Introduction to improper fraction to decimal

Introduction :

A fraction is a part or parts of a whole. If the numerator value is larger than its denominator value, the fraction is called an Improper fraction. For example 4/3, 7/2 is all improper fractions. An improper fraction value is always larger than the value1. The special kind of fraction is known as decimal fractions. That having the denominator to the powers of 10. 

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Convert the Improper Fraction to Decimal

Step 1: First we can convert the divide the numerator value by denominator value. It involves two cases. They are described in step 2

Step 2: On the first step numerator is surely greater than the denominator. But the remainder of this step value is lesser than the denominator. This is the type of proper fraction.

Step 3: So we put a point on the quotient value then we can add zero to the remainder value.

Step 4: Now the numerator value is greater than the denominator. Again we can do the same procedure. Now we can get the decimal form of the given improper fraction.

These are the main steps to followed by converting the improper fraction to decimal value.

Example Problem-improper Fraction to Decimal:

Consider the improper fraction 8/3.

This is an improper fraction because its numerator is greater than the denominator.
Two times 3 is 6 so we can get the remainder 2.
Then 2 is not divided by 3.
So we can add zero to 2 and put a point on the quotient value
That is 20
Now 20 can be divided by 3.
6 x3 are 18.
Then the remainder is 2.
Again 2 is not divided by 3
So we can use the same procedure.
Then the decimal value is 2.66…..
This value is going on.
So we can convert this decimal as 2.67
This is the procedure to convert the improper fraction to decimals.

Consider another improper fraction 15/4

This is an improper fraction because its numerator is greater than the denominator.
Three times 4 is 12 so we can get the remainder 3.
Then 3 is not divided by 4.
So we can add zero to 3 and put a point on the quotient value
That is 30
Now 30 can be divided by 4.
7 x4 are 28.
Then the remainder is 2.
Again 2 is not divided by 4
So we can use the same procedure.
Now the value is 20
20 is divided by 4
5 times 4 is 20
So the remainder is zero
Therefore the quotient value is 3.75
This is our required decimal

Introduction to rectangular prism volume

Introduction to rectangular prism volume.

                          Rectangular prism volume article deals with the volume of the rectangular prism and the model problems related to volume of the rectangular prism.

Definition of rectangular prism volume:

                      The amount of space occupied by the three dimensional rectangular prism. The volume of the rectangular prism is measured in cube units ( cm³ ,m³).volume can be calculated to three dimensional shapes only.

                                                                                              
                                                                                    

Formula Torectangular Prism Volume:

When the length, breadth and height of the rectangular prism are known, the formula to find the volume is

                               Volume of the rectangular prism = L*B*H cube. Units

                                     L is the length of the rectangular prism

                                     B is the breadth of the rectangular prism

                                     H is the height of the rectangular prism.

Model Problem to the Rectangular Prism Volume:

Problem: 1

                What is the volume of the rectangular prism when the length is 12cm, breadth is 8cm and the height is 10cm?

           Solution:

                      Length of the rectangular prism = 12cm

                      Breadth of the rectangular prism = 8cm

                      Height of the rectangular prism = 10cm

              Formula:

                               Rectangular prism’s volume = L*B*H cube. Units

                                                                             = 12*8* 10

                                                                             = 12*80

                                                                             = 960 cm³

                      Volume of the rectangular prism is 960 cm³

Problem: 2

                what is  the volume of the rectangular prism when the length is 9cm, breadth is 6cm and the height is 11cm

           Solution:

                      Length of the rectangular prism = 9cm

                      Breadth of the rectangular prism = 6cm

                      Height of the rectangular prism = 11cm

              Formula:

                          Rectangular prism’s volume    = L*B*H cube. Units

                                                                             = 9*6* 11

                                                                             = 54*11

                                                                             = 594 cm³

                      Volume of the rectangular prism is 594 cm³

Problem: 3

                Finding the volume of the rectangular prism when the length is 7cm, breadth 3cm and the height is 5cm

           Solution:

                      Length of the rectangular prism = 7cm

                      Breadth of the rectangular prism = 3cm

                      Height of the rectangular prism = 5cm

              Formula:

                               Rectangular prism’s volume = L*B*H cube. Units

                                                                             = 7*3* 5

                                                                             = 21*5

                                                                             = 105 cm³

                      Volume of the rectangular prism is 105 cm³

Algebra questions and answers

Algebra is a branch of math which mainly deals with the representation of numbers as letters or alphabets of English language.Algebra is studied by kids of grade 5 onwards.The first section is pre-algebra , then algebra 1 and algebra 2.

The algebra introduces the concept of the single variable. It is a part of a binary method (binary operators are addition, subtraction, multiplication, division) is replaced by box. The box is replaced by a letter such as x or y denote a variable, and a, b, or c denote constants. In this article we shall discuss about some algebra questions and answers.

For Ex : X + 3 = 7

Algebra deals with formulas which make simplification very easy and new techniques to solve expressions. For example the FOIL method is a new technique which can be used to simplify multiplication of expressions in an easy and accurate way. Same way the remainder theorem discussed here is a shortcut method of finding the remainder without actually dividing a polynomial.


Answers Related to some Questions of Algebra:

Qu 1:  In Algebra Foil Method to solve the following expression: (3+7x)(6+2x)

Sol:   From the foil method in algebra,

          Step 1:   (3) (6) + (3) (2x) + (7x) (6) + (7x) (2x)

          Step 2:   18 + 6x + 42x + 14 x^2

          Step 3:   18 + 48x +14x^2 (Simplify)

This is a very simple process.

Foil Method in algebra:

 The Foil method is used in algebra to multiply the two polynomials mainly binomials

  The general form is: (K+L)(M+N) = KM            + KN           + LM           + LN

                                                        |                 |                 |                |

                                                       (First)     (Outside)      (Inner)        (Last)

Answers Related to Remainder Theorem Questions in Algebra:

Remainder Theorem in Algebra

 Let f(x) be any polynomial greater than or equal to one and let b be any real number. If f(x) is divided by the linear polynomial x – b, then the remainder is f(b).

  Proof: Let f(x) be any polynomial with degree greater than or equal to one. Suppose that when f(x) is divided by x – b, the quotient is g(x) and the remainder is r(x), i.e.,

f(x) = (x – b) g(x) + r(x)

  Since the degree of x – b is 1 and the degree of r(x) is less than the degree of x – b, the degree of r(x) = 0. This means that r(x) is a constant, say r.

  So, for every value of x, r(x) = r.

Therefore, f(x) = (x – b) g(x) + r

 In particular, if x = b, this equation gives us

f (b) = (b – b) g(b) + r 

            = r,This proves the theorem.

Qu 2: Find the remainder when x^4 + x^3 – 2x^2 + x + 1 is divided by x – 1 in algebra.

Sol: Step 1:Here, f(x) = x^4 + x^3 – 2x^2 + x + 1, and the zero of x – 1 is 1.

 Step 2: Plug in x=1        So, f (1) = (1)4 + (1)3 – 2(1)2 + 1 + 1

            = 2

 By the Remainder Theorem, 2 is the remainder when x^4 + x^3 – 2x^2 + x + 1 is divided by x –1.     

How to find Prime numbers

Introduction to prime numbers : let us first understand What is prime number in math ?A natural number greater than 1, which has no factors except 1 and itself is called a prime number.Example of prime numbers are: 2, 3, 5, 7, 11, 13, 17,…. and so on.what about 1 . Is the Number 1 a Prime Number? so , no 1 is not a prime number because 1 is neither prime nor composite. Every natural number except 1 is, either a prime number or a composite number.and now let us see Is Two a Prime Number?yes  2 is the only prime number which is even. All other prime numbers are odd.Let us now understand the concept of finding prime numbers.

How to find prime number?Eratosthenes, a Greek mathematician, gave a simple method to mark out primes. His method is known as the Sieve of Eratosthenes.We first list the numbers up to 100, except 1 which is neither prime nor composite.
1. Begin with 2 which is prime. So keep it but cross out all its multiples.
2. Next, the number is 3 is prime. Thus we keep it but cross out all its multiples. Some of these numbers have already been crossed out.
3. The next number not crossed out is 5. It is also prime. So, keep it and cross out all its multiples.
4. Continue this process keeping only the primes and striking off their multiples until we cannot strike off any more numbers.

Thus, the prime numbers from 1 to 100 are:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.Eratosthenes, probably, made holes in the paper instead of crossing out the numbers. Therefore, his paper must have looked like a sieve. That is why perhaps this method is known as sieve method.

From the above set of primes between 1 and 100, we do not see any pattern. We will not see any regular pattern even if we take numbers between 1 and 10000. Mathematicians from ages tried unsuccessfully to find a simple formula which will give all the prime numbers and only the prime numbers. It is now known that no simple formula exists, so the only way to find whether the given number is prime is to see if it has any factor other than 1 and itself.now let us know What is the largest known prime number? The largest known prime number is 243112609 - 1, It is the largest integer that is currently known to be a prime number.

Formula for Standard Deviation

In Statistics, Standard Deviation is the measure of variability or spread of scores within a set of data. It is calculated as the root mean square deviation of the values from their arithmetic mean
Standard Deviation Equation or Formula for Standard Deviation

Standard Deviation

The given data with ‘n’ data values, there are two types of data:
1. Sample data (selection from a bigger population)
2. Population data (from a group of sample)
The standard deviation formula or the standard deviation equation is given as,
Population Standard Deviation, s = square root of [sigma(xi-x(bar))^2/(n)]
Sample Standard Deviation, s = square root of [sigma(xi-x(bar))^2/(n-1)]
[ s is the standard deviation, xi = all the data items of a sample data (i is 1 to n), x(bar) = mean of the sample data, n=number of data items]

How to do Standard Deviation:
To find the Standard Deviation the steps involved are:
• First we need to count the number of data items in the given sample, this gives us ‘n’
• The mean of the data is calculated, x(bar)
• Subtract the mean from each data item and square the difference, [(x-x(bar)]2 tabulate this values
• Find the sum of the above tabulated values, sigma [(x-x(bar))^2]
• Divide the sum with the number of data items (n); sigma [(x-x(bar))^2]/n
• Once all this done, find the square root; square root {sigma [(x-x(bar))^2]/n}
Using the formula square root of {sigma [(x-x(bar))^2]/n} gives us the standard deviation of the given sample data
Consider a sample data, 5, 8, 11, 13, 18, 7, 14, 12. Let us find the standard deviation of the given sample data using a Standard Deviation Chart
There are eight scores in the given sample data, so n=8
The mean =(5+8+11+13+18+7+14+12)/8= 88/8 = 11

Data Values (x)        [x-x(bar)]2
5         (-6)^2=36
8        (-3)^2=9
11   (0)^2=0
13 (2)^2=4
18 (7)^2=49
7 (-4)^2=16
14 (3)^2=9
12 (1)^2=1

Sigma  [x-x(bar)]^2= 36+9+0+4+49+16+9+1= 124

Sigma  [x-x(bar)]2/n = 124/8 = 15.5

Standard Deviation =Square root{ Sigma  [x-x(bar)]2/n} = square root {15.5} = 3.94
So, the standard deviation of the given sample data is 3.94

Standard Deviation Graph
The standard deviation is a statistic which tells us how the various samples or data items of a sample data are distributed around the mean in a set of data. In a normal distribution, the graph of the standard deviation is in the shape of a bell curve. When the samples are mostly together then the graph we get is a steep bell curve; which shows that the standard deviation is small. When the samples are spread apart then the bell curve we get is relatively flat; which shows that the standard deviation is relatively large.

Radicals learning

Let's learn what are like radicals and unlike radicals in today's post.

Radicals are nothing but the roots of an expression and thus it holds huge importance in the study of square roots. The typical radical definition is that radicals are the opposites of exponents. The square root symbol is known as the radical.

There are two types of radicals:

• Like radicals
• Unlike radicals

Like radicals: The radicals that has the same index and radicand are called like radicals. If the roots of the numbers are similar they are termed as like radicals. This is the like radicals definition.

Unlike radicals: On the other hand when the roots of the numbers differs, they are termed as unlike radicals.

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Decimals in words

Let's learn about Decimals in words in today's post.

The heart of our number system is considering by place value. Many ways can be represent the decimal numbers. But the important one is place value. The numbers in a base-10 numeral system is specified as decimal notation. A dot with a decimal number, like to present in 5.702. Decimal powers in decimals, (1, 10, 100, and 1000) and secondary symbols for half these values (5, 50, and 500) are contained as roman numerals.

Next time i will help you with some other concept such as like decimals.

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