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.

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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