Define Least Common Denominator

In the previous post we have discussed about What are Rational numbers

and In today's session we are going to discuss about Least Common Denominator,  We all generally deal with the addition and the subtraction of two or more fractions while studying the basic math and the primary step which we have to perform to carry out such types of the additions and the subtractions of the different fractions is to find out the least common denominator of the two or more number of the fractions. So in this article we will study about the least common denominator and we will also see the method to calculate it. The lowest common denominator is generally denoted by LCD in the context of the math.

So first let us start with the definition of the least common denominator. The lowest common denominator in the theory of the basic mathematics can be called as the common multiple which is the smallest, of two or more number of the denominators when considered for any of the set or the group of the fractions. We can also modulate our definition of the lowest common denominator in another way and say that it is the smallest of those types of the integers which are positive and which are denoting the different multiples of any number of the denominators of the fractions.

Now let us take some of the simple examples to understand the concept of the lowest common denominator more precisely. Suppose we have to calculate the lowest common denominator of the two fractions 7/9 and 4/13. So the maximum of the common factors of the 2 denominators 13 and 9 is 1 only. So after multiplying 13 and 9 we obtain 117 and then we divide it by 1 to obtain 117 as the lowest common denominator.

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What are Rational numbers

We have different types of number in mathematics and all of the plays a very significant role in many areas like science, physics, engineering, aeronautics and many more. They are natural numbers, whole numbers, real, rational, irrational, prime numbers, integers, complex numbers, etc.
But today we are going to discuss about a very important question: what are rational numbers, almost everybody uses this number, but do we know it?
So, the answer to the question: what are rational numbers, is, rational numbers are those numbers which can be written in the form of a fraction or a quotient like a/b, where a and b are the integers and b is not equal to zero.(want to Learn more about Rational numbers, click here),
The question: what are rational numbers, also shares one important point, which is: the decimal expansion of the rational numbers always either terminates itself after some finite sequence of digits or it repeats some finite sequence of digits again and again. For example: 1.33333…, 2.54, 1/10, etc.
There is another type of number which is totally opposite of what a rational number is, that number is an irrational number, which cannot be written in the form of a quotient or a simple fraction like a/b because the decimal expansion of an irrational number continues forever without repeating some finite sequence of digits over and again.
Rational numbers are of course dense in nature as we know that in between every two integers there exists many rational numbers.
But if you see according to Cantor’s proof, as we know that the real numbers cannot be counted or uncountable but rational number are countable and real number line is the mixture of rational numbers and irrational numbers, so they say that almost all the real numbers are irrational in nature.
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Comparing Fractions and Decimals

Let us first study about fractions and decimals. Fraction numbers are the numbers which can be expressed in the form of numerator / denominator. Also if we look at the decimal number, it is the combination of the whole number and its decimal part. In order to learn about comparing fractions and decimals, we will either convert the decimal to fraction and fraction to decimals. Let us write the two numbers one in the decimal form and the other in the fraction. So we say that if the numbers are 1.25 and 4 / 10. Let us first convert  1.25 in the  fraction by removing the decimal. So we will write 1.25 as 125 / 100. Now we take the fraction 4/10, it can be written as (4 * 10) / ( 10 * 10) =40 / 100
  Now we observe that the two fractions are with the same denominator. So we conclude that the smaller numerator represent the smaller fraction. SO here 125 > 40, thus we say that  1.25 > 4/10.  In case we have the fractions like ¾ to be compared by  3.25, we will write ¾ as ( 3 * 25 ) / ( 4 * 25 )
= 75 / 100
On another hand we have 3.25 as  325 / 100
 Thus we observe that the two numbers are now with the equal denominator. So we say that the smaller numerator represent the smaller number. Thus here 75 / 100  < 325 / 100
 So we can say ¾  < 3.25

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Converting Fractions to Decimals

In the previous post we have discussed about How to Convert Decimals to Fractions and In today's session we are going to discuss about Converting Fractions to Decimals. We know that the fractions are written in the form of numerator  / denominator. In case we have the denominator as the power of 10, we say that the fraction is a decimal fraction. On other hand we say that the fraction is a vulgar fraction. Let us learn about Converting Fractions to Decimals. We will first talk about the fractions which have the denominators as 10, 100, 1000, 10000 . . . . etc. Now we will check that how many zeroes appear in the denominator and then we will remove the denominator and place the decimal point at the same number of places as equal to the number of zeroes. So if we have 123 / 10, we will write it as 12.3 as the denominator has only 1 zero. On the other hand, if we have the fraction as 3546 /100, here the denominator has 2 zeroes, so it will be written as  34.56 , (know more about Fraction, here
 In a vulgar fraction, we will multiply the numerator and the denominator with the number such that the vulgar fraction changes into the decimal fraction. Let us take the fraction 3/5. Now we make the denominator 5 to the decimal number. For this we will multiply the numerator and the denominator by 2. Thus we get: ( 3 * 2) / ( 5 * 2)
= 6 / 10
 Now it has changed to the decimal fraction so it can be written as decimal number as  0.6 Ans

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How to Convert Decimals to Fractions

In the previous post we have discussed about How to Convert Fractions to Decimals and In today's session we are going to discuss about How to Convert Decimals to Fractions.  Today we will be learning how to convert decimals to fractions, but before converting we need to have good knowledge of fraction and decimal, if we talk about fraction, it contains two part numerator and denominator, the upper one is called as numerator and lower one is called as denominator.  If we have a number such as 2/5 then 2 is the numerator and 5 is the denominator. If we talk about decimal then things written in left of decimal are considered as whole numbers and the things written in right side considered as fraction. Now our task is to convert the decimal number to fraction, for that we need to follow some simple steps given below,
Step 1: take the decimal value and write it as it is, then count the number of digit right side to the decimal point.
Step2: if there are 2 digits then remove the decimal and divide the number by 100, if there are 3 digits then by 1000 and so on…
Step 3: after the above step the number will be in fractional form, we just need to simplify the fraction.
If we follow above three steps then we can convert any number to fraction.
If we have a number .45 and we have to convert it into fraction then we just need to divide it by hundred as there are only two digit after the decimal so our number will now look like 45/100, we can simplify it as 9/20, this is the required conversion, in this way we can convert decimal to fraction.
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How to Convert Fractions to Decimals

In the mathematics any number which is written in the form of ‘i/j’ is known as fraction.
As we know that the numerator and denominator is present in a fraction, and the upper number of a given fraction is known as numerator and the lower part of a fraction is known as denominator. If in any fraction the numerator value always greater than the denominator value, these types of fractions is known as improper fraction and the fraction which has numerator value smaller than the denominator value; this type of fraction is known as proper fraction
For example:     15 and 8
                         60       24
Now we see how to convert fractions to decimals.
We will see some of the steps for converting the fraction to decimal number so that we can easily converted the value:
Step1: For converting the fraction value to the decimal value first we take any fraction number.
Step2: If we have improper fraction, then the numerator value greater than denominator value.
Step3: If we divide the numerator value by the denominator value then we get the decimal number.
Suppose we have any mixed number 75/20.
For convert the fraction numbers to decimal number we have to follow all the above following steps:
Step1: First write the fraction number:
        75/20,
Now we see that the given number is in the improper from:
= 75,
    20 
Now we divide the denominator value by the numerator value.
On dividing 75 by 20 we get
⇨75 = 3.75.
   20  
 After solving this value we get a decimal value 3.75;
Suppose the decimal number is 8.50, convert it into fractions:
The decimal number is:
8.50 we assume 1 in the denominator so that we easily find its fractional value.
= 8.50,
     1
So avoid the point by putting zero in the denominator part of the given fraction.
= 850,
   100
So the number is in fraction form.
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