Inequality in Math

Introduction to Inequality in math:
In math, inequality is a statement in relation to the relationship of a size or order of two items. In mathematical term, if the reason of the inequality is the equivalent for the all ideals of the variables for which are the members are distinct, and then the inequality is known as "unqualified" inequality. In this article we are going to see inequality examples.

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Example problems for Inequality:


Example 1:

Solve the inequality 2x+7 < 13.

Solution:

Given, inequality is 2x+7 < 13.

Subtract 7 with both sides, 2x+7-7 < 13-7

=>    2x  <  6

Divide 2 with both sides, `(2x)/(2)` < `(6)/(2)`

=> x < 3

The answer is, x < 3.

Example 2:

Solve the inequality 3x-2 > 16.

Solution:

Given, inequality is 3x-2 > 16.

Add 2 with both sides, 3x-2+2 > 16+2

=>    3x  >  18

Divide 3 with both sides, `(3x)/(3)` > `(18)/(3)`

=> x > 6

The answer is, x > 6

Example 3:

Solve the inequality x+3 `>=` 5.

Solution:

Given inequality is, x+3 `>=` 5.

Subtract the number 3 with both sides of inequality,

(x+3) - 3 `>=` 5 - 3

x  `>=` 2

The answer for this example is, x  `>=` 2.

Example 4:

Solve the inequality 7-x `>=` 8.

Solution:

Given inequality is, 7-x `>=` 8.

Subtract the number 7 with both sides of inequality,

(7-x) - 7 `>=` 8-7

-x `>=` 1

Multiply (-1) with both sides of an equation,

(-1) (-x)  `>=` 1 (-1)

When we doing this process, we need to change the symbol `>=`with `<=`.

Therefore, we get, x `<=`-1

The answer for this example is, x `<=`-1.

These are few examples in math inequality.

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Practice problems for Inequality:


Practice problem 1:

Solve the inequality x+3 < 2.

Answer: x < -1

Practice problem 2:

Solve the inequality 2-x > 0.

Answer: 2 > x

Practice problem 3:

Solve the inequality 3-x `>=` 5.

Answer: x `<=` -2

That's all about Inequality in math.

Math Assessments Geometry

Introduction to math assessments geometry:

Educational assessment is the process of documenting, usually in measurable terms, knowledge, skills, attitudes and beliefs. Assessments can focus on the individual learner, the learning community , the institution, or the educational system as a whole. (Source - Wikipedia)
In this article of math assessments geometry, math assessments questions and answers related to geometry are given. In addition, practice problems for math assessments are given.

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Math geometry assessments questions with answers:


1) Find the Circumference of a circle with radius 23 cm.

Solution:

Circumference of circle  = 2`pi`r

= 2 (3.14) 23

= 144.44 cm

2) Find the midpoint of the line joining ( 3, 7) and ( 6, 11 )

Solution: Given x1 = 3   x2 = 6

y1 = 7  y2 = 11

Midpoint =  ( `(x_1 + x_2)/2` , `(y_1 + y_2)/2` )

=  ( `(3 + 6)/2` , `(7+11)/2` )

=  ( `9/2` , `18/2` )

=  `( 4.5, 9 )`

3) Find the area of a square of side length 33.7 cm

Solution:

Area of a square  =  a^2

= 33.72

= 1135.69 cm2

4) Find the volume of cone given the radius is 11.4 cm and height is 12.7 cm.

Solution:

Volume of cone = 1/3 `pi` r2 h cubic units.

= 1/3  (3.14) * 11.42 * 12.7

=  0.33 * 3.14 * 129.96 * 12.7

=  1710.24 cm^3

5) Find the perimeter of the square with side length of 14.7 feet.

Solution:

Perimeter of square  = 4 * a

= 4 * 14.7

= 58.8 feet

6) The right triangle has the legs of  lengths 4 cm and 15 cm. what is the length of the hypotenuse?

Solution:       Given a = 4  and b = 15

By pythagorean theorem

c^2  =  a^2 + b^2

=  42 + 152

=  16 + 225

c^2   =  241

c = 15.52 cm

Length of the hypotenuse  =  15.52 cm

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Practice geometry assessments questions:


1) Find the Circumference of a circle with radius 13.5 cm.

2) Find the midpoint of the line joining ( 8, 14) and ( 12, 18 )

3) Find the area of a square of side length 20.5 cm

4) Find the volume of cone given the radius is 7 cm and height is 10 cm.

5) Find the perimeter of the square with side length of 22 feet.

6) The right triangle has the legs of  lengths 3 cm and 11 cm. what is the length of the hypotenuse?

Answers:

1) 84.78 cm   2) ( 10, 16 )    3) 420.25 cm^2   4) 507.74 cm^3   5) 88 ft   6) 11.4 cm

Geometry Math Activities

Introduction to Geometry Math Activities:

Geometry math deals problems with segments and construction terms.The term ‘Geometry’ meant for  a study of properties of figures such as shapes and  relationship for them. Geometry is the important branches of Mathematics. In real  life geometry plays very an important role from learning  that the concept of geometry have begun from ancient times. Geometry gives the ideas for many  geometrical shapes and figure construction.

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Geometry Math Activities Problems Square:


The area of a square A = side × side

Example 1:
The length of the side of a square table mat is 1 m 25 cm. Find the area for the mat.

Solution:
Length of the side of the square table mat=1m 25cm=125cm.
Hence, area of the mat = 125 × 125 sq cm
= 15625 sq cm

Example 2:
The length of square board side is 14 cm find its area

Solution:
Hence, area of the board = 14*14
=196 cm.
Example 3:
The floor of a room is in the form of a square of side 5 m. Find the perimeter.

Solution:
Side of the square=5m
The perimeter (P) of the floor is given by
P= 4×s
=4×5m = 20m
Thus, the perimeter of the floor of the room is 20 m.

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Geometry Math Activities Problems rectangle:


Area of Rectangle =length × Breadth
perimeter of a rectangle = 2 × length + 2 × breadth = 2 × (length + breadth)

Activities Problems Example 1:
The length of a rectangle board  12 cm and its breadth is 5 cm. Find  area for the rectangle.


Solution:
Length of the rectangle = 12 cm
Breadth of the rectangle = 5 cm
Hence, the area of the rectangle = 12×5sq cm=60 sq cm

Activities Problems Example 2 :
The length and breadth of a rectangular blackboard are 200 cm and 100 cm respectively. Find the perimeter.

Solution:
Length of the blackboard ( l) = 200 cm
Breadth of the blackboard (b) = 100 cm
Hence, perimeter (P) of the blackboard is given by
P = 2 × ( l+b)
= 2 × (200 cm + 100 cm)
= 2 × 300 cm = 600 cm
Thus, the perimeter of the blackboard is 600 cm.

Skills Tutor Math

Introduction to skills tutor math:

Let us study about the skills tutor math. The word tutor refers to a person who is teaching others about their doubts in various subjects through online which is a network connection that is made available all over the world.
The term skills tutor math is said to be as the method where we learn about various math problems with the clear explanations of their steps used to solve it.  Examples are discussed. Please express your views of this topic What is the Ratio by commenting on blog.

Example Problems - Skills tutor math:


Skills tutor math – Example 1:

Execute the division technique to calculate the ratio values for the number 13 by 52.


Solution:

Step 1: Given numbers: 13 and 52

Step 2: Follow the steps as given below to determine the ratio:

= `13/52`

= `1/4`

Step 3: Thus we have the calculate ratio of the given numbers 13 and 52 is 1:4.



Skills tutor math – Example 2:

To calculate the value of ‘g’ and to identify whether its value is positive or negative values carry out to calculate the equation which is given as 5g + 8 = -17.


Solution:

Step 1: Given equation: ‘5g + 8 = -17’.

Step 2: To calculate the value of ‘g’ follow the steps given below:

5g + 8 = -17

5g + 8 – 8 = -17 – 8 (‘1’ is subtracted on both sides)

5g = -17

`(5g)/5 = -25/5` (divide by ‘5’ on both sides)

g = -5

Step 3: By calculating the equation we obtained the value of ‘g’ as ‘-5’ – negative value.



Skills tutor math – Example 3:

Rajah is having 67 cakes with him and now he gave 41 cakes to his friends. Execute the steps that help to calculate the remaining number of cakes left with him?


Solution:

Steps 1: Given:

Rajah is having 67 cakes

Rajah gave 41 to his friends.

Step 2: To calculate the total number of cakes that Rajah have with him follow the steps as below:

= 67 – 41

= 26

Step 3: Thus the remaining number of cakes out of 67 that Rajesh have with him is calculated as ‘26’.

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Practice Problems - Skills tutor math:


Execute the division technique to calculate the ratio values for the number 24 by 30. (Answer: 4:5)
To calculate the value of ‘g’ and to identify whether its value is positive or negative values carry out to calculate the equation which is given as 8g + 1 = 17. (Answer: 2 – positive number)
Rajah is having 67 cakes with him and now he got 41 more cakes from his friends. Execute the steps that help to calculate the total numbers of cakes? (Answer: 108 cakes)

Math Number Model

Introduction to math number model:

Math number model is a math problem. Math number has real number, fractional number, natural number, integer, rational number, mixed number and decimal numbers. Number is basic for all the operation of math. Math number is satisfies or saying the real number construction. Let us see math model number in this article.


Math Number Model:


Math number model:

Math number model is a math problem like 8+2=_. Math number problem is helpful for understanding of math. The grade level kids learn the math number through the math number model.

Math number model is available for the following operations.

Addition
Subtraction
Multiplication
division

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Math Problem:

Math problem:

Math number model for addition:

Addition is one of the types of math number model. Here we use one dash. This dash is used to write the answer. Addition use two operands and one operator. We can put dash in operand place or the answer place. As like the following

Example:

2 + 1 = _
_ + 3 = 7
9 + _ = 15
Solution:

3
4
6
Math number model for subtraction:

Subtraction is one of the types of math number model. Subtraction use two operand and one operator. The following example explains the work of math number model in math problem.



Example:

5 – 2 = _
8 -_ = 4
_ - 6 = 4
Solution:

3
4
10


Math number model for multiplication:

Multiplication is one of the types of math number model. Multiplication use two operand and one operator. The following example explains the work of math number model in math problem.

Example:

6 * 4 =_
2 *_ = 16
_ * 7 = 21
Solution:

24
8
3
Math number model for division:

Division is one of the types of math number model. Division using two operand and one operator. The following example explains the work of math number model in math problem.

Example:

10 `-:` 2=_
25 `-:` _=5
_ `-:` 10=2
Solution:

5
5
20

Study Substitution

Introduction to Substitution:-

In the substitution of solve equation, through a particular variable, another variable can be solve if any one equation is solve. A linear equation is the grouping of the variables, even and operators, which represent a straight line. For example x+y = three Here x and y are variables. Three is the constant +, = are operators. For study the system of equations, Substitution method is used. There are three methods to study substitution a system of linear equations Substitution method, Elimination Method, Graphical method. In this article let us see study substitution method. Please express your views of this topic solving systems of equations by substitution answers by commenting on blog.


Steps involved in study Substitution:-


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

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

Step 2: Then Substitute this in the next equation to get a single variable equation.

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

Step 4: Once we get the rate of one variable, substitute the rate in any of the equation to get the rate of the subsequent variable.

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Example problems for study substitution:-


Example 1:-

Study the following system of linear equations using the method of substitution.

x - y = -5

3x+8y = -48

Solution:-

Rearrange the first equation,

x - y = -5

y = x + 5

Substitute this value for y into the second equation;

3x + 8(x + 5) = -48

Expand and simplify the equation:

3x + 8x + 40 = -48

11x = -88

x = -8

Substitute x back into one of the original equations;

-8 - y = -5

y = -3

Solution:-

x = -8, y = -3

Example 2:-

Study the following system of linear equations using Substitution method:.

x + y = 25

-4x + y = 10.

Solution:-

Rearrange the first equation,

x + y = 25

y = 25 - x

Substitute this value for y into the second equation;

- 4x + (25 - x) = 10

Expand and simplify the equation:

-4x + 25 - x = 10

-5x = 10 - 25

-5x = -15

x = 3

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.

How To Reduce Math

Introduction to reduce in math

In math, reduction or reduce refers to the process of rewriting an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reduce a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reduce a radical". (Source: From Wikipedia). Here we will see some example problems to how to reduce a fraction or a radical expression in math.


Example problems to reduce fractions in math


Here we will see some example problems to learn how to reduce a fraction in math.

Example 1

Reduce the fraction `25/365` to simplest form.

Solution

The given fraction `25/365` is not the simplest form, because the numerator and denominator of the fraction has some common factors. By finding the common factors between the numerator and denominator, we can reduce the fraction further into simplest form.

To find the common factors of the numerator and denominator, the prime factorization is given as,

25 = 5 * 5

365 = 5 * 73

So the fraction `25/365` can be written as, `((5)(5))/((5)(73))`

So the simplest form or reduced form of the fraction `25/365` is `5/73`

Example 2

Reduce the fraction `28/118`

Solution

The prime factorization of 28 = 2 * 2 * 7

The prime factorization of 118 = 2 * 59

So, the fraction `28/118` can be written as `((2)(2)(7))/((2)(59))`

So the reduced form of the fraction `28/118` is `14/59`


Example problems to reduce radical expressions in math


Here we will see some example problems to learn how to reduce a radical expression in math.

Example 1

Reduce the radical expression, `sqrt(856)`

Solution

The prime factorization of 856 = 2 * 2 * 2 * 107

So the expression `sqrt856` can be written as, `sqrt((2)(2)(2)(107))`

= 2`sqrt214`

2`sqrt214` is the reduced form of `sqrt856`

Example 2

Reduce the radical expression `sqrt250` into simplest form

Solution

The prime factorization of 250 = 2 * 5 * 5 * 5

So, `sqrt250` = `sqrt((2)(5)(5)(5))`

= `5sqrt((2)(5))`

= `5sqrt10`