Prime Model

Introduction to prime model:

In this article we shall discuss about prime model. Here, prime model is also denoted as prime number model. A Prime Number is a complete number, bigger than 1, so as to can be uniformly divided just by 1 otherwise itself. "Prime Factorization" is recognized which prime numbers need to multiply as one to get the original number.

Here, few prime numbers are:  1, 7, 13, and 19 etc...

The prime factorization model of a number is multiplying prime factors of a number.

Here, simple example is 38 = 2 x 19.

Examples of Prime Number Model:

The example of 1 - 100 prime number model is shown given below that,

Prime number of 1 - 10:

The prime number of 1 - 10 is 2, 3, 5 and 7.

Prime number of 10 - 20:

The prime number of 10 - 20 is 11, 13, 17 and 19.

Prime number of 20 - 30:

The prime number of 20 - 30 is 23 and 29.

Prime number of 30 - 40:

The prime number of 30 - 40 is 31 and 37.

Prime number of 40 - 50:

The prime number of 40 - 50 is 41, 43 and 47.

Prime number of 50 - 60:

The prime number of 50 - 60 is 53 and 59.

Prime number of 60 - 70:

The prime number of 60 - 70 is 61 and 67.

Prime number of 70 - 80:

The prime number of 70 - 80 is 71, 73 and 79.

Prime number of 80 - 90:

The prime number of 80 - 90 is 83 and 89.

Prime number of 90 - 100:

The prime number of 90 - 100 is 97. Please express your views of this topic Perfect Number by commenting on blog.

Example Problems Based on Prime Factorization Model:

Example problems based on prime factorization model is given below that,

Example:

How to find prime factorization model for 78?

Solution:

Step 1:

To create through the smallest amount prime number, which is 2, then the value is

`78/2 = 39`

Step 2:

Here 39 is not a prime number, therefore we require factoring it over again:

`39/3 = 13`

Step 3:

13 is a prime number,

78 = 13 × 3 × 2. This is the answer; all factors are a prime number. Since a result should be Correct.

Step 4:

The prime factorization for 78 is 13 × 3 × 2.

Standard Deviation Bars

Introduction about standard deviation bars:

In this article we are going to see about standard deviation bars. Bars are nothing but a bar chart or the pictorial representation of the data values; it should be plotted using the given data’s. Standard deviation is a statistical one and it be supposed to be measure the variability. The standard deviation is the root mean square deviation of the values from their mathematics mean. Let see how standard deviation bars represents.

Standard Deviation Bars

Standard deviation formula:

The formula for standard deviation is.

s.d= `sqrt((sum(X-M)^2)/(n-1)) `

Where,

S = sum of values

X = individual value

M = mean of all values

n = number of values

Problems on Standard Deviation Bars:

Example 1:

Find the Standard deviation for 1, 2, 3, 4, 5 and 6 then draw the standard deviation bars.

Solution:

Step 1:

Find the mean and deviation.

Mean =` (1+2+3+4+5+9)/6`

= `24/6`

M = 4

Step 2:

Find the sum of (X-M) 2

9+4+1+0+1+25= 40

Step 3:

Given n = 5, then find the total number of values using formula n-1.

n-1= 6-1

= 5

Step 4:

Find Standard Deviation using the formula:

S.D = `sqrt((sum(X-M)^2/(n-1)))`

= `sqrt(40/5)`

=` sqrt(8) `

S.D = 2.82

Example 2:

Find the Standard deviation for 3, 6 and 9 then draw the standard deviation bars?

Solution:

Step 1:

Find the mean and deviation.

Mean = `(3+6+9)/3`

= `18/3`

M = 6

Step 2:

Find the sum(X-M) 2

9+0+9= 18

Step 3:

Given n = 5, then find the total number of values using formula n-1.

n-1= 3-1

= 2

Step 4:

Find Standard Deviation using the formula:

S.D= `sqrt((sum(X-M)^2)/(n-1))`

= `sqrt(18/2)`

= `sqrt(9)`

S.D   = 3


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Practice problems for standard deviation bars:

1. Find the Standard deviation for 4, 8 and 12 then draw the standard deviation bars?

Answer: 3.46

2. Find the Standard deviation for 4, 10 and 13 then draw the standard deviation bars?

Answer: 4.58

3.. Find the Standard deviation for 5, 10 and 15 then draw the standard deviation bars?

Answer: 5

Inverse Property of Addition and Multiplication

Introduction to inverse property of addition and multiplication:

For solving the expression in mathematics, the inverse properties of addition and multiplication are useful. The result of inverse property for addition is 0 and the result of inverse property for multiplication is 1. The inverse property requires a number and its inverse.

Example: Inverse of a term +a is –a for addition `1/a` for multiplication.

Explanation of Inverse Property of Addition and Multiplication:

Statement of inverse property of addition:

Inverse property of addition states that when a number or variable is added to its inverse number or variable, the result of this addition becomes zero. For addition the inverse of a given number or variable is obtained by changing the sign of given number or variable.

Example:

Consider a variable ‘t’. An inverse term of ‘t’ is –t. Addition of new opposite equal terms gives 0.

t + (-t) = t – t =0

Inverse property of multiplication:

Inverse property of multiplication states that when a number or variable is multiplied by its inverse, the result becomes one. For multiplication the inverse of a number or variable is the reciprocal of a given number or variable. Looking out for more help on Mathematical Expressions in algebra by visiting listed websites.

Example:

Consider a variable is ‘t’. The inverse of this variable is t-1 which is `1/t`.

t × `1/t`  = 1

Example Problems to Inverse Property of Addition and Multiplication:

Example: 1

Which is the inverse element of 61 for addition?

a) +61

b) -(-61)

c) `1/61`

d) -61

Solution:

Given number is 61.

Inverse property result is 0.

61 + x = 0

61 is subtracted on both sides.

61 + x – 61 = 0 – 61

x = -61

Answer: d

Example: 2

Which of the following is the inverse element of 9 for multiplication?

a) 9-1

b) `(1/9)^-1`

c) +9

d) -9

Solution:

Inverse property of multiplication result is 1.

9  X x = 1

9 is divided on both sides.

`(9x)/9` = `1/9`  = 9-1

Answer: a

Practice Problems to Inverse Property of Addition and Multiplication:

Problem: 1

What is the inverse element of `7/8` for addition?

Answer: `-7/8`

Problem: 2

What is the inverse element of 100 for multiplication?

Answer: `1/100`

Post a Math Problem

Introduction to post a math problem:

Post a math problem is that several math problem posted on the internet for the students help. There are many websites that post a math problems to help the students. Among the entire website tutor vista is the famous and wonderful website which has excellent tutoring team to help the students any time with all the homework problems. The tutoring team will be online 24 x 7 to help the students.In the tutor vista website any student can post a math problem at any time and they can immediately get help. In this article let us see sample math problems posted in this website. Understanding Associative Property of Addition Definition is always challenging for me but thanks to all math help websites to help me out.

Post a Math Problem:

Example 1:

Find the solution of p in the equation 7p + 4p = 55

Solution

Given equation is 7p + 4 p = 55

Add leht side of the equation since both are in terms of p

7p+ 4p = 55 p

So 11p = 55

Divide both sides by 11

`(11p)/11` = `55/11`

p = 5.

Check the value by substituting p = 5 in the given equation

7(5)+4(5) = 55

35 + 20 = 55

55 = 55

So the answer p = 5 is correct.

Example 2:

Solve for x in the given equation 10x + 2 = 47

Solution

The given equation is 10x+2 = 47

Subtract 2 on both sides

So 10x + 2 -2 = 47 - 2

By subtracting 2 the equation is formed as 10x = 45

Now divide by 10 on both sides

`(10x)/10` = `45/10`

x = 4.5

So we get the answer as x = 4.5.

Now we can check this whether our answer is correct or not. For checking our answer substitute the value x = 4.5 in the given equation at the place of x. Is this topic What are Rational Numbers hard for you? Watch out for my coming posts.

So given equation is 10x + 2 = 47

Substitute x = 4.5

10(4.5) + 2 = 47

45 + 2 = 47

47 = 47

So both sides are equal and our answer x = 4.5 is correct.

Post a Math Problem:

Here are some of the question. Solve and find out the solution and check as shown above.

1. Find the value of k of the equation 3k = 27

2. Find the value of p of the equation 8p - 3p = 75

3. Find the value of p of the equation 12 p = 42 + 102

4. Find the value of m of the equation 15m - 7m = 2m +66

5. Find the value of s of the equation 5s + 50 - 3s = 60

Answers

1. k = 9

2. p = 15

3. p = 12

4. m =11

5. s = 5

Law of Sines Equation

Introduction to law of sines equation

The trigonometric law of sines equation is used to calculate the unknown side of the triangle. In triangle we recognize the either sides or angle we can calculate the sizes of the other sides and angles. If we can consider the right triangle, we can make use of simple trigonometric ratios to determine the unidentified lengths of the side of the triangle.  Within a general triangle, you need using other technique; they are the laws of sines and cosines formulas. Let us see about the law of sines equation.

Law of Sines Equation

Assume the following triangle

In the above triangle include the inside angles A, B and C.

If any three values are recognized subsequently we can obtain the other three values.

Total of the inside angles of the triangle equivalent to one eighty degree.

A+B+C = 1800

We can find the sides of triangle using sine rule. I have recently faced lot of problem while learning college math problems with answers, But thank to online resources of math which helped me to learn myself easily on net.

`a/sinA = b/sin B = c/sin C`

Examples for Law of Sines Equation

Example 1 for law of sines equation

Compute the unknown side of the triangle.

Solution

The total of the internal angles equal to one eighty degree

A + B + C = 180º

Therefore

C = 180º - (A+B)

= 180º - (30º+70º)

= 180º - 100º

C = 80º

To compute side c using the sine rule

`b/sinB = c/sinC`

`c = (38 sin 80^0)/sin 70^0`

= 38 x 1.0480

c = 39.824

To compute side a using the sine rule

`a/sinA = b/sin B`

`a = (38 sin 30^0)/sin 70^0 `

= 38 x 0.5320

a = 20.216

Thus the sides of the given triangle a = 20.216 and c = 39.824

Example 2 for law of sines equation

Compute the unknown side of the triangle.

Solution

The total of the internal angles equal to one eighty degree

A + B + C = 180º

Therefore

C = 180º - (A+B)

= 180º - (30º+70º)

= 180º - 100º

C = 80º

To compute side c using the sine rule

`b/sinB = c/sinC`

`c = (45 sin 80^0)/sin 70^0`

= 45 x 1.0480

c = 47.16

To compute side a using the sine rule

`a/sinA = b/sin B`

`a = (45 sin 30^0)/sin 70^0 `

= 45 x 0.5320

a = 23.94

Thus the sides of the given triangle a = 23.94 and c = 47.16

Practice Subtracting Fractions

Introduction to practice subtracting fractions:

To practice subtracting fractions, first we convert both denominators to the number. Fractions are  reduced to their lowest terms so that they would be easier to recognize. To find fraction’s lowest terms, you need to divide the numerator and the denominator by anycommon factors. Here we need to practice subtracting fractions that is learning subtracting fractions problems. In this article let us see problems to practice subtracting fractions.

Practice Subtracting Fractions:

Subtracting fractions is a process of collecting all  like fractions. If the denominators are the same then just subtract the numerators.

Example 1:

`9/ 8` - `4/ 8`

Solution:

If the denominators are the same then just subtract the numerators.

`9/ 8` - `4/ 8` =  `5/8`

Example 2:

`1/3` - `2/5`

Solution:

If the denominators are different then first find the LCM of denominator and make the denominator same then subtract the numerator.

`1/3` - `2/5`    LCM = 15  ie. Both 3 and 5 of denominator is multiple of 15.

`1/3`   - `2/5`  = `(1*5) / (3*5)` - `(2*3)/(5*3)`   = `5/15` - `6/15` = `-1/15` .

Example 3:

`11/ 8` - `4/ 8`

Solution:

If the denominators are the same then just subtract the numerators.

`11/ 8` - `4/ 8` =  `7/8`

Example 4:

`1/3` - `1/4`

Solution:

If the denominators are different then first find the LCM of denominator and make the denominator same then subtract the numerator.

`1/3` - `1/4`    LCM = 12  ie. Both 3 and 4 of denominator is multiple of 12.

`1/3`   - `1/4`   = `(1*4) / (3*4)` - `(1*3)/(4*3)`  =  `4/12` - `3/12` = `1/12` .

Practice Subtracting Fractions:

Example 5:

`12/ 8` - `5/ 8`

Solution:

If the denominators are the same then just subtract the numerators.

`12/ 8` - `5/ 8` =  `7/8`

Example 6:

`12/7` - `1/8`

Solution:

If the denominators are different then first find the LCM of denominator and make the denominator same then subtract the numerator.Please express your views of this topic Free math problem solver by commenting on blog.

`12/2` - `1/8`    LCM = 8  ie. Both 2 and 8 of denominator is multiple of 8.

`12/2` - `1/8`  = `(12*4) / (2*4)` - `1/ 8`   = `48/8` - `1/8` = `47/8` .

Example 7:

`18/ 8` - `9/ 8`

Solution:

If the denominators are the same then just subtract the numerators.

`18/ 8` - `9/ 8` =  `9/8`

Example 8:

`4/3` - `2/5`

Solution:

If the denominators are different then first find the LCM of denominator and make the denominator same then subtract the numerator.

`4/3` - `2/5`    LCM = 15  ie. Both 3 and 5 of denominator is multiple of 15.

`4/3` - `2/5`  = `(4*5) / (3*5)` - `2/15`  = `20/15` - `2/15` = `18/15` .