Learn Basic Statistics Exam

Introduction to Learn Basic Statistics Exam

Statistics is the formal science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments. Now we will learn the basic statistics exam . (Source: Wikipedia).

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Learn Basic Questions for Statistics Exam


The following are the basic questions and solution for the exam

Question 1:

Find the mean for the following series. 4,8,9,10,12.

Question 2:

What is the mode for the following numerical number series? 3,7,8,10,12,10.

Question 3:

Find out the range of the following series. 10,20,30,12,55.

Question 4:

Calculate the median of the following series.15,13,19,16,30.

Question 5:

Find the mode of the following series. 32,10,12,17,28,39.

Question 6:

Find out the range of the following series. 14,18,24,28,30,33,36.

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Solutions for Statistics Exam


Solution 1:

Average of the given series is known as the mean. Mean is (.4+8+9+10+12)/5. So the solution is 8.6.

Solution 2:

We learn,the duplicate value of the given series is called as the mode. Therefore the mode is value is 10.

Solution 3:

We learn,Subtract the smallest value from the highest value is known as the range. Here the range is 55-10= 45.

Solution 4:

The central value of the given series is known as the median of the series. Before finding the median value we must arrange the series from low to high value. So the arranged values are 13,15,16,19,30.

Therefore solution is 16.

Solution 5:

The basic concept of mode is the duplicate value. The given series there is no repeated value. So the value of mode is null or empty.

Solution 6:

Range is the subtraction of the lowest value from the highest value. Highest values is 36. Least value is 14.The given series range value is 36-14=22.

Learn Unit Vectors

Introduction to learn unit vector:

Physical quantities are divided into two groups, i.e. scalars and vectors. Scalar quantities are those having only magnitude like work done, length, mass etc. Vector quantities are those having magnitude as well as direction like displacement, force, acceleration etc.

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Learn Unit Vectors:


Vectors are symbolically denoted by a line segment with a direction. The length of the line segments gives the magnitude and the direction of the arrow denotes the direction of the vector.

A vector whose magnitude is one unit is called a unit vector, a unit vector is represented with   a letter that names the vector with a cap. The cap in the letter is the indication that it is a vector.

Denoted by â, read as ‘a cap’. Thus, │â│=1.

If│ │ represents the magnitude of a vector, then │â │=1.

The vectors are extensively used in linear algebra. The variable in linear algebra exists in two dimensional x or y axis or y and z axis. The vector not only gives the magnitude of the variable, they also give the direction of the variables.

Vectors are usually defined by the corresponding coordinates. A unit vector in a two dimensional space will have two co-ordinates and a vector in a three dimensional space will have three co-ordinates. A vector with more than one co-ordinate will have the magnitude equal to the square root of the sum of the squares of the co-ordinates.

To find the magnitude of the vectorV (1, 3), we add the squares of the co-ordinates 1 and 3.

This is equal to 10. Now the square root of 10 is greater than 1. ThereforeV (1, 3) is not a unit vector. The basic unit vectors for the three dimensions individually are represented as

X (1, 0, 0), y (0, 1, 0) and z (0, 0, 1)

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Conclusion to Unit Vectors:

Vectors are physical quantities that have a direction and magnitude. Unit vectors have magnitude equal to one unit.  Vectors in two dimensional and three dimensional spaces are represented by the co-ordinate values. Vectors are an important part of linear algebra studies.

Learn Triangles Area

Introduction to learning area of triangles

A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted as `Delta ABC`. (Source: From Wikipedia).

Types of triangles

Equilateral triangles (3 equal sides and angles).
Isosceles triangles (Two equal sides and angles)
.Scalene triangles (No equal sides and angles).
Right triangles (Special case - any triangle with right angle).
Here, we are going to learn how to find the areas of triangles.


Learning formulas for finding the area of triangles


Here we are going to learn basic arithmetic formulas to find the area of different types of triangles.

Area of equilateral triangles
The area of an equilateral triangle can be found by using the formula,

A = `sqrt(3)/4` s2 square units, s - side of the triangle

Area of isosceles triangles
The area of an isosceles triangle can be found by using the formula,

A = `1/2` bh square units, b and h are base and height of the triangle respectively.

Area of scalene triangles
The area of a scalene triangle can be found by using the formula,

A = `sqrt(s(s-a)(s-b)(s-c))` square units

s = `(a + b + c)/2`. a, b, and c are the sides of the triangle


Example problems for finding the area of triangles


Here we are going to learn how to find the area of a triangle.

Example 1

Find the area of a triangle whose sides are equal to 16 cm.

Solution

Area of equilateral triangle = `sqrt(3)/4` s2

= `sqrt(3)/4` * 16 * 16

= `sqrt(3)` * 4 * 16

= `64sqrt(3)`

So the area of the given triangle is `64sqrt(3)` square cm.

Example 2

Find the area of a triangle with height 5 cm and base 4 cm.

Solution

Area = `1/2` bh square units

= `1/2` * 4 * 5

= 10

So, the area of the given triangle is 10 square cm.

Example 3

Find the area of a triangle with sides, 2 ft, 5 ft, and 6 ft.

Solution

Area of a scalene triangle = `sqrt(s(s-a)(s-b)(s-c))`

s = `(a + b + c)/2`

s = `(2 + 5 + 6)/2`

= `13/2`

= 6.5

Area = `sqrt(6.5(6.5-2)(6.5-5)(6.5-6))`

= `sqrt((6.5)(3.5)(1.5)(0.5))`

= `sqrt(17.0625)`

= 4.13

So the area of the given triangle is 4.13 square ft.

Ways to Help to Learn Ratios

Introduction to ways to help to learn ratios:
The ratios contain the fractional numbers. The ratio of two numbers a and b in the same units is the fractions a/b, it can be written as a: b., where a represent the antecedent and b represent the consequent. We can represent (a: b)> (c: d) as (a/ b)> (c/ d). The multiplication and division of the terms of the ratio by the same number does not affect the ratio.

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Example problem for learn ratios:

Example 1 to learn ratios:

Divide 350 in the ratio 2:3.

Solution:

The sum of the ratio terms = 2+3=5

For the ratio 2,

First part= 350 x (`2/5` ) =140

For the ratio 3,

Second part= 350 x (`3/5` ) =210

Example 2 to learn ratios:

A mixture has the alcohol and water in the ratio of 4:2. If 5 liters of the water is mixed with the mixture, the ratios can be changed to 4:5. What is the quantity of alcohol in that mixture?

Solution:

Let the quantity of alcohol and water is 4x liters and 2x liters respectively. Then the ratio is,

`(4x)/(2x+5)`= `(4)/(5)`

20x =4(2x+5)

20x= 8x+ 20

28x=20

x=0.71

The quantity of the alcohol =4x 0.71 = 2.8 liters.

Example 3 to learn ratios:

Find the simplified ratio for 49: 324.

Solution:

The given ratio is 49: 324

The above ratio can be written as 72: 182.

The ratio can be simplified as 7: 18.

The ratio 121: 169 can be simplified as 11: 13.

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Practice problem for learn ratios:


A bag consists of 50 p, 25 p and 10 p coins in the ratio of 2: 3: 4, amounting to Rs. 206. What is the number of coins of each type?
Answer: 50 p coins are 192, 25 p coins are 288 and 10 p coins are 384.

Worker A takes 2 hours to do a particular work. Worker B takes 5 hours to do the same work. How long it take both of them A and B, working jointly but independently to do the same work?
Answer: `10/7 ` days

A and B together can complete a piece of work in 6 days. If A alone can finish the same work in 12 days, in how many days can B alone complete that work?
Answer: 12 days

Learn Fractions The Easy Way

Introduction for Learn Fractions the Easy Way:

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator.

Source – Wikipedia.

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Learn Fractions the Easy Way – Addition:


Learn addition of fractions: `1/6 + 1/6` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `1/6+1/6`

= `(1+1)/6`

By simplifying the fractions we get

= `2/6`

= `1/3` is the solution.

Learn addition of fractions: `1/12 + 1/12` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `1/12+1/12`

= `(1+1)/12`

By simplifying the fractions we get

= ` 2/12`

= `1/6 ` is the solution.

Learn addition of fractions: `2/24 + 4/24` .

Solution:

The numbers in the denominators are same so we go to next step.

We can add the numerators and put the denominator as same.

= `2/24+4/24`

= `(2+4)/24`

By simplifying the fractions we get

= `6/24`

= `1/4` is the solution.

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Learn Fractions the Easy Way – Subtraction:


Learn subtraction of fractions: `1/6 - 2/6` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `1/6-2/6`

= `(1-2)/6`

By simplifying the fractions we get

= `-1/6` is the solution.

Learn subtraction of fractions: `3/12 - 1/12` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `3/12-1/12`

= `(3-1)/12`

By simplifying the fractions we get

= `2/12`

= `1/6` is the solution.

Learn subtraction of fractions: `2/24 - 4/24` .

Solution:

The numbers in the denominators are same so we go to next step.

We can subtract the numerators and put the denominator as same.

= `2/24-4/24`

= ` (2-4)/24`

By simplifying the fractions we get

= `-2/24`

= `-1/12` is the solution.

Learn Multiplication

Introduction for learn Multiplication:

In math, any two numbers can be manipulated by using operations. Basically, there are four different operators. Subtraction, addition, division and multiplication are the operations carried out. Here multiplication is an operator, which is denoted by (cross) × , (star) * . (dot) •. There are some basic rules for the multiplication of two numbers. In this article, we shall learn about multiplication operation. Also we shall learn to solve problems based on multiplication operation.

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Learn Multiplication Properties:

7 * 5 = 35

Here   7 is the multiplier

5 is the multiplicand

35 is the product.

For example:

3 * 5

Three times 5: 5 + 5 + 5 = 15.

Or five times 3: 3 + 3 + 3 + 3 +3 = 15

Properties of Multiplication:

There are several properties that are used while multiplying the given expressions.

1. Learn Distributive Property:

a * (b + c) = (a * b) + (a * c)

For example:

7 * (5 + 3) = (7 * 5) + (7 * 3)

Solution:

Left Handed Side  = 7 * (5 + 3)

= 7 * 8

= 56

Right Handed Side = (7 * 5) + (7 * 3)

= 35 + 21

= 56

Left Handed Side  = Right Handed Side

Hence the proof.

2. Learn Commutative Property:

a * b = b * a

For example:

7 * 5 = 5 * 7

Solution:

7 * 5 = 35

5 * 7 = 35

Both are same.

So 7 * 5 = 5 * 7

Hence the proof

3. Learn Associative Property:

a * (b * c) = (a * b) * c

For example:

7 * (5 * 3) = (7 * 5) * 3

Solution:

Left handed side:

7 * (5 * 3) = 7 * (15)

= 105

Right Handed side:

(7 * 5) * 3 = 35 * 3

= 105

Both are same.

So, 7 * (5 * 3) = (7 * 5) * 3.

Hence the proof

4. Learn Multiplicative Identity Property:

a * 1 = a

For example:

7 * 1 = 7

5 * 1 = 5

3 * 1 = 3

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Example Problems to learn Multiplication operations:


Example 1:

What is the Multiplication of 8 and 4.

Solution:

We can express the given problem as 8 * 4.

8 times 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32.

Or 4 times 8 = 8 + 8 + 8 + 8 = 32

Therefore the multiplication of 8 and 4 is 32.

Example 2:

What is the Multiplication of 9 and 3.

Solution:

We can express the given problem as 9 * 3.

9 times 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27.

Or 3 times 9 = 9 + 9 + 9 = 27

Therefore the multiplication of 8 and 4 is 27.

Third Grade Math

Third Grade math:

The mathematics is the basic term. The grade 3 math are the included by arithmetic operations, and basic algebra. The grade 3mathematics contains multiplication, division, addition, subtraction, fractions and decimals, basic geometry, roman numbers. The following math based on the grade 3mathematics only.

Third Grade Time Facts:

1 day = 24 hr

1hr     = 60 min;

1 min  = 60 seconds,

1 hr    = 60 x 60 seconds = 3600 seconds

Third Grade multiplication:

The grade 3 multiplication is two parts these are the multiplicand, multiplier.

Third Grade Division:

The grade 3 division is three parts these are the dividend, quotient, divider, and reminder.

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Third Grade Math Examples:


Solve Third grade Math multiplication:

4487 x 4

Step 1:

Find the multiplier and multiplicand.

Multiplier = 4

Multiplicand = 4487

Step 2:

Start with left hand side to multiplicand to multiply by 4.

4487 x 4

1 7 9 4 8

Step 3:

Therefore the answer is 17948.

Third Grade Time Facts Example:

20 min =? Find how many seconds

Solution:

1 mins = 60 seconds

Therefore,

20 mins = 60 seconds x 20 = 1200 seconds

Answer:

20 min = 1200 seconds.

Example for expanding number:

Find the number 789 arrange the digits in a place value chart as shown below

Hundreds Tens Ones

7             8       9

Solution:

From the chart above, we see that:

The value of 7 is 7 x 100      = 700

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 789 is 700 + 80 + 9.

Third Grade Time Facts Example:

1 hr 20 min =? Find how many mins

Solution:

1 hr = 60 mins

Therefore,

1 hr 20 mins = 60 mins + 20 mins = 80 mins

Answer:

1 hr 20 min = 80 mins

Example for expanding number:

Find the number 1589 arrange the digits in a place value chart as shown below

Thousands Hundreds Tens Ones

1              5             8       9

Solution:

From the chart above, we see that:

The value of 1 is 1 x 1000   = 1000

The value of 5 is 5 x 100   = 500

The value of 8 is 8 x 10       = 80

The value of 9 is 9 x 1         = 9

Therefore, the expanded form of the number 1589 is 1000 + 500 + 80 + 9.

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Practice Problems for Third grade math:


Practice Problem 1:

Solve:

9854 x 4

Practice problem 2:

Expand the form 6795

Answer key:

39416
6000 + 700 + 90 + 5

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`

Probability Math 7

Introduction to probability math for grade 7:

Probability is the method of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory,  that is used extensively in  areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

I like to share this Probability Math Problems with you all through my article.

Example problems for probability math 7:


Ex: 1    For two events A and B, P(A) = 0.5, P(B) = 0.6 and P(A `U ` B) = 0.8. Find the

(i) P(`A/B` )

(ii) P(`B/A` ).

Sol:   P(A) = 0.5,

P(B) = 0.6 and

P(A`uu` B) = 0.8

Now,

P(A`uu` B) = P(A) + P(B) –P(A`nn` B)

P(A`nn` B) = P(A) +P(B) –P(A `U` B)

= (0.5 + 0.6 – 0.8)

= 0.3

Thus, P(A`nn` B) = 0.3

Therefore (i) P(`A/B` ) =`(P(AnnB))/(P(B))` =`0.3/0.6` = `3/6` = `1/2 ` = 0.5

(ii) P(`B/A` ) =` (P(AnnB))/(P(A))` = `0.3/0.5` = `3/5` = 0.6

Hence, P(`A/B` ) = 0.5 and P(`B/A` ) = 0.6

Ex: 2    A die is rolled. If the outcome is an odd number, What is probability that it is prime?

Sol:   When a die is rolled, sample space is S = {1, 2, 3, 4, 5, 6}

Let A = Event of getting an odd number, and

B = Event of getting a prime number.

Then, A = {1, 3, 5}, B = {2, 3, 5} and A B ={3,5}.

Therefore  P(A) = `(n(A))/(n(S))` = `3/6` = `1/2`

P(B) = `(n(A))/(n(S))` = `3/6` = `1/2` and

P(A`nn` B) =` (n(AnnB))/(n(S))` = `2/6` = `1/3.`

Suppose A has already occurred and then B occurs.

Now, `P(B/A)` = `(P(AnnB))/(P(A))` = `(1/3) / (1/2)` = `(1/3 xx 2/1)` = `2/3.`

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Practice problems for probability math 7:


1. A die is rolled. If the outcome is an even number, What is the probability that it is a number greater than 2?

[Ans: `2/3` ]

2. A pair of fair dice is thrown. Find the probability that the sum is 10 or greater if 5 appears on the first die.

[Ans: `1/3` ]

Angles to Learn in Math

Introduction to angles to learn in math:

In geometry, the angles are formed by the two line segments arising from a particular point. Thus, it forms the angles in the vertices and it can be also called as the vertex angles. There are many types of angles to learn in math. Now we are going to see about the angles to learn in math.

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Angles to learn in math:


Now we are going to see the angles to learn in math and the types of angles in math as explained one by one below.

Acute angle:

The acute angle is the angle where the measurements will be with in 90 degrees. Some of the example degrees are 28, 37, 46 etc.

Obtuse angle:

The obtuse angle is the angle where the measurements will be higher than 90 and lesser than 180 degrees only. Some example degrees are 91, 100, 179 etc.

Straight angle:

The straight angle is the angle nothing but the line having 180 degrees.

Reflex angle:

The reflex angle is the angle where the measurements will be higher than 180 degrees and lesser than 360 degrees. Some example degrees for reflex angles are 190, 250 etc.

Complementary angle:

The complementary angles are the angles whose measurements can be calculate as the sum of the two angles equals 90 degrees. Some example degrees are 45 and 45

Supplementary angle:

The supplementary angles are the angles whose measurements can be calculated as the sum of the two angles equals to 180 degrees. Some example degrees are 50 and 130.

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Problems for angles to learn in math:


Example 1:

Find the angles of supplementary in the ratio 6: 12.

Solution:

The angles are given in the ratio 6: 12

Let us assume the two angles be 6y and 12y

The angles are supplementary and so it can be given as

6y + 12y =180

18y =180, divide by 18 on both the sides,

y = 10

The supplementary angles are 60° and 120°

Example 2:

Find the acute angle of a triangle when one angle is 30 degree.

Solution:

Now we calculate the acute angle from the data as follows,

The two acute angles measures must be less than 90°.

If one of the acute angles a triangle is 30°, then its measure of the acute angle is 89° - 30° = 59°. The angles should be less than 90 degrees.

Math Problem Solving

Introduction to math problem solving:

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. (Source: From Wikipedia). Now, we are going to see some of the solving problems in math.

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Solving math problems:


Example problem 1:

Solve the equation for x: 5x + 20 = 8x + 50

Solution:

5x + 20 = 8x + 50

Subtract 20 on both sides of the equation

5x + 20 - 20 = 8x + 50 – 20

5x = 8x + 30

Subtract 8x on both sides of the equation

5x – 8x = 8x + 30 – 8x

-3x = 30

Divide by -3 on both sides of the equation

-3x / -3 = 30 / -3

x = -10

So, the answer is x = -10.

Example problem 2:

Simplify the expression: 12x – 12 + 22x - x + 22

Solution:

Add the like terms in the given expression

12x – 12 + 22x - x + 22 = 12x + 22x - x – 12 + 22

= (12 + 22 -1) x + (-12 + 22)

= 33 x + 10

So, the answer is 33x + 10.

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Few more solving math problems:


Example problem 3:

Length and breadth of a rectangle are 20 cm and 13 cm respectively.

(i) Find its area.

(ii) Find its perimeter.

Solution:

(i)    Area of the rectangle = Length × Breadth

= l × b

= 20 * 13

= 260 Sq. cm.

(ii)Perimeter of rectangle = 2 (l + B)

= 2 (l + b)

= 2 (20 + 13)

= 2 * 33 = 66 cm.

So, the answer is

(i) Area = 260 sq. cm.

(ii) Perimeter = 66 cm.

Example problem 4:

Two angles of a triangle are of measures 80 and 42. Find the measure of the third angle.

Solution:

Let us take the third angle be x.

Sum of three interior angles of the triangle is 180 degrees.

80 + 42 +x = 180 degree

By solving this, we get

122 + x = 180 degree

Subtract 122 on both sides, we get

122 + x - 122 = 180 – 122

x = 58 degrees.

Practice math problems with answers:

1)  Two angles of a triangle are of measures 70 and 42. Find the measure of the third angle.(answer: 68 degrees)

2)  Solve the equation for x: 10x + 20 = 8x + 50 (Answer: x=15)

Making Rubrics Math

Introduction to making rubric math:
A rubrics math is a plan, a graph or chart that defines accurately what the expectations are for an assignment. The rubrics help to change more subjective prospect into very define and detailed expectations. Students can use rubrics when doing assignments to help conduct their content and presentation and teachers can use a rubric to help make grading easier and less subjective.

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More about rubrics math:


Rubrics are fairly easy to making and use and it can really have a constructive impact on student’s act and teacher grading.
In fact, the time taken to making rubrics can be a fraction of the time the rubrics really saves in the long run.
The rubrics math gives extra information to students and parents than; a math problem is correct or incorrect.
It tells accurately what was good or bad.
If rubrics were used, students should not have to ask "why" they established a particular grade and teachers will have an easy break of the score if that query is asked.

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Making Rubrics Math:

Step 1:

To making rubrics, first, define all goals for a project.
For example, a math assignment can have goals such as set up terms problems correctly, computation, checking of work, etc.
Step 2:

Arrange the list of goals in sort of result.
The objectives will be written in a column beside the left side of a paper.
Step 3:

Under each objective, listing each one of the specific criteria for that objective.
For example, one objective could be viewing good punctuation in a written assignment.
In a math class, the calculation could be busted down into borrow, carrying, etc.
Step 4:

Assign a precise percentage of the rating or number of point to each one objective.
For example, In a math class, a teacher might grade evenly on each of several criteria.
Step 5:

To make grading easier, use a scale for rating each goal.
List the scale along the top of the paper along with the criteria for each point on the scale.
This could be a Like art style scale where each norm is rated from 1 to 5.
A rating could also be "poor", adequate", "good", and "excellent."
Step 6:

Save copies of each rubric after making.
After you have made one, you can change it but you should never have to make one from scratch again.
Making a file for the rubrics so they can easily be pulling when needed.

Learn Online Factoring Radicals

Introduction  to learn online factoring radicals:

The factorization is the  process of factoring the given polynomial equation . basically  factorization  is used to find the common factors  of polynomial equation .. we factorize the radicals  equation  .

These are the steps to  solve  factoring radical

Step 1: to remove the  radical symbol for the given equation

Step 2: factorize   the equation

Step 3:  Solve the equation


learn online factoring radicals problem explanation:


we learn how to solve radical problem:

Solve for x if √2x+3=x  Squaring both sides of the equation gives us  2x+3= x2

Setting terms equal to zero gives  0x2-2x-3

The expression factors  0=(x-3)(x+1)  Setting each factor equal to 0 gives two possible answers: x = 3 or x = – 1.

We check each answer in the original equation:  If x = 3 we have

√2(3)+3=3

√9=3

If x = – 1 we have  √2(-1)+3=-1

is impossible since the square root cannot be negative.

Therefore the only answer is x = 3.

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Examples for learn online factoring radicals


some problems explain for  online  factoring radicals:

1. To solve radical problem for online learning  √x2-2=9 ?

Solution :

1. To solve √x2-2=9 we first square both sides of the equation. The result is x - 2 = 81. This equation is simple to solve. We have x = 83

2. A more complicated situation is√x+2=x In this case we still begin by squaring both sides of the equation. The result is x+2=X2

To finish solving this needs us to set all terms equal to zero and either factor or use the quadratic formula. We get x2-x-2=0

This factors (x-2)(x-1)=0  and the solutions are x = 2 or x = - 1.

We must check each of these solution in the original equation to see if the value of x gives a solution x = 2 gives

√2+2=2   or √4=2 is correct

x = - 1 gives √-1+2=-1  and √1= -1 is impossible

2.   Solve for x if√x+2=√2-x

Solution :

We square both sides. This gives x + 2 = 2 – x.

Solving for x gives 2x = 0. The only solution is x = 0.

Checking this in the original equation gives√0+2=√2-0  or √2=√2

Therefore the solution is x = 0.

4th Grade Math Solving

Introduction to 4th grade math solving:

Mathematics is the vast area, which involves both simple problems and complex problems. Solving 4th grade math problems is very easy, because 4th grade math problems involves simple basic concepts. Once we understand the basic concepts, solving 4th grade math problems looks very easy.

In this article of  4th grade math solving, example problems and practice problems related to 4th grade math are given.

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Solving example problems for 4th grade math:


Example 1:

Calculate the perimeter of Cube having the side length of 10 cm.

Solution:

Perimeter  =  12 a

=  12 * 10

=  120 cm

Example 2:

Thrice a given number is 45. Find the number.

Solution:   Let the unknown number be x

3 x  =  45

x  = `<< 45/3>>`

=  15

Example 3:

Out of 420 seats in a theatre,360 seats are occupied. Find the percentage of seats occupied.

Solution:

Total seats   =  420

Occupied seats  =  360

Percentage   = `<< 360 / 420>>`   x 100

=  `<< 36/42>>`   x 100

=  85.7

Example 4:

Robert bought a doll for `$` 27 and he sold it for `$` 36. What is his gain?

Solution:

Cost price of doll  =  $ 27

Selling price of doll  =  $ 36

Profit  or  Gain   =  Selling price - Cost Price

=  36 - 27

=  $ 9

Example 5:

Julie buys an ornament that costs `$` 270. If the sales tax rate is 4%. What is the total amount she must pay for the ornament?

Solution:

Sales tax  =  4% of the price tax

= 4%  x  270

= 0.04 x 270

= 10.8

Final price = price before the tax + sales tax

= 270 + 10.8

= $ 280.8

Example 6:

Evaluate:  a3. b2   when  a = 2 and  b = 2

Solution:

a3x b2   =  23 x 22

=   8 x 4

=  32

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Practice problems for 4th grade math:


1) Calculate the perimeter of Cube having the side length of  5 cm.

2) Thrice a given number is 60. Find the number.

3) Out of 380 seats in a theatre,270 seats are occupied. Find the percentage of seats occupied.

4) Hamilton bought a doll for `$` 17 and he sold it for `$` 23. What is his gain?

5) Jenifer buys an ornament that costs `$` 370. If the sales tax rate is 3%. What is the total amount she must pay for the ornament?

6) Evaluate:  a^2. b^3  when  a = 4 and  b = 3

Answer key:

1) 60 cm      2) 20       3) 71.05         4)  `$` 6         5)  `$` 381.1      6) 432

Let Learn Our Numbers

Introduction to Learn Our Numbers:

A mathematical object can be used to measure and counting the items in mathematics is said to be number. A number can be represented in notational symbol such as numerals. Numbers can be used for unique id, telephone numbers, mobile numbers, serial numbers of the items, ISBN’s that is code. Let us learn about the numbers we are using in our day-to-day life. Having problem with Complex Number Calculator keep reading my upcoming posts, i will try to help you.


Classification of Our Numbers


Let us learn about what are the classifications of numbers in our math. A number can be used in different cases in sets is called number systems.

There are

Natural numbers
Integers
Real numbers
Rational numbers
Real numbers
Complex numbers
Computable numbers

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Demonstration about learn our Number Systems

Natural Numbers:

Digits 1, 2, 3, 4, 5, 6, 7, 8, 9, written with base ten number system and the set of all natural numbers can be denoted as N.

Let us learn the examples of natural numbers: 4, 2, 7, 9, 1, 5, etc.

Integers:

In a set of negative numbers,  a number which is followed by positive number and including zero and positive numbers are said to be integers. Integers can be represented as Z.

Let us learn the examples of natural numbers: 5, 8232, 748, -663, -44, 376737.

Rational Numbers:

A  non-zero natural number denominator and positive integer can be written in the numerator. The fraction m/n can be represented as equal parts. The absolute value of “m” is greater than that of “n”.

Let us learn the examples of natural numbers: 3/7, 8/9, 4/5, 2/7, 1/3, 5/6.

Real Numbers:

Real numbers can be represented as decimal numerals. The place value of right of the decimal point in a real number is  given in the original form in one-tenth of the place value of the digits to its left.

Let us learn the examples of natural numbers: 395.62, 739.320, 74783.89, 262378.236, π = 3.141.

Complex Numbers:

The roots of quadratic polynomials and the roots of square and cubic equations give the complex numbers. The square roots of negative numbers, or the square root of negative one can be denoted by i, is in the form of a + ib.

Let us learn the examples of natural numbers: 1+ i`sqrt(3)``sqrt(5)`

Here a and b are said to be real numbers in the form of a + ib, a is said to be real part of the complex number and ib is said to be imaginary part of the real number.

Sum of 100 Using Math

Introduction for sum of 100 using math:

In mathematics, sum of 100 using math are associated to the value concerned in positive integers. Moreover, sum of 100 using math is the capability the process of determining the certain integer or the form. Now, in the issue sum of 100 using math are viewing to sum of 100 with the arithmetic operations such as addition, subtraction, multiplication and division. We are going to notice a few of the measures to solve sum of 100 using math in detail.


Example problems for sum of 100 using math:


Example problem 1 for sum of 100 using math:

1) Add the numbers: 60 + 40.

Solution:

Step 1: Given 60 + 40

Step 2: Add both numbers:

= 60 +40

= 100

The answer is 100.

Example problem 2 for sum of 100 using math:

2) Add the numbers: 50 + 50.

Solution:

Step 1: Given 50 + 50

Step 2: Add both numbers

= 50 +50

= 100

The answer is 100.

Example problem 3 for sum of 100 using math:

3) Add 20 + 80.

Solution:

Step 1: Given 20 + 80

Step 2: Add both numbers:

= 20 +80

= 100

The answer is 100.

Example problem 4 for sum of 100 using math:

4) Add 65 + 35.

Solution:

Step 1: Given 65 + 35

Step 2: Add both numbers:

= 65 +35

= 100

The answer is 100.

Example problem 5 for sum of 100 using math:

5) Subtract 155 - 55.

Solution:

Step 1: Given 155 - 55

Step 2: add both numbers:

= 155 - 55

= 100

The answer is 100.

Example problem 6 for sum of 100 using math:

6) Subtract 240 - 140.

Solution:

Step 1: Given 240 - 140

Step 2: Subtract second value from first value

= 240 - 140

= 100

The answer is 100.

Example problem 7 for sum of 100 using math:

7) Subtract 552 - 452.

Solution:

Step 1: Given 552 - 452

Step 2: Subtract second value from first value

= 552 - 452

= 100

The answer is 100.

Example problem 8 for sum of 100 using math:

8) Subtract 110 - 10.

Solution:

Step 1: Given 110 - 10

Step 2: Subtract second value from first value

= 110 - 10

= 100

The answer is 100.

Example problem 9 for sum of 100 using math:

9) Multiply: 10 * 10

Solution:

Step 1: Given 10 * 10

Step 2: Subtract second value from first value

= 10 * 10

= 100

The answer is 100.

Example problem 10 for sum of 100 using math:

10) Divide: 600 / 6

Solution:

Step 1: Given 600 / 6

Step 2: divide 600 by 6

= 600 / 6

= 100

The answer is 100.

Example problem 11 for sum of 100 using math:

11) Divide: 1000 / 10

Solution:

Step 1: Given 1000 / 10

Step 2: divide 1000 by 10

= 1000/10

= 100

The answer is 100.

Example problem 12 for sum of 100 using math:

12) Divide: 700 / 7

Solution:

Step 1: Given 700 / 7

Step 2: divide 700 by 7

= 700/7

= 100

The answer is 100.

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Practice problems for sum of 100 using math:


1) Add 25 + 75

Ans: 100

2) Add 67 + 33

Ans: 100

3) Subtract 285-185

Ans: 100

4) Multiply 50 * 2

Ans: 100

5) Divide: 300 / 3

Ans: 100

Function Table Math

Introduction of function table math:

A math function table is used for given possible outputs of a function which is a kind of rule. To clearly recognize function tables and their idea, we need to recognize functions, and how they relate to variables. In this math function table, you can understand each part of the puzzle. Let we learn about function math table.

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Math function table is:


First we should understand the variables .A variable is a usually a number (value) that w don’t know.
A rule will be applied to a variable.
The function to figure out what your need will be.
Function tables are basically lists of possible values of a variable and the function's result. These are few steps for how math function table should be.
Example of function table1:

A Function table is a table of order pairs that following rules. Here Input and output is called function tables labels. Input denoted by A and output denoted by B.

Input (A) :    5   10   15   20   25   30

Output (B):  2    7    12   17    ?    ?

A rule says how one number is related to another. (Calculate)

You can use numbers to complete this math table it the same time apply the rule for the function table.

Rule: given A values subtract by 3 (A-3=B) therefore

5-3=2

10-3=7

15-3=12

20-3=17

25-3=22

30-3=27

So the next number are 22, 27

Example of function table2:

Input (x)   6    10   15   18   20    23

Output(y) 11   15   20   ?     ?     28

Solution:

Step 1: Find the rule.

Step 2: Here we add 4 to each input number to get the output number.

The rule for this table is adding 4 by given input.

Therefore 6+5 = 11

10 + 5 = 15

15+5=20

18+5=23

20+5=25

23+5=28

Step 3: The answer is

Input (x)   6    10   15   18   20    23

Output(y) 11  15   20    23   25    28.

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Practice problem of function table math:

Find the rule. Write the rule as an equation.

Use the equation to complete the table.

Input:    11   9   7    5    3

Output: 9    7    ?   ?     ?

Answer: 5 3 1

Doing Math Problems

Introduction of doing math problems:
Math is very important term in our day to day life. We have different concepts in math. And commonly formulas are used to solve the complex problems .We have various types of formulas in math. Algebra is the one of the important terms in mathematics. Here we are going to see some example math problems. Is this topic Calculus Problem hard for you? Watch out for my coming posts.


Doing math problems:


Doing simple algebra problem:

Example 1:

g- 43 = 604.

Solution:

Step 1: g - 43 = 604.

Step 2: g - 43+ 43 = 604 + 43. (Add 43on both the sides).

Step 3: g = 647(so, the value of g is 647).


Doing simplification in algebra:

Example 2:

Given:

20x-5(12x-10x+2) +4x.

Solution:

Step 1: First we need to simplify the brackets. So we multiply (12x-10x+2) with 5

Step 2: So,20x-60x+50x-10+4x

Step 3: It can be written as 20x-60x+50x-10+4x

Step 4: So, the answer is 14x-10.


Doing parenthesis problem in math :

Example 3:

Given :

(14/2) * (45-9)

Solution :

Step 1: First we need to simplify the parenthesis ,so

Step 2: We get 14/2 = 7 and (45-9) =36.

Step 3: Here we need to multiply 7*36.

Step 4: So, the answer is 252.


More math problems


Doing inequality problem in math

Example 4:

Solve for 4(a+1) <2a br="">
Solution:

Step 1: It can be written as 4a+4<2a 2a="" both="" br="" on="" sides="" the="" ubtract="">
Step 2:4a+4-2a<2a-2a br="">
Step 3:2a+4<3 4="" both="" br="" on="" sides="" subtract="" the="">
Step 4:2a+4-4<3-4 .="" br="">
Step 5:2a<-1 .so="" a="-1/2.<br">
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Doing subtracting algebraic expression in math:

Example 5:

Given:

Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.

Solution:

30ab + 12b + 14a – (24ab – 10b – 18a)

Step1: 30ab + 12b + 14a – 24ab + 10b + 18a

Step2:30ab – 24ab + 12b + 10b + 14a + 18a

Step 3:6ab + 22b + 32a.


Adding polynomials in math :

Example 6:

(6x+7y) + (2x+1y)

Solution:

Step 1: First we need to clear the parenthesis so, 6x+7y+2x+1y.

Step 2: Now we need to combine the like terms, so 6x+2x+7y+1y.

Step 3: Here we need to add the like terms, so 8x+8y.

Step 4: So the answer is 8(x+y).

Calculating Interquartile Range

Introduction to learn calculating inter quartile range:

Inter quartile Range is also called as H-Spread.

Inter quartile Range = (Q3 - Q1)

If Q1 be the first or lower quartile and Q3 be the third or upper quartile, then (Q3 - Q1) is called the inter quartile range.

For a simple series the data are to be arranged in ascending order of magnitude. Then

Q1=the value of the (N+1)/4th term,

Q3=the value of the 3(N+1)/4th term.

For a grouped frequency distribution, cumulative frequencies (less than type) are to be calculated first. Then

Q1=the value that corresponds to cumulative frequency N/4

Q3=the value that corresponds to cumulative frequency 3N/4


Example Problem to learn calculating inter quartile range:


Find the inter quartile range of following set of numbers

12, 4, 5, 1, 42, 9, 23

Solution for learn calculating inter quartile range:

The following are the steps to find the inter quartile range of a set of numbers.

Step 1:- Arranging of numbers

The initial step is to modify the given data in order, from smallest to biggest.

1, 4, 5, 9, 12, 23, 42

Step 2:- Calculating 1st quartile Q1.

The next step is to find the lower median (1st quartile Q!).

Here the number of terms (N) is 7.

The formula used to calculate Q1 is (N+1) / 4

Q1 = (7+!) / 4.

Q1 = 8/4 = 2nd term.

So second term in the series is 4.

1st quartile Q1 is 4.

Step 3:- Calculating 3rd quartile Q3.

Now find the upper median (The 3rd quartile Q3).

Here the number of terms (n) is 7.

The formula used to calculate Q3 is 3(N+1) / 4.

Q3   = 3 (7 + 1) / 4 = 3 (8) / 4

= 24 / 4

= 6th term.

So the 6th term in the sequence is 23

The 3rd quartile Q3 is 23.

Step 4:- Calculating inter quartile range.

The formula used to find the inter quartile range is

Inter quartile range = Q3 – Q1.

Q1 the first quartile = 4

Q3 the third quartile = 23

Plug in the Q1 and Q3 values in the standard formula Q3 – Q1.

Inter quartile range = 23 – 4 = 19

learn calculating inter quartile range solution is 19.

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Practice Problem for learn calculating inter quartile range:


Find the inter quartile range of following set of numbers

3 , 6, 1 ,2 ,7 , 11 , 04, 33, 61, 29,15


Answer learn calculating inter quartile range: 26

Geometric Group Theory

Introduction to learn geometric group theory:-

Let we will see about learn geometric group theory. Learn of geometric group theory is an area in mathematics. Those are dedicated to the study of finely produced groups. These could be way of discover the associations among algebraic properties of those groups. These are made in a separate area. They should have become an obviously identifiable group of math in among late 1980s and early 1990s.

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Further about learn geometric group theory:-


•    Another essential idea in learn geometric group theory is to regard as finitely created groups themselves as geometric objects.

•    This is done by learning the Clayey graphs of learn geometric group theory.

•    In addition to graph structure, these should be endowed with structure over a metric space. This is known as word metric.

•    learn geometric group theory directly interrelated with,

1.    Low dimensional topology

2.    Algebraic topology

3.    Computational group theory

4.    Geometric analysis

•    There are also much relations with,

1.    Complexity theory, mathematical logic

2.    Study of Lie Groups and their discrete subgroups

3.    Dynamical systems

4.    Probability theory

5.    K-theory.

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Historical background for learn geometric group theory:-


•    learn geometric group theory produce out from the combinatorial group theory

•    Largely studied properties of discrete groups through investigative group presentations, which portray groups as quotients on free groups.

•    Nowadays, combinatorial group theory should be an area that is largely subsumed by learns geometric group theory.

•    Additionally, term " learn geometric group theory " came from studying separate groups using probabilistic.

•    These measures,

1.    Theoretic

2.    Arithmetic

3.    Analytic

4.    Other approaches

•    That should be lie outside of conventional combinatorial group theory arsenal.

•    Exterior precursors of geometric group theory comprise study of networks in Lie Groups, particularly Mostow rigidity theorem.

•    Study of Kleinian groups and progress should be attained in low-dimensional topology, hyperbolic geometry in between 1970s and 1980s.

How To Do Distributive Property

Introduction Distributive Property :-

The distributive property or distributive law makes numbers easier to work with. In mathematics when we use the distributive property, we are actually mounting up the simplified ones.

The Distributive Property in Algebra:

Is left-distributive over + if, given any elements x, y, and z of S,
x · (y + z) = (x · y) + (x · z);

is right-distributive over + if, given any elements x, y, and z of S:
(y + z) · x = (y · x) + (z · x);

is distributive over + if it is both left- and right-distributive.
(Source:- Wikipedia)

The problems solved here helps you learn the distributive property easily. I like to share this The Definition of Distributive Property with you all through my article.


Solved problems Based on Distributive Property:-


Learning problem 1

13 ( 4 + 6 ) solve it by using 'Distributive Property.

Solution:-

= 13 ( 4+ 6 )

The Distributive Property states that

a(b + c) = ab + ac

here

a = 12

b = 4

c = 6

Multiply each number within the parentheses by the number outside the parentheses

13(4 + 6) = 13 • 4 + 13 • 6

= 52 + 78

= 130

Learning Problem 2

11 (5 + 6) solve it by using 'Distributive Property.

Solution:-

= 13 (4+ 6)

The Distributive Property states that

a (b + c) = ab + ac

Here

a = 11

b = 5

c = 6

Multiply each number within the parentheses by the number outside the parentheses

11(5 + 6) = 11 • 5 + 11 • 6

= 55 + 66

= 121

Learning Problem 3

10 (2 + 6) solve it by using 'Distributive Property.

Solution:-

= 10 (2+ 6)

The Distributive Property states that

a (b + c) = ab + ac

Here

a = 10

b = 2

c = 6

Multiply each number within the parentheses by the number outside the parentheses

10(2 + 6) = 10 • 2 + 10 • 6

= 20 + 60

= 80

Learning Problem 4

7 (2 + 6) solve it by using 'Distributive Property.

Solution:-

= 7 (2+ 6)

The Distributive Property states that

a (b + c) = ab + ac

Here

a = 7

b = 2

c = 6

Multiply each number within the parentheses by the number outside the parentheses

7(2 + 6) = 7 • 2 + 7 • 6

= 14 + 42

= 56

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Practice Problems Based on Distributive Property:-


1) 1 ( 2 + 6 ) solve it by using 'Distributive Property.

Answer:- 8

2) ( 4 + 2 ) 3 solve it by using 'Distributive Property.

Answer:- 18

3) 12 ( 4 + 2 )  solve it by using 'Distributive Property.

Answer:- 72

4) ( 4 + 5 ) 2 solve it by using 'Distributive Property.

Answer:- 18

5) ( 7 + 2 ) 5 solve it by using 'Distributive Property.

Answer:- 45

Radius Math Term

Introduction to radius math term:

In day to day life, we often came across some unique math terms. Radius is one of the special math terms that falls under this category.
Radius of a circle is nothing but the line segment from the center of the circle to its perimeter. In other terms, half the diameter is the radius.
In this article of radius math term, we are going to find the radius of the circle by several methods. I like to share this Partial Fraction Decomposition Calculator with you all through my article.

Formulas for math term radius:


Radius from circumference:

If the circumference of a circle ( C ) is given, the radius can be calculated by the following formula:

r  = C / 2`pi`

Radius  from diameter:

If the diameter (D) of the circle is given, the formula for finding the radius is

r  = `<< D/2>>`

Radius from area:

If the area of the circle is given, then the radius can be calculated using the formula

r =  `sqrt(A/pi)`

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Example problems for math term radius:


Example 1:

Find the radius, if the circumference of the circle is 90 cm

Solution:

Radius of a circle, r = C / 2`pi`

= 90 / (2 * 3.14)

= 90 / 6.28

= 14.33 cm

Example 2:

Find the radius of the circle, if its diameter is 62 cm.

Solution:

Radius of a circle, r = `<< D/2>>`

= `<< 62/2>>`

= 31 cm

Example 3:

Given the area of a circle is 94 m2. Find its radius.

Solution:

Radius of a circle  r =  `sqrt(A/pi)`

= `sqrt(94/3.14)`

=  5.5 cm


Practice problems for radius math term:


1) Find the radius, if the circumference of the circle is 110 cm.

Answer:  17.52 cm

2) Find the radius of the circle, if its diameter is 92 cm.

Answer: 46 cm

3) Given the area of a circle is 124 m2. Find its radius.

Answer: 6.28 m

Application of Matrices

Introduction to learn applications of matrices::
A Matrix in plural matrices or less commonly matrices, is a rectangular array of numbers. Matrices are a key tool in linear algebra. One use of matrices is representing linear transformations, which are higher-dimensional analogs of linear functions of the form f(x) = cx, where c is a constant; matrix multiplication corresponds to composition of linear transformations.
(Source : wikipedia)

In this article, we shall learn the applications of matrices. I like to share this Augmented Matrix with you all through my article.



Learn Application of matrices to check properties:


(1) Matrix addition is commutative:

If A and B are any two matrices of the same order then A + B = B + A. This property is known as commutative property of matrix addition.

(2) Matrix addition is associative:

I.e. If A, B and C are any three matrices of the same order.

Then A+ (B + C) = (A+B) +C.  This property is known as associative property of matrix addition.

(3) Additive identity:

Let A be any matrix then A + O = O + A = A. This property is known as identity property of matrix addition. The zero matrix O is known as the identity element with respect to matrix addition.

(4) Additive inverse:

Let A be any matrix then its matrix is –A then the property is A + (- A) = (- A) + A = O. This property is known as inverse property with respect to matrix addition. The negative of matrix A  i.e. - A is the inverse of A with respect to matrix addition. Please express your views of this topic answers for algebra 2 problems by commenting on blog.


More Applications to learn matrices:


(1) In general, matrix multiplication is not commutative i.e. AB ? BA

(1) In general, matrix multiplication is not commutative i.e. AB ? BA

(2) Matrix multiplication is always associative.

I.e. A (BC) = (AB) C

(3) Matrix multiplication is always distributive over addition.

I.e. (i) A (B + C) = AB + AC

(ii) (A + B) C = AC + BC

(4) AI = IA = A where I is the unit matrix or identity matrix. This is known as Identity property of matrix multiplication.

This is how, we can learn the applications of matrices.

Learn Online Inequalities

Definition of learn online inequalities:

Inequality is described as two real numbers or two algebraic expressions are communicated with functioning a symbol as ‘<’ (less than), ‘>’ (greater than), ‘≤’ (less than or equal) and ≥ (greater than or equal). Learn online inequalities are the method of learning the inequalities by online. The various inequalities are learned online as follows,

Numerical inequalities
Literal inequalities
Double inequalities
Strict inequalities
Slack inequalities
Linear inequalities

Types :


From learning online inequalities, they can be explained as follows,

1) Numerical inequalities:

Inequalities which enclose arithmetical lone without any variables is known as numerical inequalities

Eg: 5 < 8; 5 > 4

2) Literal inequalities:

Inequalities which have one or more variables are labeled as literal inequalities.

Eg: p< 5; q > 2; m ≥ 4; n ≤ 6

3) Double inequalities:

An inequality which contains two sign (< or > or ≤ or ≥) is named as double inequality.

Eg: 2 < b < 8; 3 ≥ t ≥ 8

4) Strict inequalities:

If an inequality holds a symbol < or >, then it is learned as strict inequalities.

Eg: Ax + B < 0; Ax2 + Bx + C > 0

5) Slack inequalities:

If an inequality involves a sign ≤ or ≥, then it is called slack inequalities.

Eg: Ax + By ≤ C; Ax + By ≥ C

6) Linear inequalities:

An inequality may have one variable with linear is called linear inequality through one variable; If it contains two variables, then it is called linear inequality through two variables.

Eg: Ax + By < C; Mx + C > Y


Rules & Example for learn online inequalities :


RULES :    Inequality contains the following rules for learning online,

Rule 1: All sides of an inequality can be added or subtracted by means of equal numbers without affecting the symbol.

Rule 2: Same numbers may be multiplied or divided as of both sides of an inequality.

Ex :  Solve online 40 u < 200 when

(i) ‘u’ is a natural number,

(ii) ‘u’ is an integer.

Sol :      Given 40 u < 200

From online,

40u / 40 < 200 / 40 (Rule 2)

u < 5.

(i) When ‘u’ is a natural number, then the statement gives,

1, 2, 3, 4

The solution set is {1, 2, 3, and 4}.

(ii) When ‘u’ is an integer, then the solution is given as,

..., – 3, –2, –1, 0, 1, 2, 3, 4

The solution set is {...,–3, –2,–1, 0, 1, 2, 3, 4}

Sat Math Practice Problems

Introduction:

Scholastic Assessment Test or Sat reasoning test is a test which is used to get admissions in US universities and colleges. Sat test deals with quantitative questions and English skills. Sat test is conducted for 3 hrs and 45 minutes. It consists of three parts; they are i) Critical reasoning ii) Math aptitude and iii) Writing.  Math section of Sat questions deal with quantitative questions and logical reasoning questions. Math questions are given with multiple choices. Students should Practice math problems to get good scores in Sat test. I like to share this Define Geometry with you all through my article.


Sat Math Problems:


Example 1:

There are 240 balls, 4 times as many are brown, and the rest is black. How many are green and how many are black colors?

Solution:

There are 4 times as many brown balls as there is black color,

Hence, there must be 4 brown for each 1 of black color.

Given that 4 + 1 = 5,

Therefore,

240/5 = 48

On solving this we get, 48 sets of balls with 4 greens and one of black color in each set.

The total is then,

48 * 4 = 192 green and 48 of black color

Answer Check:

Number of green balls = 192 balls

Remaining black balls = 48

Total balls = 192 + 48

= 240 balls.



Example 2:

Mani drives from his house to hills 150 miles away, and at the end of the day drives home. If Mani drives at a standard speed of 50 miles per hour, how long does Mani takes to drive the round trip?

Solution:

Here Mani takes 150 miles to reach the destination,

The total distance covered by Mani during the round trip = 150 + 150

= 300 miles

Mani drives at an average of 50 miles per hour.

Using the formula

Distance = speed x time

300 = 50 x X

Divide 50 on both sides,

300/50 = 50X/50

6 = X

Mani takes 6 hrs to complete the round trip.

Answer is 6 hrs.


Sat Math Practice Problems:

Practice Problems1:

In a class of 78 students 41 are taking Tamil, 22 are taking English and 9 students are taking both Tamil and English. How many students are not enrolled in any of the course?

A) 10

B) 15

C) 24

D) 34

Answer: C


Practice Problems 2:

Six years ago rani was X times as old as raji was. If rani is now 17 years old, how old is raji now in terms of X?

A) 12/X + 6

B) 11/X + 6

C) 17X

D) 18/X

Answer: B

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Practice Problems 3:

Which of the following numbers can be used to demonstrate that all prime numbers are not odd?

A) 2

B) 5

C) 11

D) 13.

Answer: A

Direction Vectors

Introduction:

In mathematics a direction vector that describes a line segment D is any vector of the direction vector,

AB?

Where, A and B are two distinct points on the line D. If v is a direction vector for the D, so is kv for any nonzero scalar k; and these are in fact all of the direction vectors for the line D. Under the some definitions, the direction vector is required to be a unit vector, in which case each line has exactly two direction vectors, which are negatives of each other equal in magnitude, opposite in direction. (Source:Wikipedia)

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Direction vector for a line in two-dimensional:


Any other line in two-dimensional Euclidean space can be described as the set of solutions to an equation of the form

ax + by + c = 0

Where a, b, c are real numbers. Then one direction vector of (D) is (- b,a). Any multiple of (- b, a) is also a direction vector.


Basic properties:


The following section uses the Cartesian coordinate system with basis vectors

a=a1e1+a2e2+a3e3 and
b=b1e1+b2e2+b3e3
Are equal if

a1=b1, a2=b2, a3=b3.


Magnitude and Direction of a Vector:


Let v can be a vectors given in component form by

                        v = < a,b >

The magnitude of the || v || of vector v is given by

                 || v || = sort (a 2 + b 2)

and the direction of the vector v is angle t in standard position and in counterclockwise direction is such that

                  tan(t) = v / u

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Vector methods:


Vectors and vector addition
Unit vectors
Base vectors and vector components
Rectangular components in 2-D
Rectangular coordinates in 3-D
Direction cosines
A vector connecting two points
Dot product
Rectangular coordinates
Projection of a vector onto a line
The cross product
The triple product
Rectangular coordinates
Triple vector product

Example:

The equation of a line is 2x - 3y + 15 = 0.

2x-3y=-15

2(-3)-3(3)=-15

-6-9=-15

So (-3, 3) is direction vectors for this line

Geometry in Our Daily Life

Introduction to Geometry in our daily life:

Geometry is a part of mathematics which is concerned with questions of shape, size, the relative position of figures and the properties of space. In earlier, geometry was a collection of empirically discovered principles which concerns about lengths, areas, angles and volumes which were developed to meet some practical need in surveying, construction, and various crafts. There are various fields of life where geometry is considered as an important field of study. Please express your views of this topic Similar Polygon by commenting on blog.


Geometry in Daily Life

The general applications of geometry in our daily life are as follows:

Geometry is the very useful to define relative physical locations.
Geometry can be used to analyze or design physical structures and objects and to determine the various location and elevation of physical features on the Earth's surface.
Major examples of the geometry in real life:  The shape and volume of food containers, the design of buildings, and the layout of streets and roadways. I have recently faced lot of problem while learning Finding Surface Area of a Cylinder, But thank to online resources of math which helped me to learn myself easily on net.

Major Applications of Geometry in Daily Life

Major Applications of Geometry in Daily Life are as follows:

In real life, Geometry is particularly useful in home building and improvement projects. If we want to find the area of the floor of a house, we can use geometry.
In turn, this information is very useful for laying carpet or tiles and also for telling an estate agent regarding the information that how big our house is when we want to put it on the market. Geometry involved in many our daily life problem.
If we need to reupholster a piece of furniture, it is necessary to estimate the amount of fabric that we need by calculating the furniture’s surface area.
Geometry also finds its application in hobbies. In order for the fish to thrive, the water in a goldfish tank needs to have a certain volume as well as surface area. We can calculate it easily using geometry.
Pastimes like quilting and some other design projects will use geometry extensively. How the shapes of a quilt block fit together can be understand which is basically dependent on geometry; so that is determining the amount of fabric we need. Geometry is used for find the angle of the object.