplied values,

16 * 3 = 48

Finally we get the answer for given numbers are 48.

Reciprocal Math Terms

Introduction for reciprocal:

The reciprocal number is usually specified the following technique. The number is n it is normally indicated the reciprocal is `1/n` . Another technique for the indicated the reciprocal number is x/y the multiplicative opposite of a fraction is `y/x` . The example reciprocal of 19 is `1/19` . We converse the description of reciprocal significance. Let us notice about reciprocal significance in this article.

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Reciprocal math terms:


1) Reciprocal equation on math terms:

Reciprocal equation one which remains unchanged in appearance when the reciprocal of the unidentified quantity is replacement for that quantity.

2) Reciprocal proportion on math terms:

Proportions such that, of four terms obtain in order, the first have to the second the similar ratio which the fourth has to the third, or the first has to the second the same ratio which the reciprocal of the third has to the reciprocal of the fourth. Thus, 2:5:: 20:8 appearance a reciprocal proportion, because 2:5:: 1/20:1/8.

3) Reciprocal quantities on math terms:

Reciprocal quantities are some two numbers which create unity as soon as multiplied collectively.

4) Reciprocal ratio on math terms:

The reciprocal ration is the ratio among the reciprocals of two numbers; as, the reciprocal ratio of 5 to 7 is that of `3/5` to `1/7` .

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Example problems for reciprocal math terms:


1) Solve the reciprocal term: `4/x` =`4/2`

Solution:

Here, taking reciprocals on both sides,

`x / 4` = `2/4`

x= 2*`4/4`

x=`8/4`

Answer: x=2

2) Calculate the reciprocal value for `12/9` .

Solution for reciprocal of a number:

Reciprocal is `12/9` = `9/12`

3) Calculate the Reciprocal value for `17/5` .

Solution for reciprocal of a number:

Reciprocal is `17/5` = `5/17`

4) Calculate the Reciprocal value for `14/9`

Solution for reciprocal of a number:

Reciprocal is `14/9` = `9/14`

5) Calculate the Reciprocal of the fraction `5/2`

Solution:

Reciprocal is

`5/2` =`2/5`

6) Calculate the Reciprocal of the fraction `4/7`

Solution:

Reciprocal is

`4/7` = `7/4`

7) Reciprocal of 75

Solution:

1 divided by a number specifies the reciprocal of that number.

Reciprocal of 75 = `1/75`

8) Calculate the Reciprocal of `1/39` .

Solution:

1 divided by a number specifies the reciprocal of that number.

Reciprocal of `1/39` = 39

9) Calculate the reciprocal of `63/59` .

Solution:

1 divided by a number specifies the reciprocal of that number.

Reciprocal of `63/59` = `59/63` .

Boolean Algebra

The two-valued logic in algebra is called the Boolean Algebra. It was first given by an English mathematician by name George Boole. The arithmetic operations which are performed on the Boolean quantities have only two outcomes either true or false, 0 or 1. And hence the Boolean logic forms the basis for the computation in binary computer systems.

Any algorithm or computer circuit can be represented using a system of Boolean equations. In the Boolean system the two possible values are zero and one. The Boolean algebra symbols used in Boolean operations are,  “.” which represents the logical operation “AND”, it is also denoted by ‘^’.  The symbol ‘+’ is used to represent the logical operation ‘OR’ which is also denoted by ‘v’. Logical negation or complement or not is denoted by  (~)or  (‘), for instance NOT A is denoted as A’ or  ~A (read as ‘negation A’)
The Boolean algebra Properties are:
Commutative law: A+B=B+A; A.B=B.A
Associative Law: (A+B)+C=A+(B+C); A.(B.C)= (A.B).C
Distributive Law: A(B+C)=(A.B)+(A.C); A+(B.C) = (A+B)(A+C)
Idempotence property: A+A=A; A.A=A
Involution Law: (A’)’= A
Law of Complements (negation): A+A’=1; A.A’=0
Boolean algebra theorems are as given below:
Simplification Theorems:
A.B+A.B’=0
(A+B)(A+B’)=A
A+AB=A
A(A+B)=A
(A+B’)B=AB
AB’+B=A+B
De-Morgan’s Theorems:
(A+B+C…..)’= A’B’C’…
(ABC…..)’=A’+B’+C’….
[f(A1,A2, A3…An,0,1,+,.)]’=f(A1’,A2’,A3’….An’,0,1,+,.)
Duality Property:
(A+B+C+….)D= ABC….
(ABC…)D= A+B+C…..
[f(A1,A2, A3…An,0,1,+,.)]D = f(A1’,A2’,A3’….An’,0,1,+,.)
Multiplying out and factoring theorem:
(A+B)(A’+C)=AC+A’B
AB+A’C=(A+C)(A’+B)
Consensus Theorem:
AB+BC+A’C=AB+A’C
(A+B)(B+C)(A’+C)=(A+B)(A’+C)
Absorption: A(A+B)=A; A+AB=A
Prove that A+BC=(A+B)(A+C)
Proof: Here to prove the given Boolean equation we expand the left hand side expression, apply distributive law, absorption law and idempotence (AA=A=A+A)
(A+B)(A+C)=AA+BA+AC+BC (using distributive law)
=A+BA+AC+BC   (using idempotence property)
=A+BC           (using absorption)


A Boolean function can be represented using a Truth table. The truth table for the logical operation AND would be,
AND    0      1
0       0      0
1       0       1
The truth table for the logical operation OR would be,
OR   0      1
0     0      1
1    1       1

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Boolean algebra Problems
Simplify: [[A(A+B)]’+B’A’]’
Solution: [[A(A+B)]’+B’A’]’
=[A.(A+B)]’’. [B.A’]’
=[A.(A+B)].(B’+A)
=[(A+AB)(B’+A)]
=A(1+B)(B’+A)
=A(1)(B’+A)
=A(B’+A)
=AB’+ AA
=AB’+A
=A[B’+1]
=A(1)
=A

Simplify (A+C)[AD+AD’]+AC+C
Solution: Given,
(A+C)[AD+AD’]+AC+C
= (A+C)A(D+D’) + AC + C       [using distributive law]
=(A+C)A+AC+C            [using complement identity]
=A[(A+C)+C] + C            [using associative law]
=AA+AC+C            [using distributive law]
=A+(A+1)C            [using idempotent, identity and distributive laws]
= A +C                [using identity twice]

Simplify (AB)’(A’+B)(B’+B)
Solution: Given,
(AB)’(A’+B)(B’+B)
=(AB)’(A’+B)            [using complement law and identity law]
=(A’+B’)(A’+B)            [using De-Morgan’s law]
=A’A’+A’B+B’A’+B’B        [using distributive law]
=A’+B’B                [on simplification, OR distributes over AND]
=A’                [Complement and identity laws]

7th Grade Math Need Help

Introduction to  7th grade math need help

7th grade math need help is about the problems and chapters of math that are studied and revised in the grade 7. 7th grade math need help  involves chapters like addition, subtraction, multiplication and division, fractions, decimals, measurements, area, volume, surface area, statistics, word problems, scientific notation etc.These topics will be simpler and easier one to learn and to perform calculation with the problems . 7th grade math need help will be more interesting one to work out the problems.


Examples on 7th grade math need help


Add the six digit number 8 4 57 1 2 + 1 2 4 2 5 1
Solution

8 4 5 7 1 2

1 2 4 2 5 1 +

----------------

9 6 9 9 6 3

----------------

2. Subtract `3/7`  - `1/3`

Solution

Here the denominators are different

So we have to find the LCM

The LCM of 7, 3 = 21

` (3xx3)/ (3xx7)` = `9/21`

`(1xx7) / (3xx7)` = `7/21`

Now we subtract

`9/21- 7/21`

`(9-7)/21`

`2/ 21` is the solution.

3. Find the area and perimeter of the rectangle if length is 9 cm and width is 6 cm.

Solution

Length of the rectangle = 9 cm

Width of the rectangle = 6 cm

Formula to calculate the area of the rectangle = length * width

So

Area of the rectangle given = 9 * 6

= 54 square centimeter

Perimeter of the rectangle = 2(length + width)

= 2 (9 + 6)

= 2(15)

= 30 cm

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More problems on 7th grade math need help


4. Find the area and perimeter of a square of the side a = 10cm

Solution

The side of the square = 10 cm

Formula to calculate the area of the square = `a^2` or (side * side)

Area of the square = 10 * 10

= 100 square centimeter.

Formula to calculate the perimeter of the square is 4* side

Perimeter of the given square = 4 * 10

= 40 cm

5. Find the number suffixes of the series given 35, 40, 45, 50, 55

Solution

The given series is 35, 40, 45, 50, 55

In this series the number is increased with 5

So the number suffixes of this series is 60, 65 and goes on

Math 8 Inequalities

Introduction to math 8 inequalities:

In mathematics, an inequalities is a statement about the relative size or order of two objects or about whether they are the same or not.

· The notation a < b means that a is less than b.
· The notation a > b means that a is greater than b.
· The notation a ≠ b means that a is not equal to b.
In this article we shall discuss about math 8 inequalities. (Source: wikipedia)

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Math inequalities example problem


Example:

Solving the inequalities 4x – 8 > 2x +10

Solution:

The given inequalities is

4x – 8 > 2x +10

Adding the 8 on both side of inequality equation

4x -8+8> 2x +10+8

4x>2x+18

Subtract 2x on both side of the inequality equation

2x>18

Simplifying the x

x>18/2

x>9

Example:

Solving the following inequality equation -3< 4(x+3)-3<16

Solution:

Given inequality equation is

-3< 4(x+3)-3<16

Multiply the factor values for given equation

-3<4x+12-3<16

-3<4x+9<16

Subtracting nine on both sides of inequality equation

-3-9<4x+9-9<16-9

-12<4x<7

Divide by 4 for all terms

-3<x<1.75

Conclusion:

The solution includes all real number value the interval is (-3, 1.75)

Example:

Solving the following inequality equation -2< 4(x+6)-3<10

Solution:

Given inequality equation is

-2< 4(x+6)-3<10

Multiply the factor values for given equation

-2<4x+24-3<10

-2<4x+21<10

Subtracting 21 on both sides of inequality equation

-3-21<4x+21-21<10-21

-24<4x<-11

Divide by 4 for all terms in equation

-6<x<-2.75

Conclusion:

The solution includes all real number value the interval is (-6, -2.75)

Example:

Solving the inequality 2x – 6 > 2x +12

Solution:

The given inequality is

2x – 6 > 2x +12

Adding the 6 on both side of inequality equation

2x -6+6> 2x +12+6

2x>2x+18

Subtract 2x on both side of the inequality equation

2x>18

Simplifying the x

x>18/2

x>9

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Math inequalities practice problem

Problem:

Solving the inequalities 2x – 8 > 2x +8

Answer:

x>10

Problem:

Solving the inequality 2x – 8 > 2x +8

Answer:

The solution includes all real number value the interval is (-2, 1.75)

Transposing Math Functions

Introduction to transposing math functions:

            Transposing math functions involves the process of interchanging or converting one form of the given function into another form. For example the non linear function is transposed into linear form and the polynomial function is converted into normal function form. The math functions mainly deals with linear and non linear functions. Transposing of linear and nonlinear functions is carried out below with the help of certain operations. The following are the example problems for transposing math functions.

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Transposing math functions example problems:

Example 1:

Transpose the given math functions and find the coefficient value.

Sqrt (3 u + 1) = u - 3

 

Solution:

Given equation is
sqrt (3 u + 1) = u - 3

Let us squaring on both sides, then the above equation becomes 
[sqrt (3 u + 1) ] ² = (u - 3) ²

Solve the above equation 
3 u + 1 = u ² - 6 u + 9

Write the above equation in factor form. 
u ² - 9 u + 8 = 0

The above form is a quadratic equation with 2 solutions 
u = 8 and u = 1

Example 2:

Transpose the given math functions and find the coefficient value.

                    f(u) = u ³ – 48u + 5

Solution:

Given function is

f(u) = u ³ – 48u + 5

The math function of f is the set of all real numbers. The derivative f ' is given as

f '(u) = 3 u ² - 48

f '(u) is defined for all real numbers. Let us now solve f '(u) = 0 

3 u ² - 48 = 0

Add 48 on both sides,

 3 u ² – 48 + 48 = 48

    3 u ² = 48

       u ² = 16
u = 4 or u = -4

Since u = 4 and u = -4 are the coefficient value.

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Transposing math functions practice problems:

1) Transpose the given math functions and finds the coefficient value.

                      u ² – 4u + 13 =  0

Answer: u = 2 + 3i or u = 2- 3i.

2)  Transpose the given math functions and finds the coefficient value.

               2 u ² + u - 6 = 0

Answer: u = -2 or u = 3/2

Perimeter Problems in Math

Introduction about perimeter:

In math, perimeter can be calculated for 2D and 3D shapes. The length of the boundary of any closed figure is called perimeter of that shape. The perimeter is expressed in units. In this article we shall see how to calculate the perimeter of basic 2D shapes with example problems.

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Math perimeter Formulas to solve problems:


Square:

Math Formula:

Perimeter of the square (P) =4 x a units

Rectangle:

Math Formula:

Perimeter (p) =2(l x w) units

Circle:

Math Formula:

Circumference (perimeter) of the circle = 2pr units

( r is the radius of the circle)

Triangle:

Math formula:

Perimeter of equilateral triangle (P) =3 a units

a – side length

Kite:

Math formula:

Perimeter of kite (P) = 2a + 2b units

a , b – side length.

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Perimeter problems in math -Example problems:


Square:

The square has the side length 7cm.find the perimeter of the square.

Solution:

Given:

a= 7 meters

Perimeter of the square = 4 x a

=4 x 7

Perimeter of the square = 28 meters

Rectangle:

The rectangle has length and width 5cm and 4cm respectively. Find the perimeter of the rectangle.

Solution:

Given:    Length= 5 meters, Width =4 meters

Formula:

Perimeter of the rectangle   = 2(l + w)

=2(5+ 4)

= 2 (9)

Perimeter of the rectangle = 18 meters

Circle:

The radius(r) of a circle is 10 inches. Find the circumference (perimeter) of that circle?

Solution:

Given: r = 10 inches

Formula:

Circumference of the circle = 2pr.

= 2 x 3.14 x 10

Circumference of the circle = 62.8 inches

some more example problems:

Triangle:

Find the perimeter of equilateral triangle whose side 14 cm.

Solution:

All sides of equilateral triangle area equal.

Side of triangle, a = 14 cm

Formula:

Perimeter of equilateral triangle (P) = 3a

= 3 x 14

Perimeter of equilateral triangle = 42 centimeters

Kite:

The kite has length 8cm and width 4 cm. find the perimeter of the kite.

Solution:

Given:

Length (a) = 8 cm

Width (b) = 4 cm

Perimeter of kite = 2a + 2b

= 2 x 8 + 2 x 4

= 16 + 8

= 24 centimeters