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
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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)
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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)
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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 ---
Improper faction =
[(Quotient x divisor)+ numerator ] / denominator
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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 :
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
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How to add fractions with different denominators -
Method 1 --
Example: 7 / 5 + 8 / 3 =
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
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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
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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
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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
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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
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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:
Method 1 --
Example:
9 / 5 - 8 / 3 = ?
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 example