Fraction :
Fraction is a number which
denotes the equal part of a thing or a number. In other words it can be says that a small or tiny part, amount, or proportion of something. It is expressed in the form of
a/b where a and b are integers. ‘a’ is called the numerator and ‘b’ is called
the denominator. In fraction problem in aptitude a≠0 and b≠0
Example :
Let one is a full part and it can be fractioned into
Half part = 1
2
One-fourth part = 1
4
Study on Types of fractions :
(1) Proper fraction :
When the numerator is less
than the denominator,the fraction is called as proper fraction.
Example:
8, 4, 2, 3, etc... All the numerator are larger than denominator.
9 9 5 7
(2)Improper fraction :
When the numerator is
greater than the denominator,the fraction is called improper fraction.
Example:
3, 7, 9, 4, etc... All the numerator are less than denominator.
2 6 5 3
(3) Decimal fractions :
9/10 is written as .9 ; 79/100 is written as .79
333/1000
is written as .333
(4) Recurring decimals :
(i) 1/3 =.333...= -.3; 5/7=.714285....
Since the number repeating after decimal it is called recurring number
Since the number repeating after decimal it is called recurring number
(ii) Convert 
into a vulgar fraction
into a vulgar fraction = 0.333
10×. = 3.333...
= 3.333...
(iii) convert .159 3 into a vulgar
fraction.
.159 3 =.15939939393.....
Or
100×.159 3 =100×.159393939393..=15.939393939... ....(I)
And
10000×.159 3 =1000×.159393939...=1593.939393... ...(II)
From
(II)-(I),we get
9900×.159 3 =1593-15=1578
Or
.159 3 =1578/9900
Rule:A mixed recurring decimal is equal to
a vulgar fraction which has for its numerator the difference between the number
formed by all the digits to the end of the first period and that formed by the
digits which do not recur ;and for its denominator the number formed by as many
nines as there are recurring digits, followed by as many zeros as there are
non-recurring digits.
e.g.,
.
.472=(472-47)/900=425/900
. .
. .
And 9.0061=9 61-00 = 9 61
9900 9900
9900 9900
(5) Decimals :
A collection of digits (0,1,2,3,...9)after a period(called the decimal point)is called a decimal fraction.
A collection of digits (0,1,2,3,...9)after a period(called the decimal point)is called a decimal fraction.
Example: 0.629,.579,0.0321,12.720...etc.
.5407,is
read as decimal five four zero seven and not as five thousand four hundred
seven.
(6) Modulus or absolute value:
The modulus or absolute value of any signed number (be positive or negative)is always taken as positive and is equal to the distance of the number from zero datum. It is denoted by writing the number between two vertical lines .if ‘A’ is any signed number ,its modulus or absolute value is written as |A| . If A is positive |A| =A .If A negative ,|-A| =A, so what we do effectively is that we simply drop the sign attached to the number .when modulus or absolute vale is taken.
The modulus or absolute value of any signed number (be positive or negative)is always taken as positive and is equal to the distance of the number from zero datum. It is denoted by writing the number between two vertical lines .if ‘A’ is any signed number ,its modulus or absolute value is written as |A| . If A is positive |A| =A .If A negative ,|-A| =A, so what we do effectively is that we simply drop the sign attached to the number .when modulus or absolute vale is taken.
Example :
|-1|=1
|8|= 8
Addition of fraction :
three step process for adding the fractions 1 + 2
3 5
Step 1. Getting numerator value
Cross-multiply the two fractions and add the results together to get the numerator of the answer.
ie (1X5)+(3X5) = 11 This will be the numerator of final answer
Step 2. Getting Denominator value
Multiply the two denominators together to get the denominator of the answer.
ie 3X5 = 15 This will be the denominator of final answer
Step 3. Final Answer
Writing the step 1 and step 2
1 + 2 = 11
3 5 15
Multiplication of fractions :
Remember the following :
(a) In mixed fraction ,we change it in proper or improper fraction.
(b) If the fraction is multiplied by a whole number ,then its numerator is multiplied by whole number and denominator remain the same.
(c) Product of two fractions=product of numerators of two fraction÷product of denominators of two fraction
Rules to be followed
When you solve the problem using addition(+),subtraction(-), Multiplication(X) and division(/)simultaneously,we use “VBODMAS” rule.
V Vinculum (—)
B Bracket [{(-)}]
O Of
D Division ÷
M Multiplication ×
A Addition +
S Subtraction -
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