Introduction of Coins as Money

Money is the only factor which every single works for and in this materialistic world one can buy anything and everything with money. Money can be termed as an essential factor for living in today’s world. There can never be a question What Coins are Worth Money since even a penny makes something complete. There are people in this world who seek for the same coin which many take it for granted and leave behind. To understand the worth of a penny one should know What is Money and the answer for that will explain and serve the purpose.

Coins are of different value according the number valued on it. Money Coins are of different size and of different value. Today, these coins are valued more, that is their value is increased earlier there has been just a low value coin and now the government has started providing coins of high value. The value of a coin can be well explained by a beggar who begs for a penny to get his / her breakfast. A coin lost will make the person understand the worth and value of it.

Coins are actually better for blind people, since it is made of steel and can be felt and sense the value of the coin just by touching it. Money Coins Pictures actually help in serving the above usage to avoid duplicate coins when given to a blind person. The best part is, a blind person can find out the money note the difference between duplicate and original.

The above is the advantage of coins, but there are disadvantages in using the coins. The coins are very small in size and it is possible for a person to lose the same out of negligence. And they make the wallet filled up and often spoil the wallet when piled up and not used. There are people who think that it is cheap if they use a coin to buy things in their daily life. The importance of coin is realized in bus when the ticket conductor has no change and we are forced to get down of the bus. The irritation increases when the same bus conductor takes some coins worth .50 or 1 rupee since he has no change to provide the passenger. The coin is good and very important to a section of people and another part take it for granted.

Conditional and Biconditional statements

A conditional statement is a statement which is performed by if true or false. For eg: if p and q are two propositions, "if p then q" is known as conditional statement or implication. A statement is called biconditional when it is expresses the idea that the presence of some property is a necessary and sufficient condition for the presence of some other property.

Conditional and Biconditional Statements:

Conditional statements and biconditional statements of different propositions may be obtained by conjunction, disjunction and negation of propositions.

Conjunction Statement:
If p and q are two propositions, then compound proposition, "p and q" is known as conjunction of the proposition. It is indicated by p q. The conjunction of two propositions p and q are true, if both p and q are true and in all other cases it is false.

Disjunction Statement:
If p and q are two propositions, then the compound proposition "p or q" is called the disjunction of p and q. It is indicated by p v q. The disjunction p v q of two proposition p and q are false if both p and q are false and in all other cases, it is true.

Negation Statement:
Let p be any proposition. The suggestion "not p" is called the negation of p. It is indicated by ~p. The negation p is false if p is true and also the negation p is true if p is false.

Example for Conditional and Biconditional Statements:

Consider the proposition, “If it is rainy then it is cloudy”, which we say is a conditional statement.
Let us consider, p =“It is raining”, q =“It is cloudy”. Then the proposition can be written as “If p then q”. We symbolize this as, p à q. This can also be deliberated as “p implies q”. We never want something false to follow from something true; i.e. we do not want “If pq” to be true if p is not true and then q is not true.

Factors of a Number

The term factor of a number is a part in which a number can be broken down. All the factors of a number when multiplied together give the number. For example number 12; let us try with a factor tree, which helps in figuring out all different factors.

To Find the Factors of a Number 12, we can see that one is divisible by 12 so one is a factor. Then 2, 3,4 are too divisible so they all are factors of 12 too. We see if 5 is a factor or not, as 5 is not divisible by 12 so 5 is not a factor of 12. Then we take 6 and see the other numbers too. Hence we can conclude that All Factors of a Number 12 are 1, 2, 3, 4, 6 and 12.

Because these are also parts that can give us 12 so these are all numbers which can be considered as Factors of Number 12. Number one is the factor of all the numbers. From the algebra perspective we can see it this way, suppose we have x^2+3x . Let’s us understand by knowing first what do they have in common. So they both have an x, hence x is considered as a factor here.  And about the left overs, x times x is x ^2 and x times what is positive 3 after taking x as common, this equation can be written as X(x+3).

So we have factors not just in numbers but also in algebraic expressions in terms of variables. Factors are basically the numbers, which a larger number can get divided by.  Similarly if we have number, its factors will be 1, 3 and 9. We can find the Missing Factor by simply dividing the factor we know by the number we have. For example: - if we have number 15 and 1 and 5 are factors given to us.

To determine its missing factors, we can divide 15 by 5 which would give us 3. Hence 3 is also a factor. Therefore 1, 3, 5 and 15 are the factors of 15. Let us do one more example of finding the factors like what are the factors of number 8. As starting with the lowest number and its partner of course one times 8 gives us 8 only. Then 2, 4 and 8 are divisible by 8 too. Thus, 1,2,4,8 are all factors for number 8.

Classifying triangles

Triangle is one of the polygon. The triangle has three sides and it falsehood in the equivalent flat surface and the calculation of internal angle measures to 180 degrees. The external angle is like to the measure of isolated interior angles in their classifying triangles. The sum of any two sides is greater the third side.

The triangles can be classifying on the basis of length of sides and the size of angles

Classifying Triangles on the Basis of Length:

The triangles can be classifying on the basis of length of sides and the size of angles.

• Equilateral Triangle,
• Isosceles Triangle,
• Scalene Triangle.

Triangles are classifying as

Equilateral Triangle:

The triangle has identical length of sides. Each angle measures to 60 degrees. It is a type of normal polygon.

Isosceles Triangle:

The triangle has two conflicting sides are parallel to each other. It also has two one and the same angles. The base angles opposite to the equal sides are equal

Scalene Triangle:

The triangle sides are unequal is normally known as scalene triangle. These types of triangles are having unequal sides

Classifying Triangles on the Basis of Angles:

Classifying triangles by using angles:

• Right angles triangle,
• Acute triangle,
• Obtuse triangle

Right Triangle:

If one angle of a triangle is a 90 degree angle, followed by the triangle is known as Right angled triangle or right triangle. Right angle is the same to 90 degrees. It follows the Pythagoras theorem.

In a right-angled triangle,

The square on the hypotenuse = sum of the squares on the legs

Acute Triangle:

When all the three angles of a triangle are acute, it is normally named as an acute triangle. Acute angle is an angle which is a slighter amount than 90 degrees.

Obtuse Triangle:

When one of the angle is obtuse in triangle, that the triangle is namely represented as an obtuse angled triangle, or an obtuse triangle. An Obtuse angle is an angle which is superior than 90  and a lesser amount of than 180 .

How to calculate Interquartile Range?

Inter quartile range is the variability measure by dividing an ordered dataset into three quartiles. It is used in the calculations of statistics instead of total ranges. Interquartile Range (IQR) is also sometimes called as the middle-fifty or midspread which measures the statistical dispersion of data.

Definition of Interquartile range

When a given set of data is divided into three quartiles based on median of those values, which will be discussed later, IQR can be defined. IQR is defined as the difference of the third or upper quartile (seventy fifth percentile) to the first or lower quartile (twenty fifth percentile) of the data in an ordered range. Half of this range of value is termed as semi-inter quartile range. The Statistics interquartile range is used to summarize the extension of data which is spread. This is considered as more effective than the median or mode values since it shows the range of dispersion rather than a single value.

Steps to Calculate the Interquartile range
Let us consider a dataset having 9 numbers 19, 20, 4, 9,8,11,15,10,12 and calculate the inter quartile range for that.
Step 1: Arrange the given set of data from smallest to largest number. Therefore the order changes to 4,8,9,10,11,12,15,19,20.
Step 2: Find the median of the series. Median is the exact middle number of a series, if the total numbers are odd. If the total number in the set is even, then the average of two middle numbers will be the median. In the above case since total numbers 9 is odd, the 5th data will be the median, which is 11.
Step 3:  Now we have to find the Q1 from left side numbers of the median and Q3 from the right side numbers of the median. From the left side 4 numbers we will get the median as (8+9)/2=8.5, which is Q1.  From the right side numbers we will get the median as (15+19)/2=17, which is Q3.
Step 4: Now, the formula for finding interquartile range is, IQR = Q3-Q1. Therefore we get the IQR as 17-8.5=8.5. Thus 8.5 is the Inter quartile range of the given series.

Thus the separation of quartile decides the value of the IQR and one should be keen on calculating the quartile values.
Alternative definition IQR can also be defined as the distance between the smallest and largest values which are present in the middle 50 percent of the dataset.  Consider a dataset having numbers 1, 3, 4,5,5,6,7,11.  After neglecting the upper and lower quartiles of the dataset, we get the remaining middle numbers as 4,5,5,6. Hence from this the IQR can be calculated as 6-4=2.

Converting Fractions to Decimals

How to Convert Fractions to Decimals
The manual method to convert Fraction to Decimal is by dividing the numerator with the denominator using the long division method for instance, 4/5 here 4 is divided by 5 using the long division method, 4 is a number less than 5 and hence we start with a decimal point in the numerator to make 4 -> 40. Now that the number is 40 using the decimal point we can divide 40 with 5 as 5 x 8 = 40, so the quotient would be 0.8 which is the decimal form of 4/5. Another method used in converting Fractions to Decimals manually is to,
• find the number which when multiplied with the denominator gives a multiple of 10.
• Once the number is found both the numerator and the denominator is multiplied with that number
• The numerator is written with an appropriate placement of the decimal point according to the multiple of 10 in the denominator
For example, 4/5 fraction to decimal first we find the number which when multiplied with 5 gives a multiple of 10. 20 times 5 is equal to 100, so the required number is 20. Now the numerator and the denominator both are multiplied with 20 which gives, 4x20/5x20=80/100, the denominator being 100 the decimal point has to be placed two places towards left from the right which gives .80 or 0.8

When we Convert Fraction to Decimal at times we might not be able to make the denominator a multiple of 10 in such cases an approximate decimal is calculated by multiplying the denominator which  gives the nearest value of multiple of 10, for instance 1/3 and 2/3 fractions to Decimals would be multiplied with 333 in the numerator and denominator which gives 333/999 and 666/999 and the decimal point is placed 3 places towards left from the right as 999 is near to 1000 which has three zeroes, so the approximate decimals are 0.333 and 0.666, the accuracy is only till three decimal places.

To convert Fraction to Decimal using a long division can be given as follows, 2/3 would be 2 divided by 3
2 is less than 3 and hence cannot be divided.  In such case a decimal point is used to make 2,  20. 20 when divided by 3 would be a repeated decimal of 6 which is written as 0.66666…. Rounding of the decimal is done if required.

                                   0.666…  (Goes on)

                                3|20

                                  - 18

                                      20

                                    - 18

                                       20

                                     - 18

                                         2  

Simplifying Fractions

Simplifying Fractions Algebra
Fractions are part of a whole number written as numerator/denominator, the numerator and the denominators are numbers that have factors other than 1 and itself, in short composite numbers. The process of simplifying fractions is a simple method of reducing fractions. Let us now learn how to simplifying fractions which leads to a reduced fraction. In simplifying fractions following are the steps to be followed:
• First we need to find the common factor of the numerator and the denominator. For instance, the common factor of 4 and 8 is 4 as 4 divides both 4 and 8 evenly.
• Next step is to divide the numerator and also the denominator with the common factor of the numerator and the denominator
• The process is to be repeated till there are no common factors for the numerator and the denominator
• Once the composite numbers of the numerator and denominator have no common factors left, the fraction is a reduced fraction or a simplified fraction

Consider the following Simplifying Fractions Examples
Simplify the fraction 48/108,
The common factor of 48 and 108 is 2, dividing 48 and 108 with 2, 48/2=24 and 108/2=54,
The common factor of 24 and 54 is 2, dividing 24 and 54 with 2, 24/2=12 and 54/2=27,
The common factor of 12 and 27 is 3, dividing 12 and 27 with 3, 12/3=4 and 27/3=9.
There are no common factors of 4 and 9 other than 1 and hence the simplified fraction is 4/9

There is another method used in Reducing Fractions or simplifying fractions, it is the GCF method. In this method, the greatest common factor of the numerator and the denominator are found. Then the numerator and the denominator are divided by the greatest common factor which gives the reduced fraction. So, in this method first the largest number that goes exactly into the numerator and the denominator is found,  9/27, here the largest number that divided 9 and 27 exactly is 9 and hence the reduced fraction would be 9x1/9x3= 1/3

Examples of Simplifying Fractions
Simplify the fraction 48/108
The greatest common factor of 48 and 108 is,
48= 2 x 2 x 2 x 2 x 3
108= 2 x 2 x 3 x 3 x 3
The greatest common factor is, 2 x 2 x 3= 12
The numerator and the denominator are divided with the greatest common factor
48/12 = 4 and 108/12=9, the simplified fraction is 4/9 which has no other common factor other than 1