By what fraction 5 3/7 be divided to get 4/7

Given mixed fraction is 5 3/7

• 5 3/7 is a mixed fraction.
• 5 - is whole number part
• 3/7 - is proper fraction part ( fraction part of mixed fraction)

Step 1 - Change the mixed fraction into improper fraction.

5 3/7 can be changed into improper fraction by multiplying the whole number part (5 ) into denominator of proper fraction part ( 7)

5 x 7 = 35

Step 2 - 

Add the answer in step 1 with numerator of fraction ( 3)

35 + 3 = 38

So 37 is the numerator for the improper fraction

and denominator of fractional part is the denominator.

So the mixed fraction , 5 3/7 = 38 / 7 improper fraction

Let assume 'y' is the fraction which, when the given mixed fraction is divided with 'y' , we need to get an answer as 4/7

the equation is (38/7) / x = 4/ 7

solving for y , we get 38/7 = 4/7 X (y)

y = (38 / 7) X ( 7 / 4)

y = 38 / 4

The fraction 5 3/7 should be divided by 38/4 to get result of 4/7

Visit this page on this website, to learn more about fractions 

How to find greater fraction [ 10 best examples]

How to find greater fraction

How to find greater fraction is a common problem type that students need to learn to solve while learning fractions.

Finding the greater values are easy when there are same numerator or same denominators for given fractions.

• If two fractions have same numerator then the fraction when smaller denominator is bigger

• If two fractions have same denominator then the fraction when bigger numerator is bigger

Problem comes when there are different numerator and denominator values.

How to find greater fraction ?

There are two methods which can be used to find the greater fraction:

This blog contains 10 examples in total and 5 examples for each method.

Method 1

Make the denominators for all the given fractions equal

Step 1- Make the denominators for all the given fractions equal by multiplying both numerator and denominator with a suitable number

( Making denominator values equal to the LCM of all denominators is easier but not mandatory)

Step 2 - Now that all the denominators are equal - fraction with higher numerator value is greater fraction.

Below are the 10 solved examples that help understand how to find which fraction is greater.

• Learn how to find greater fraction using method 1 in the Examples 1 through 5 ,

• Learn how to find greater fraction using method 2 in the Examples 6 through 10

=================

Example 1 -

Lets find the greater fraction among

 4/5 , 7/15 and 9/20 ?

Solution:

LCM of 5 , 15, 20 is 60 -

Lets make all denominators equal to 60 by multiplying appropriately.

• 4/5 = (4 x 12) / (5 x 12) = 48/60

• 7/15 = (7 x 4) / (15 x 4) = 28/60

• 9 / 20 = (9 x 3) / (20 x 3) = 27/60

As all the denominators are equal -- the fraction with

greater numerator is greater in value

Answer - 48 / 60 is the greater fraction.

==============================

Example 2 -

How to find greater fraction among 

2/50 , 3/40 and 4/60 ?

Solution:

LCM of all denominators 50 , 40, 60 is 600 -

Lets make all denominators equal to 60 by multiplying appropriately.

• 2/50 = (2 x 12) / (50 x 12) = 24/600 

• 3/40 = (3 x 15) / (40 x 15) = 45/600

• 4/60 = (4 x 10) / (60 x 10) = 40/600

As all the denominators are equal -- the fraction with greater numerator is greater in value

45 / 600 is the greater fraction

=============================

Example 3 -

How to find greater fraction among following mixed fractions

2 (2/5) , 2 (3/4) and 2 (4/60) ?


Solution:

Step 1 -- convert the given fractions into improper fractions

2 (2/5) = 12/5

2 (3/4) = 11/4

and 2 (4/6) = 16/6

Step 2 -- LCM of all denominators 5 , 4, 6 is 60 -

Lets make all denominators equal to 60 by multiplying appropriately.

• 12/5 = (12 x 12) / (5 x 12) = 144/60 

• 11/4 = (11 x 15) / (4 x 15) = 165/60

• 16/6 = (16 x 10) / (6 x 10) = 160/60

As all the denominators are equal -- the fraction with greater numerator is greater in value

165 / 60 is the greater fraction

===============================

Example 4 -

How to find greater fraction among following mixed fractions

2 (2 / 5) , 2 (3 / 4) and 3 (3 / 5) ?


Solution:

This is a easy problem to solve - 3 (3 / 5) is greater as

the values of 2 (2 / 5) and 2 (3 / 4) lie between 2 and 

3 --whereas the value of 3 (3 / 5) lies between 3 and 

4.

==============================

Example 5 -

How to find greater fraction among following negative fractions

- 2 / 5 , - 3 / 4 and -13 / 7 ?


Solution:

LCM of all denominators 5 , 4, 7 is 140 -

Lets make all denominators equal to 60 by multiplying appropriately.

• - 2 / 5 = (-2 x 28) / (5 x 28) = - 56 / 140

• - 3 / 4 = (-3 x 35) / (4 x 35) = - 105 / 140

• - 13 / 7 = (-13 x 20) / (7 x 20) = -260 / 140

As all the denominators are equal -- the fraction with smaller numerator is greater in value

- 56 / 140 is the greater fraction as given fractions are negative.



=================================

                           Method 2

How to find which fraction is bigger using method 2


In this method ,

we need to divide the numerator with denominator

and find which fraction has greater value.


Example 6 -

How to find which fraction is bigger among 

7/15 , 18/25 , 36/40 ?

Solution:

Divide numerator by denominator for all given fractions.

• 7/15 = 0.467
• 18 / 25 = 0.72
• 36 / 40 = 0.90

Among the 3 answers, 0.90 is greater than 0.72 and 0.467 so 36 / 40 is the greater value.

=============================

Example 7 -

How to find which fraction is bigger among 

20/15 , 30/25 , 50/40 ?

Solution:

Divide numerator by denominator for all given fractions.

• 20 /15 = 1.33
• 30 / 25 = 1.20
• 50 / 40 = 1.25

Among the 3 answers, 1.25 is greater than 1.2 and 1.33 so 50 / 40 is the greater value.

================================

Example 8 -

How to find which fraction is bigger among 

- 200 /15 , -30 / 25 , 1 / 40 ?

Solution:

Among the 3 fractions, 1/40 is greater than -200/15 and -30 / 15 as it is positive fraction.

All positive fractions will be greater than negative fractions.

=============================

Example 9 -

How to find which fraction is bigger among the given mixed fractions

1(2 / 15) , 1 (6 / 25) , 1 (7 / 40) ?


Solution:

All the 3 fractions have same whole number part ( =1)

so converting the fractions into their improper fractions is not required in such cases.

Just find the values for the fractional parts of the fractions.

• 2 / 15 = 0.13
• 
  
• 6 / 25 = 0.24
• 
  
• 7/ 40 = 0.175

As 0.24 is greater among the three, 1 (6 / 25) is greater than 1(2 / 15) and 1 (7 / 40)

==================================

Example 10 -

How to find which fraction is bigger among the given negative fractions

-12 / 15 , -16 / 25, -17 /35) ?

Solution:

Divide numerator by denominator for all given fractions.

• - 12 /15 = - 0.80
• -16 / 25 = - 0.64
• -17 / 35 = -0.48

Among the 3 answers, -0.48 is greater than -.64 and 0.80 so -17 / 35 is the greater value.

======================

Example 11 - 

Which fraction is bigger 1/2 or 3/4?

Solution:

Method 1 - 

LCM of 2, 4 is 4 

Make both denominators equal to 4

• 1/2 = (1x2) / (2x2) = 2 / 4 

• 1/4 = (1x1) / (4x1) = 1/ 4

2/4 is greater than 1/4 as it has greater numerator.

  How to find greater fraction is a important concept and with little amount of fraction, one can easily solve the problems taking less amount of time. 

Coding for Kids Classes [ Is it lucrative for kids ]

 Coding for Kids Classes 

[ Is it lucrative for kids ]

In today's digital world,  "Are more and more parents opting coding classes for kids"?

About thirty to forty years back there were no mobiles, no computers,no internet and one can say that the world was not yet started to be digital. Those were the days when no one or very few would have thought that the world will become almost completely digitized.

People, in those non-digital days, used to stand in a queue in the bank for long hours for cash deposit and cash withdrawals. People used to stand in lines for  reserving tickets for their journeys investing much time, and children used only notebooks, slates and texts for their studies.One could say there was almost zero digital atmosphere in those olden days.

But slowly the world started realizing that the scope and applications of coding and  it began to use programming in more and more projects and it became highly dependable and extremely popular.

Today the scenario has completely changed due to the invention of internet which is super fast and also due to it's sphere of usability where it can be accessed from many devices like mobiles, computers, tablets and so on. Most of the financial transactions are completed within minutes and just by few clicks on these devices.

Though users are able to see photos, videos, articles etc,on the screens of the devices, there is a lot of programming takes place at the back-end. Websites, apps and other software cannot be built without coding. Hence coding or computer programming has a very high demand in this growing digital world.

Today, Coding has entered in the list of essential skills required for children as there are tons of career opportunities for people skilled in coding.

What does coding mean in education? and what is coding used for?

Coding is alternate name for computer programming. Computers does not understand our languages. They understand programming languages. Programming ( coding ) is a process of writing instructions to computers for fulfilling different types of tasks. Without giving instructions it is not possible to make a computer work.

 Coding is used for creating websites, apps , coding games and other software applications.

Many parents have this query in mind - 

"Whether coding for children is right or wrong?"                              

  and 

"Whether coding make you smarter"

            

                Learning coding at a young age will make kids grow in their creative ability, logic and cognitive skills. Another advantage of learning coding at a young age is that children have great grasping power and good memory. So they understand lessons faster and remember more easily. Coding for beginners is also fun for kids as it involves teaching with the help of visual aids and also involves activities like building blocks which look great for most of the children. Consequently, children get this essential skill set which the most employers are searching for before hiring the candidates.  

In the recent times we are seeing a lot of advertisements for coding classes for children on internet. These increasing number of advertisements makes one understand that the demand and popularity for coding has considerably gone up, and more and more children are joining the coding classes in the current scenario.

There are few institutions which are offering free trial classes for getting a better idea of coding for kids. There are few websites which offer free coding classes up to a certain level of course beyond which one needs to pay for subscriptions to get the access for full course. In terms of study materials, there are dozens of books sold online.

Does coding require math knowledge? 

Coding and maths are different from each other but knowledge of maths makes coding a lot easier to learn.

If one needs to know, 

how much do coding classes cost for kids? 

The answer is not simple - it depends on the factors such as institute, course curriculum, and duration.

Having said it is preferable but not mandatory to join coding classes at very young age in elementary classes.  It also makes sense to note that few kids may not like coding or they may find it difficult to understand the coding language.  Forcing such kids to join coding classes is definitely not advisable. 

Is coding compulsory in India?

One can guess that future of coding in India is going to be bright.Big changes are planned in the educational field in the India.As per the New educational policy 2020, coding will be taught as a subject starting class 6 as a mandatory course in schools in India. This new policy on coding education in India will make children fully ready for future.

Going by the today's scenario where people are depending more and more on the software products, one can expect that the requirement for people with coding knowledge would grow in the future. 

Finally, just want to conclude this post by summing up the above paragraphs :

Coding is learning the language of instructing computers and smart devices. Coding for kids is a great idea as it is one of the lucrative essential skill set. It is a combination of fun and learning.It not only improves the creative and cognitive powers of the kids but also gives a competitive edge to be more successful in their life.

Hope this post was a little bit informative.

Fractions [ Concept - Math Operations - Examples ]

                  Fractions 

 [ Concept - Math Operations - Examples ]

Fractions are important concept in mathematics. 

It is important to know mathematical operations with fractions. Questions on fractions are quite common in entrance examinations. Hence this blog covers fraction question and answers and fractions multiple choice questions along with the concept. 

Learning about this concept starts right in the class 6.

Fraction Definition:

Fraction is used when there is a need to represent a certain part with respect to a whole.

Lets understand this with a example, 

suppose if there is 1 cake, to represent 1 cake we do not need to use  fractions. 

suppose if  that cake is divided into two halves, then to represent each part of the whole cake, we need to use fractions.

It is important to understand the meaning of fractions and fractions representation.

What does it mean If  a boy eats 1 half of the cake.

It means there were 2 parts ( half + half) and boy eat 1 part (1 half) .

this can be represented in [numerator / denominator]  format where denominator represents total number of  parts of a whole and numerator represents the fractional number of parts in the total number of parts.

So half can be represented as 1 / 2 ,  it means there are two parts of a whole ( say, a cake) , in that 1 part.

similarly,

• 3/8  means there are 8 parts in total and in that 3 parts 
• 5 / 7 means there are 7 parts in total and in that 5 parts 
• 18 / 55 means there are 55 parts in total and in that 18 parts 

==================

            Proper Fractions

How to represent proper fractions?

We have already discussed fractions are representative as numerator / denominator format

Fractions where numerator is less than the denominator , it is proper fraction 

Examples:  5 / 18 , 3 / 17 , 155 / 277

As numerator <  denominator,   All Proper fractions are values less than 1 ( if both numerator and denominator are positive)

======================

Improper Fractions

How to represent Improper fractions?

Fractions where numerator is greater than the denominator , it is proper fraction 

Examples:  18 / 5 , 13 / 7 , 155 / 97

As numerator >  denominator,  the value of a improper fraction is greater  than 1 ( if both numerator and denominator are positive)

=========   

     Mixed Fractions

How to represent mixed fractions?

If improper fractions are written as a combination of whole number and a part (Part will be a proper fraction), it is called mixed fractions.



Examples: 15 2/ 3 , 19 7/ 8 etc

How to convert  improper fraction as mixed fraction ?

55/4 is a improper fraction and it can be written as a mixed fraction by dividing the numerator by denominator

                            

     

divisor       4) 55 ( 13 - Quotient

                      52  

                      3 -----Remainder

Mixed fraction =  Quotient [ Remainder / divisor ] 

 =  13 3/4  ---

How to convert mixed fraction as improper fraction 

Improper faction = 

[(Quotient x divisor)+ numerator ] / denominator

---------------------------------------

         Equivalent fractions

 

What is the meaning of equivalent fractions ?

Equivalent fractions are equivalent forms of single fraction where the value of all the equal forms will be equal.

Examples:  

 20 / 40  = 10 / 20  = 5 / 10  = 4 / 8  = 1 /2  

All the above forms are equal in their value. 

1/2 is called the simplest form of the fraction 20 / 40 .

                  

Fraction addition :

How to add fractions with same denominators

Adding fractions with same denominators is easiest.  Just add the numerators and write the same denominator

Examples:    

1)    13 / 4  +  5 /  4   =   ( 13 + 5 ) / 4   = 18 / 4 

 2)   (131 / 7)  + ( 55 /  7 )  +   (15 / 7 ) = 

  ( 131 + 55  + 15 ) / 7   = 201 / 7                                        

Fractions with same denominators are called Like Fractions

----------------------------

How to add fractions with different denominators -

Fractions with unlike denominators are called Unlike fractions. Adding fractions with unlike denominators  can be achieved in two methods

Method 1 

Step 1 - multiply the  numerator  and denominator of fraction 1 by the denominator fraction 2

Step 2 - multiply the  numerator  and denominator of fraction 2 by the denominator fraction 1

Now the denominators of both the fractions will become equal , 

Step 3 -  add the fractions using add like fractions method explained above.

Method 1 --

Example:   7 / 5   +  8 / 3   =  

Step 1 - multiply the numerator  and denominator of fraction 1 by the denominator fraction 2

  = (7 x 3) / (5 x 3)  =  21 / 15 

Step 2 - multiply the  numerator  and 

 

= (8 x 5) / (3 x 5)   =  40 / 15    

Now the denominators of both the fractions will become equal = 15

Step 3 -  add the fractions using add like fractions method explained above.

21 / 15   +  40 / 15    =  61 / 15 

This method becomes time consuming when there more than 2 factions to be added ,

so following LCM method is easier.

           

Method 2 -  

How to add fractions with LCM 

Step 1 - find the LCM for all the denominators given 

step 2 - multiply numerator and denominator of  each fraction  with suitable multiple so that the denomination matches the LCM value ( after multiplication)

Step 3-  add numerator values of all the fractions and put the total as final numerator  - and - write LCM obtained as final denominator

Example -  

7 / 5   +  3 / 4  + 7 / 8  =  

Step 1 - LCM of  5, 4 , 8  =  40 

Step 2 -  make all denominators = 40 by multiplying with correct multiplier

(7 x 8) / ( 5 x 8 ) + (3 x 10) / (4 x 10) +

 (7 x 5) / (8 x5)

Step 3 -  Add all the three fractions like fractions.

= 56 / 40  + 30 / 40  +  35 / 40 

 =  (56 + 30 + 35 ) / 40  

= 121 / 40 

=====================

How to add fractions with whole numbers

While adding  fractions with whole numbers , we need to divide  the whole number by 1

and follow LCM method

Example-   

      [5 / 18  ]  + 5  

Solution:

[5 / 18  ]  + 5  =  [5 / 18  ]  + 5 / 1  

LCM of 18 , 1 

=  (5 x 1)  / ( 18 x 1 )  + ( 5 x 18) / 1 x 18 

 = 5 / 18 + 90 / 18  = (5 + 90 ) / 18  =  95 / 18 

-------------------------------------- 

How to add fractions with mixed numbers ?

While adding fractions with mixed numbers, 

Step 1:  convert mixed number to improper fraction , 

step 2 :  Follow addition method discussed above as per same / different denominators  present.

Example:   13 / 25 +  3 (2 /5)

Solution:  

3 (2 /5)  is a mixed fraction,  

converting it into improper fraction we get,  17 / 5 

13 / 25 +  3 (2 /5)  =    13 / 25 + 17 / 5  

 =  13 / 25  +  (17 x 5) / (5 x 5) 

=  13 / 25  +  65 / 25 

= 78 / 25 

==========================

How to add fractions with same numerator ?

Fractions with same numerator is added in the same way as fractions with unlike denominator except that we can take the numerator as common and multiply it finally.

Example:   15 / 7  + 15 / 9

Solution:

15 / 7  + 15 / 9   can be written as  15( 1/ 7 + 1/ 9 )

 =  15 (  ( 1/ 7 + 1/ 9 ) 

=  15 (  ( (1 x 9)/ (7 x 9)  + (1 x 7)/ (9 x 7 )) 

=  15 ( 9 / 63  + 7 / 63 )

= 15 ( 16) / 63 

    5

=  15  x 16  / 63 

                    21        

=  80 / 21 

==========================

      Fractions Subtraction

Understanding the above section which discusses about the fraction simplification using addition helps a lot to understand this part of the blog which discusses about fractions subtraction examples.

 

How to subtract fractions with same denominator ?

It is very easy to subtract the fractions. Knowledge of  calculations with negative numbers is essential.

Examples:    

1)   (12 / 5 )  -  ( 11 / 5)   =  ?

Solution:

(12 / 5 )  -  ( 11 / 5)   =  ( 12 - 11) /  5   =  1 / 5 

2)   (14 / 15 )  -  ( 11 / 15)   = ?

Solution: 

 

(14 / 15 )  -  ( 11 / 15)   = ( 14 - 11) /  15  

 =  3 / 15  =  1 / 5 

3)   (17 / 5 )  -  ( 19 / 5)   = 

Solution: 

 (17 / 5 )  -  ( 19 / 5)  

 = ( 17 - 19)  /  5  

 =   - 2 / 15  

=========================

How to subtract fractions with different denominators?

 Fractions with unlike denominators are called Unlike fractions. Subtraction fractions with unlike denominators  can be achieved using following steps

How to Subtract fractions with different denominators step by step:

Step 1 - multiply the  numerator  and denominator of fraction 1 by the denominator fraction 2

Step 2 - multiply the  numerator  and denominator of fraction 2 by the denominator fraction 1

Now the denominators of both the fractions will become equal , 

Step 3 -  Subtract the fractions using adding of like fractions method explained above.

Method 1 --

Example:   

9 / 5   -  8 / 3   =  ?

Step 1 - multiply the numerator  and denominator of fraction 1 by the denominator fraction 2

  = (9 x 3) / (5 x 3)  =  27 / 15 

Step 2 - multiply the  numerator  and 

 

= (8 x 5) / (3 x 5)   =  40 / 15    

Now the denominators of both the fractions will become equal = 15

Step 3 -  add the fractions using add like fractions method explained above.

27 / 15   -  40 / 15    =  - 13 / 15 

 This method becomes time consuming when there more than 2 factions to be added ,

so following LCM method is easier.

           

Method 2 -  

How to Subtract fractions with LCM method

Step 1 - find the LCM for all the denominators given 

step 2 - multiply numerator and denominator of  each fraction  with suitable multiple so that the denomination matches the LCM value ( after multiplication)

Step 3-  solve ( add / subtract) numerator values of all the fractions and put the total as final numerator  - and - write LCM obtained as final denominator

Examples:

1)   7 / 15   -  13 / 9   = ?

LCM of  15, 9   = 45 

Need to make both the denominators  = 45 , by multiplying with suitable multiplier 

(7 x 3) / (15 x 3) = 21 / 45 

( 13 x 5 ) / ( 9 x 5) = 65 / 45 

Now subtract both the fractions

[ 21 / 45 ]   - [ 65 / 45 ]  = ( 21 - 45 )  / 45  =  - 24 / 45  =  - 8 / 15

How to find greater fraction among the given fractions can be learnt by visiting to the following links.

how to find greater fraction 

how to find greater fraction example

Decimals [Maths Operations with Decimals]

 Decimals  

[Maths Operations with Decimals]

Decimals is a important topic in mathematics. decimals are not special numbers. They are part and parcel of everyday maths.

Lets understand what are decimals using an example:

Lets say, there is a person D  purchased a book sold at 60 rupees 50 paise.

Now when D gave Rs.100 to book seller, then how much does the book seller needs to return post deducting the cost of book.

To represent the transaction and calculate the money that D gets back,  decimals are used.

This blog includes

• How to represent a decimal number?
• How do you write numbers in decimal form?
• How to represent decimals on number line ?
• How to represent a fraction as a decimal value?
• How to represent fractions in decimal form where denominator is not a multiple of 10?
• How to convert Decimal to fraction in lowest terms?
• How to find the greater decimal?
• Addition and subtraction of decimals
• Multiplication and division of decimals
• Negative decimal numbers
• Word problems on decimals

============================

How do you write numbers in decimal form?

Ans:  

Decimal number is represented with the symbol ( . ), it is called decimal point.

Example:

• 1 can be represented as 1.00
• 2 can be repsented as 2.00
• 25 can be represented as 25.00

Any value between 25 and 26 , should be written after putting a decimal point next to 25

How to represent decimals on number line ?

A Number line represents all numbers, positive, negative , zero, ration numbers, decimal numbers .

If the distance between 1 and 2 is divided into 10 equal parts...then each of these parts will be 0.1 distance apart.

Each of the part can be represented using decimal points as  1.1, 1.2 , 1.3, 1.4 , 1.5, 1.6 , 1.7, 1.8,  1.9 and 2

Similarly, the values between 1.1 and 1.2 can also represented as decimals.

1.11 ,1.12 , 1.13, 1.14, 1.15, 1.16, 1.17, 1.18, 1.19 and 1.2 

Similarly 

the values between 1.11 and 1.12 can also represented as decimals.

Suppose if the value is between  the numbers 1 and 2, say, for example, 1.35 

1.35 ,  can be represented as follows

1.35  is between 1 and 1.5 , depending the scale on number line, it needs to represented

How to represent a fraction as a decimal value?

Lets start with fraction values where the denominator is 10 and its multiples

1 / 10  can be written in decimal form as 0.1  

7 / 10 can be written in decimal form as 0.7

It there is a fraction with one zero in the denominator, then the decimal point will be after one digit from left to right of the numerator.

Similarly

15 / 100  can be written in decimal form as 0.15  

67 / 10 can be written in decimal form as 0.67

It there is a fraction with Two zeroes in the denominator, then the decimal point will be after Two digits from left to right of the numerator.

What if the numerator is a single digit number?

If numerator is single digit number then add a zero before the numerator value and put a decimal,

Example,

5 / 100  can be written in decimal form as 0.05  

9 / 100  =  0.09

Note:  The values  0.09  and just .09  are one and the same. They are different forms of representing a decimal value if there is no digit present left of decimal point.

Similarly

It there is a fraction with Three zeroes in the denominator, then the decimal point will be after Three digits from left to right of the numerator.

33 / 1000  = 0.033

168 / 1000  = 0.168

============================

How to represent fractions in decimal form where denominator is not a multiple of 10?

Suppose there is a fraction ,  171 / 2 , 

There are two methods,

Method 1 : 

To represent it in a decimal form , the denominator should be converted to multiple of 10 and decimal point needs to put appropriately.

171 / 2  = 

Multiply both numerator and denominator with 5 so that the denominator value changes to multiple of 10

( 171 x 5 ) / (2 x 5 )  =  855 / 10  = 85.5 

Method 2 :

Divide 171 by 2  by normal division method   

2) 171 ( 85.5 

      16  

          11

          10  

             1 0

             1 0 

               0 

===========================

How to convert Decimal to fraction in lowest terms?

To convert decimal to lowest fraction is easy and should be done as below

It follows method which is opposite to the method 1 seen above.

For example,

If there is a decimal value as  9. 55 .

To convert this into a fraction, we just have to divide the number with 100 as there are two digits after the decimal point.

9.55 = 955 / 100  

Next the  fraction obtained ( 955 / 100 ) can be simplified.

Going by the divisibility rules (link) ,  the numbers 955  and 100 is divisible by 5 

955 / 100  = 191 / 20 

191 / 20 is the simplified value of  955 / 100 

So,  9.55 in fraction form  =  191 / 20 

This procedure is also called converting decimal as fraction in lowest terms  or fraction in lowest form

==========================

Comparing decimals

Before understanding how to compare decimals,  it is important to know following 

0.4 = is same as  .4 ,  as a zero to left of decimal point without any other digit does not change the value

also the form ,  0.40  is same as 0.4 and  .4  , as a zero at the end of the decimal number doesnot change the value of the number 

So ,

0.4 =  .4  =  0.40  = .40      ==All these four forms are equal to one another.

=======================

Decimal greater or less

How to find the greater decimal?

Suppose there are two decimal numbers., 96.36 and 95.98 , how to find largest decimal ?

Case1 : check for the part which comes before a decimal point - If one of the numbers have greater part then that decimal number is greater between the two , irrespective of the part after the decimal point.

In the above example, clearly 96  is greater than 95 , so ignore the part  after the decimal point

Therefore  96.36 > 95.98 

Case 2:  Only when both numbers have same value for the part before decimal point, then check for the part after decimal point.

95.36 and 95.98 , Here parts before decimal point are equal for both the numbers, hence check for the part after decimal point.

0.98 > 0.36  , hence 95.98 > 95.36

Case 3:  When the part after decimal point starts with zeros 

95.36 and 95.098 -  

As we know,  

0.9 >  0.8  >  0.7  >  0.6  > 0.5 >  0.4 >  0.3  >  0.2 >  0.1 >  0.09  > 0.08  >  0.07  >  0.06  > 0.05 >  0.04 >  0.03  >  0.02 >  0.01 > 0.009 > 0.008 > .....and so on

The more the number of zeros immediately after decimal point, smaller the number.

So  0.36  > 0.098

Therefore,  95.36  >  95.098

===========================

Addition and subtraction of decimals

How to add decimal numbers ?

Add decimal numbers is simple and almost same as normal addition.

Example:   Add  584.32  and  690.45 ?

     584.32  

+   690.45  

    1274.77  

But if  one of the numbers has only 1 digit after decimal point, then zero should be added / assumed

at the second place.

Example:   Add  54.36 and  60.4 ?

     54.36  

+   60.40  

    114.76

how to subtract decimals

Example :  Subtract     666.45  from   884.39 ?

     884.39  

-    666.45  

    217.94  

Example :  Subtract     3616.4594  from   6884.39 ?

As there are 4 digits after decimals in the first decimal number , the second number 6884.39 need to written as 6884.3900

    6884.3900  

-   3616.4594  

     3267.9306  

========================

How to add decimal and fraction?

Consider adding,  2.506 with fraction 1 / 2

one cannot perform the addition if the numbers are in different forms. Hence we need either change decimal value to fraction or fraction into decimal , to make both numbers in same form.

Here it is difficult timing consuming to convert 2.506 into a fraction 

But the fraction 1/ 2  can be converted into decimal value.

1/2  = 0.5  = 0.500

Now, Add both numbers  

     2.506

 +  0.500 

     3.106

============================

Multiplication and division of decimals

Multiplication of decimals:

1) Multiplication of decimals by 10, 100 and 1000

 Multiplication of decimals by 10, 100 and 1000 is very easy. 

 If a decimal is multiplied by 10 then the decimal point moves 1 place to the right from the current position.

Example :  156.356  x 10  = 1563.56

If a decimal is multiplied by 100 then the decimal point moves 2 place to the right from the current position.

Example :  156.356 x 100  = 15635.6

If a decimal is multiplied by 1000 then the decimal point moves 3 place to the right from the current position.

Example :  156.356  x 1000  = 156356

2) Multiplication of decimals with whole numbers

Multiplication of decimals with whole numbers is like normal multiplication except that after performing multiplication a decimal point needs to be added appropriately ( we need to put a decimal point after same number of digits as in the decimal number given the question )

Example :   4.55 x 15  = 

Multiply normally and put a decimal point after 2 digits from left end of the answer 

4.55 x 15 =  68.25

Example :  

 2.55 x 150  = 

Multiply normally and put a decimal point after 2 digits from left end of the answer 

2.55 x 150  =  382.50

3)Multiplication of decimals with decimal numbers

While performing multiplication of decimals with decimals , we need to count the number of digits after which the decimal is placed in each number and put the decimal point in answer after counting the places as per the total obtained. 

Example : 

1) 10.26 x 12.36  = 126.8136

2)  0.56 x 0.09 =  0.0504

If there are not enough digits to put a decimal point, we need to add '0' s appropriately and place the decimal point

3)  0.50 x .001 = 0.00050

4) Multiplication of decimals with fractions

While performing multiplication of decimals with fractions is same as discussed above.

Example : 

1)  45.25  x  2 / 5  = 90.50 /  5  = 18.10

 OR

 9.05

45.25  x  2 / 5      =  9.05 X 2 =  18.10

 =====================

  

              Division of Decimals

1) Division of decimals with 10, 100 and 1000

  Division of decimals by 10, 100 and 1000 is same as multiplication except that , in division the decimal point moves towards left, making the value of numerator smaller.

 If a decimal is divided by 10 then the decimal point moves 1 place to the left from the current position.

Example :  96.756  / 10  =  9.6756

Divided by 10 means the value in the numerator is made into 10 equal parts, so numerator value decreases.

If a decimal is multiplied by 100 then the decimal point moves 2 place to the left from the current position.

Example :  96.756  / 100  =  0.96756

Divided by 100 means the value in the numerator is made into 100 equal parts, so numerator value decreases.

If a decimal is multiplied by 1000 then the decimal point moves 3 place to the left from the current position.

Example :  96.756  / 1000  =  0.096756

Divided by 1000 means the value in the numerator is made into 1000 equal parts, so numerator value decreases.

2) How to divide decimals by whole numbers ?

While performing division with whole numbers we need to perform normal division and put decimal point after counting the number of places after which decimal point is present in question and put decimal point in the answer after counting equal number of places.

 

Example:    

1) 89.96 / 2  =  44.98

2)  89.96 / 20 = 4.498 

3) Division of Decimals by decimals

While Dividing decimals by decimals , 

Step 1 : First divisor ( denominator) should be made as whole number by multiplying with a suitable number.

Step 2: Dividend ( numerator) also should be multiplied with same number.

This makes the division is easy.

Examples : 

1) 543 / 0.3  

To make 0.3 as whole number multiply numerator and denominator with 10

( 543 x 10 )  / ( 0.3 x 10 )  =  5430 / 3  = 1810

2)  0.543 / 0.3  

=  ( 0.543 x 10 )  / ( 0.3 x 10 )  

=  5.43 / 3  = 1.81

3) 0.0891 / .011  =

To make 0.011 as whole number multiply numerator and denominator with 1000

(0.0891 x 1000) / (0.011 x 1000)  = 89.1 / 11  =  8.1

=========================

Negative decimal numbers

What are negative decimal numbers?

Can we have negative values in decimals? 

The answer is Yes.  

Decimals can also both postive or negative.

Adding negative decimals, subtracting negative decimals , multiplying negative decimals and dividing negative decimals are done in exactly same method as normal negative numbers ( not decimals).

1) Adding and subtracting negative decimals

Examples:

1)   - 1.50 + (-0.65)  = ?

- 1.50 - 0.65  =  - 2.15

2)  - 7.60 - (-9.65)  = ?

- 7.60 + 9.65 =  + 2.05

2) Multiplying and dividing negative decimal values

1)  (-1.56 ) x ( -2.35) =  + 3.666

2)  (1.06 ) x ( -2.05) =  -  2.173

3)   - (1.21 ) /  -1.1   =  1.1

4)  - (9999.9 ) /  999.99   =  - 10

 =========================

Problems on decimals
 ( including decimal word problems)

Question 1:  D and H friends.  D paid credit card bill of  H amounting Rs. 1548.56 as D was short of funds. Next month H paid D credit card bill amounting to Rs.985.06. How much does H needs to pay to D to clear the help received by D.

Solution:  

Given ,

D paid  Rs. 1548.56  on behalf of H 

H paid  Rs. 985.06  on behalf of D

Amount D paid in excess is =     1548.56  

                                                  -   985.06 

                                                       563.50

So H needs to pay Rs.  563.50  to D to clear the help received from D

Question 2:  solve the following addition  15.63 + 56.32 + 44.36 = ?

Solution:     15.63

                + 56.32 

                + 44.36  

                  116.31

Question 3: 

 Add 863.56 and 6947.23 and subtract 2315.35

Solution:   

 

       863.56

 +  6947.23  

     7810. 79

-    2315.35  

      5495.44

Question 4:  Find the largest and smallest number among the following and find their difference

18.0612 , 18.09, 18.0053, 18.0072

Solution:

The part before the decimal point is equal for all the numbers so check the part after the decimal point.

Largest =   18.09

Smallest = 18.0053

Their difference in value is  

       18.0900

-      18.0053

         0.0847

Question 5:  

Solve   (63.1 x  11.1)  - ( 50 x 45.6) 

Solution: 

(63.1 x  11.1)  - ( 5 x 45.6)

=  700.41 - 228

=  700.41 - 228.00

=  472.41